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is a <a href="/wiki/Wikipedia:WikiProject_Lists#Dynamic_lists" title="Wikipedia:WikiProject Lists">dynamic list</a> and may never be able to satisfy particular standards for completeness. You can help by <a href="/wiki/Special:EditPage/List_of_prime_numbers" title="Special:EditPage/List of prime numbers">adding missing items</a> with <a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliable sources</a>.</div> This is a list of articles about <a href="/wiki/Prime_number" title="Prime number">prime numbers</a>. A prime number (or prime) is a <a href="/wiki/Natural_number" title="Natural number">natural number</a> greater than 1 that has no positive <a href="/wiki/Divisor" title="Divisor">divisors</a> other than 1 and itself. By <a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a>, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various <a href="/wiki/Formulas_for_primes" class="mw-redirect" title="Formulas for primes">formulas for primes</a>. The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. 1 is neither prime nor <a href="/wiki/Composite_number" title="Composite number">composite</a>. <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#The_first_1000_prime_numbers">1 The first 1000 prime numbers</a></li> <li class="toclevel-1 tocsection-2"><a href="#Lists_of_primes_by_type">2 Lists of primes by type</a> <ul> <li class="toclevel-2 tocsection-3"><a href="#Balanced_primes">2.1 Balanced primes</a></li> <li class="toclevel-2 tocsection-4"><a href="#Bell_primes">2.2 Bell primes</a></li> <li class="toclevel-2 tocsection-5"><a href="#Chen_primes">2.3 Chen primes</a></li> <li class="toclevel-2 tocsection-6"><a href="#Circular_primes">2.4 Circular primes</a></li> <li class="toclevel-2 tocsection-7"><a href="#Cluster_primes">2.5 Cluster primes</a></li> <li class="toclevel-2 tocsection-8"><a href="#Cousin_primes">2.6 Cousin primes</a></li> <li class="toclevel-2 tocsection-9"><a href="#Cuban_primes">2.7 Cuban primes</a></li> <li class="toclevel-2 tocsection-10"><a href="#Cullen_primes">2.8 Cullen primes</a></li> <li class="toclevel-2 tocsection-11"><a href="#Delicate_primes">2.9 Delicate primes</a></li> <li class="toclevel-2 tocsection-12"><a href="#Dihedral_primes">2.10 Dihedral primes</a></li> <li class="toclevel-2 tocsection-13"><a href="#Eisenstein_primes_without_imaginary_part">2.11 Eisenstein primes without imaginary part</a></li> <li class="toclevel-2 tocsection-14"><a href="#Emirps">2.12 Emirps</a></li> <li class="toclevel-2 tocsection-15"><a href="#Euclid_primes">2.13 Euclid primes</a></li> <li class="toclevel-2 tocsection-16"><a href="#Euler_irregular_primes">2.14 Euler irregular primes</a> <ul> <li class="toclevel-3 tocsection-17"><a href="#Euler_(p,_p_%E2%88%92_3)_irregular_primes">2.14.1 Euler (p, p − 3) irregular primes</a></li> </ul> </li> <li class="toclevel-2 tocsection-18"><a href="#Factorial_primes">2.15 Factorial primes</a></li> <li class="toclevel-2 tocsection-19"><a href="#Fermat_primes">2.16 Fermat primes</a> <ul> <li class="toclevel-3 tocsection-20"><a href="#Generalized_Fermat_primes">2.16.1 Generalized Fermat primes</a></li> </ul> </li> <li class="toclevel-2 tocsection-21"><a href="#Fibonacci_primes">2.17 Fibonacci primes</a></li> <li class="toclevel-2 tocsection-22"><a href="#Fortunate_primes">2.18 Fortunate primes</a></li> <li class="toclevel-2 tocsection-23"><a href="#Gaussian_primes">2.19 Gaussian primes</a></li> <li class="toclevel-2 tocsection-24"><a href="#Good_primes">2.20 Good primes</a></li> <li class="toclevel-2 tocsection-25"><a href="#Happy_primes">2.21 Happy primes</a></li> <li class="toclevel-2 tocsection-26"><a href="#Harmonic_primes">2.22 Harmonic primes</a></li> <li class="toclevel-2 tocsection-27"><a href="#Higgs_primes_for_squares">2.23 Higgs primes for squares</a></li> <li class="toclevel-2 tocsection-28"><a href="#Highly_cototient_primes">2.24 Highly cototient primes</a></li> <li class="toclevel-2 tocsection-29"><a href="#Home_primes">2.25 Home primes</a></li> <li class="toclevel-2 tocsection-30"><a href="#Irregular_primes">2.26 Irregular primes</a> <ul> <li class="toclevel-3 tocsection-31"><a href="#(p,_p_%E2%88%92_3)_irregular_primes">2.26.1 (p, p − 3) irregular primes</a></li> <li class="toclevel-3 tocsection-32"><a href="#(p,_p_%E2%88%92_5)_irregular_primes">2.26.2 (p, p − 5) irregular primes</a></li> <li class="toclevel-3 tocsection-33"><a href="#(p,_p_%E2%88%92_9)_irregular_primes">2.26.3 (p, p − 9) irregular primes</a></li> </ul> </li> <li class="toclevel-2 tocsection-34"><a href="#Isolated_primes">2.27 Isolated primes</a></li> <li class="toclevel-2 tocsection-35"><a href="#Leyland_primes">2.28 Leyland primes</a></li> <li class="toclevel-2 tocsection-36"><a href="#Long_primes">2.29 Long primes</a></li> <li class="toclevel-2 tocsection-37"><a href="#Lucas_primes">2.30 Lucas primes</a></li> <li class="toclevel-2 tocsection-38"><a href="#Lucky_primes">2.31 Lucky primes</a></li> <li class="toclevel-2 tocsection-39"><a href="#Mersenne_primes">2.32 Mersenne primes</a> <ul> <li class="toclevel-3 tocsection-40"><a href="#Mersenne_divisors">2.32.1 Mersenne divisors</a></li> <li class="toclevel-3 tocsection-41"><a href="#Mersenne_prime_exponents">2.32.2 Mersenne prime exponents</a></li> <li class="toclevel-3 tocsection-42"><a href="#Double_Mersenne_primes">2.32.3 Double Mersenne primes</a></li> <li class="toclevel-3 tocsection-43"><a href="#Generalized_repunit_primes">2.32.4 Generalized repunit primes</a></li> <li class="toclevel-3 tocsection-44"><a href="#Other_generalizations_and_variations">2.32.5 Other generalizations and variations</a></li> </ul> </li> <li class="toclevel-2 tocsection-45"><a href="#Mills_primes">2.33 Mills primes</a></li> <li class="toclevel-2 tocsection-46"><a href="#Minimal_primes">2.34 Minimal primes</a></li> <li class="toclevel-2 tocsection-47"><a href="#Newman%E2%80%93Shanks%E2%80%93Williams_primes">2.35 Newman–Shanks–Williams primes</a></li> <li class="toclevel-2 tocsection-48"><a href="#Non-generous_primes">2.36 Non-generous primes</a></li> <li class="toclevel-2 tocsection-49"><a href="#Palindromic_primes">2.37 Palindromic primes</a></li> <li class="toclevel-2 tocsection-50"><a href="#Palindromic_wing_primes">2.38 Palindromic wing primes</a></li> <li class="toclevel-2 tocsection-51"><a href="#Partition_primes">2.39 Partition primes</a></li> <li class="toclevel-2 tocsection-52"><a href="#Pell_primes">2.40 Pell primes</a></li> <li class="toclevel-2 tocsection-53"><a href="#Permutable_primes">2.41 Permutable primes</a></li> <li class="toclevel-2 tocsection-54"><a href="#Perrin_primes">2.42 Perrin primes</a></li> <li class="toclevel-2 tocsection-55"><a href="#Pierpont_primes">2.43 Pierpont primes</a></li> <li class="toclevel-2 tocsection-56"><a href="#Pillai_primes">2.44 Pillai primes</a></li> <li class="toclevel-2 tocsection-57"><a href="#Primes_of_the_form_n4_+_1">2.45 Primes of the form n4 + 1</a></li> <li class="toclevel-2 tocsection-58"><a href="#Primeval_primes">2.46 Primeval primes</a></li> <li class="toclevel-2 tocsection-59"><a href="#Primorial_primes">2.47 Primorial primes</a></li> <li class="toclevel-2 tocsection-60"><a href="#Proth_primes">2.48 Proth primes</a></li> <li class="toclevel-2 tocsection-61"><a href="#Pythagorean_primes">2.49 Pythagorean primes</a></li> <li class="toclevel-2 tocsection-62"><a href="#Prime_quadruplets">2.50 Prime quadruplets</a></li> <li class="toclevel-2 tocsection-63"><a href="#Quartan_primes">2.51 Quartan primes</a></li> <li class="toclevel-2 tocsection-64"><a href="#Ramanujan_primes">2.52 Ramanujan primes</a></li> <li class="toclevel-2 tocsection-65"><a href="#Regular_primes">2.53 Regular primes</a></li> <li class="toclevel-2 tocsection-66"><a href="#Repunit_primes">2.54 Repunit primes</a></li> <li class="toclevel-2 tocsection-67"><a href="#Residue_classes_of_primes">2.55 Residue classes of primes</a></li> <li class="toclevel-2 tocsection-68"><a href="#Safe_primes">2.56 Safe primes</a></li> <li class="toclevel-2 tocsection-69"><a href="#Self_primes_in_base_10">2.57 Self primes in base 10</a></li> <li class="toclevel-2 tocsection-70"><a href="#Sexy_primes">2.58 Sexy primes</a></li> <li class="toclevel-2 tocsection-71"><a href="#Smarandache%E2%80%93Wellin_primes">2.59 Smarandache–Wellin primes</a></li> <li class="toclevel-2 tocsection-72"><a href="#Solinas_primes">2.60 Solinas primes</a></li> <li class="toclevel-2 tocsection-73"><a href="#Sophie_Germain_primes">2.61 Sophie Germain primes</a></li> <li class="toclevel-2 tocsection-74"><a href="#Stern_primes">2.62 Stern primes</a></li> <li class="toclevel-2 tocsection-75"><a href="#Super-primes">2.63 Super-primes</a></li> <li class="toclevel-2 tocsection-76"><a href="#Supersingular_primes">2.64 Supersingular primes</a></li> <li class="toclevel-2 tocsection-77"><a href="#Thabit_primes">2.65 Thabit primes</a></li> <li class="toclevel-2 tocsection-78"><a href="#Prime_triplets">2.66 Prime triplets</a></li> <li class="toclevel-2 tocsection-79"><a href="#Truncatable_prime">2.67 Truncatable prime</a> <ul> <li class="toclevel-3 tocsection-80"><a href="#Left-truncatable">2.67.1 Left-truncatable</a></li> <li class="toclevel-3 tocsection-81"><a href="#Right-truncatable">2.67.2 Right-truncatable</a></li> <li class="toclevel-3 tocsection-82"><a href="#Two-sided">2.67.3 Two-sided</a></li> </ul> </li> <li class="toclevel-2 tocsection-83"><a href="#Twin_primes">2.68 Twin primes</a></li> <li class="toclevel-2 tocsection-84"><a href="#Unique_primes">2.69 Unique primes</a></li> <li class="toclevel-2 tocsection-85"><a href="#Wagstaff_primes">2.70 Wagstaff primes</a></li> <li class="toclevel-2 tocsection-86"><a href="#Wall%E2%80%93Sun%E2%80%93Sun_primes">2.71 Wall–Sun–Sun primes</a></li> <li class="toclevel-2 tocsection-87"><a href="#Wieferich_primes">2.72 Wieferich primes</a></li> <li class="toclevel-2 tocsection-88"><a href="#Wilson_primes">2.73 Wilson primes</a></li> <li class="toclevel-2 tocsection-89"><a href="#Wolstenholme_primes">2.74 Wolstenholme primes</a></li> <li class="toclevel-2 tocsection-90"><a href="#Woodall_primes">2.75 Woodall primes</a></li> </ul> </li> <li class="toclevel-1 tocsection-91"><a href="#See_also">3 See also</a></li> <li class="toclevel-1 tocsection-92"><a href="#References">4 References</a></li> <li class="toclevel-1 tocsection-93"><a href="#External_links">5 External links</a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="The_first_1000_prime_numbers">The first 1000 prime numbers</h2> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=1" title="Edit section: The first 1000 prime numbers" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> The following table lists the first 1000 primes, with 20 columns of consecutive primes in each of the 50 rows.<a href="#cite_note-1">[1]</a> <table class="wikitable"> <tbody><tr> <th> </th> <th>1</th> <th>2</th> <th>3</th> <th>4</th> <th>5</th> <th>6</th> <th>7</th> <th>8</th> <th>9</th> <th>10</th> <th>11</th> <th>12</th> <th>13</th> <th>14</th> <th>15</th> <th>16</th> <th>17</th> <th>18</th> <th>19</th> <th>20 </th></tr> <tr style="text-align: center;"> <th>1–20 </th> <td><a href="/wiki/2" title="2">2</a></td> <td><a href="/wiki/3" title="3">3</a></td> <td><a href="/wiki/5" title="5">5</a></td> <td><a href="/wiki/7" title="7">7</a></td> <td><a href="/wiki/11_(number)" title="11 (number)">11</a></td> <td><a href="/wiki/13_(number)" title="13 (number)">13</a></td> <td><a href="/wiki/17_(number)" title="17 (number)">17</a></td> <td><a href="/wiki/19_(number)" title="19 (number)">19</a></td> <td><a href="/wiki/23_(number)" title="23 (number)">23</a></td> <td><a href="/wiki/29_(number)" title="29 (number)">29</a></td> <td><a href="/wiki/31_(number)" title="31 (number)">31</a></td> <td><a href="/wiki/37_(number)" title="37 (number)">37</a></td> <td><a href="/wiki/41_(number)" title="41 (number)">41</a></td> <td><a href="/wiki/43_(number)" title="43 (number)">43</a></td> <td><a href="/wiki/47_(number)" title="47 (number)">47</a></td> <td><a href="/wiki/53_(number)" title="53 (number)">53</a></td> <td><a href="/wiki/59_(number)" title="59 (number)">59</a></td> <td><a href="/wiki/61_(number)" title="61 (number)">61</a></td> <td><a href="/wiki/67_(number)" title="67 (number)">67</a></td> <td><a href="/wiki/71_(number)" title="71 (number)">71</a> </td></tr> <tr style="text-align: center;"> <th>21–40 </th> <td><a href="/wiki/73_(number)" title="73 (number)">73</a></td> <td><a href="/wiki/79_(number)" title="79 (number)">79</a></td> <td><a href="/wiki/83_(number)" title="83 (number)">83</a></td> <td><a href="/wiki/89_(number)" title="89 (number)">89</a></td> <td><a href="/wiki/97_(number)" title="97 (number)">97</a></td> <td><a href="/wiki/101_(number)" title="101 (number)">101</a></td> <td><a href="/wiki/103_(number)" title="103 (number)">103</a></td> <td><a href="/wiki/107_(number)" title="107 (number)">107</a></td> <td><a href="/wiki/109_(number)" title="109 (number)">109</a></td> <td><a href="/wiki/113_(number)" title="113 (number)">113</a></td> <td><a href="/wiki/127_(number)" title="127 (number)">127</a></td> <td><a href="/wiki/131_(number)" title="131 (number)">131</a></td> <td><a href="/wiki/137_(number)" title="137 (number)">137</a></td> <td><a href="/wiki/139_(number)" title="139 (number)">139</a></td> <td><a href="/wiki/149_(number)" title="149 (number)">149</a></td> <td><a href="/wiki/151_(number)" title="151 (number)">151</a></td> <td><a href="/wiki/157_(number)" title="157 (number)">157</a></td> <td><a href="/wiki/163_(number)" title="163 (number)">163</a></td> <td><a href="/wiki/167_(number)" title="167 (number)">167</a></td> <td><a href="/wiki/173_(number)" title="173 (number)">173</a> </td></tr> <tr style="text-align: center;"> <th>41–60 </th> <td><a href="/wiki/179_(number)" title="179 (number)">179</a></td> <td><a href="/wiki/181_(number)" title="181 (number)">181</a></td> <td><a href="/wiki/191_(number)" title="191 (number)">191</a></td> <td><a href="/wiki/193_(number)" title="193 (number)">193</a></td> <td><a href="/wiki/197_(number)" title="197 (number)">197</a></td> <td><a href="/wiki/199_(number)" title="199 (number)">199</a></td> <td><a href="/wiki/211_(number)" title="211 (number)">211</a></td> <td><a href="/wiki/223_(number)" title="223 (number)">223</a></td> <td><a href="/wiki/227_(number)" title="227 (number)">227</a></td> <td><a href="/wiki/229_(number)" title="229 (number)">229</a></td> <td><a href="/wiki/233_(number)" title="233 (number)">233</a></td> <td><a href="/wiki/239_(number)" title="239 (number)">239</a></td> <td><a href="/wiki/241_(number)" title="241 (number)">241</a></td> <td><a href="/wiki/251_(number)" title="251 (number)">251</a></td> <td><a href="/wiki/257_(number)" title="257 (number)">257</a></td> <td><a href="/wiki/263_(number)" title="263 (number)">263</a></td> <td><a href="/wiki/269_(number)" title="269 (number)">269</a></td> <td><a href="/wiki/271_(number)" title="271 (number)">271</a></td> <td><a href="/wiki/277_(number)" title="277 (number)">277</a></td> <td><a href="/wiki/281_(number)" title="281 (number)">281</a> </td></tr> <tr style="text-align: center;"> <th>61–80 </th> <td><a href="/wiki/283_(number)" title="283 (number)">283</a></td> <td><a href="/wiki/293_(number)" title="293 (number)">293</a></td> <td><a href="/wiki/307_(number)" title="307 (number)">307</a></td> <td><a href="/wiki/311_(number)" title="311 (number)">311</a></td> <td><a href="/wiki/313_(number)" title="313 (number)">313</a></td> <td><a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a></td> <td><a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a></td> <td><a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a></td> <td><a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a></td> <td><a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a></td> <td><a href="/wiki/353_(number)" title="353 (number)">353</a></td> <td><a href="/wiki/359_(number)" title="359 (number)">359</a></td> <td><a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a></td> <td><a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a></td> <td><a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a></td> <td><a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a></td> <td><a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a></td> <td><a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a></td> <td><a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a></td> <td><a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a> </td></tr> <tr style="text-align: center;"> <th>81–100 </th> <td><a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a></td> <td><a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a></td> <td><a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a></td> <td><a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a></td> <td><a href="/wiki/439_(number)" class="mw-redirect" title="439 (number)">439</a></td> <td><a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a></td> <td><a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a></td> <td><a href="/wiki/457_(number)" class="mw-redirect" title="457 (number)">457</a></td> <td><a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a></td> <td><a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a></td> <td><a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a></td> <td><a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a></td> <td><a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a></td> <td><a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a></td> <td><a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a></td> <td><a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a></td> <td><a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a></td> <td><a href="/wiki/521_(number)" class="mw-redirect" title="521 (number)">521</a></td> <td><a href="/wiki/523_(number)" class="mw-redirect" title="523 (number)">523</a></td> <td><a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a> </td></tr> <tr style="text-align: center;"> <th>101–120 </th> <td><a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a></td> <td><a href="/wiki/557_(number)" class="mw-redirect" title="557 (number)">557</a></td> <td><a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a></td> <td><a href="/wiki/569_(number)" class="mw-redirect" title="569 (number)">569</a></td> <td><a href="/wiki/571_(number)" class="mw-redirect" title="571 (number)">571</a></td> <td><a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a></td> <td><a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a></td> <td><a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a></td> <td><a href="/wiki/599_(number)" class="mw-redirect" title="599 (number)">599</a></td> <td><a href="/wiki/601_(number)" class="mw-redirect" title="601 (number)">601</a></td> <td><a href="/wiki/607_(number)" class="mw-redirect" title="607 (number)">607</a></td> <td><a href="/wiki/613_(number)" title="613 (number)">613</a></td> <td><a href="/wiki/617_(number)" class="mw-redirect" title="617 (number)">617</a></td> <td><a href="/wiki/619_(number)" class="mw-redirect" title="619 (number)">619</a></td> <td><a href="/wiki/631_(number)" class="mw-redirect" title="631 (number)">631</a></td> <td><a href="/wiki/641_(number)" class="mw-redirect" title="641 (number)">641</a></td> <td><a href="/wiki/643_(number)" class="mw-redirect" title="643 (number)">643</a></td> <td><a href="/wiki/647_(number)" class="mw-redirect" title="647 (number)">647</a> </td> <td><a href="/wiki/653_(number)" class="mw-redirect" title="653 (number)">653</a></td> <td><a href="/wiki/659_(number)" class="mw-redirect" title="659 (number)">659</a> </td></tr> <tr style="text-align: center;"> <th>121–140 </th> <td><a href="/wiki/661_(number)" class="mw-redirect" title="661 (number)">661</a></td> <td><a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a></td> <td><a href="/wiki/677_(number)" class="mw-redirect" title="677 (number)">677</a></td> <td><a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a></td> <td><a href="/wiki/691_(number)" class="mw-redirect" title="691 (number)">691</a></td> <td><a href="/wiki/701_(number)" class="mw-redirect" title="701 (number)">701</a></td> <td><a href="/wiki/709_(number)" class="mw-redirect" title="709 (number)">709</a></td> <td><a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a></td> <td><a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a></td> <td><a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a></td> <td><a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a></td> <td><a href="/wiki/743_(number)" title="743 (number)">743</a></td> <td><a href="/wiki/751_(number)" class="mw-redirect" title="751 (number)">751</a></td> <td><a href="/wiki/757_(number)" class="mw-redirect" title="757 (number)">757</a></td> <td><a href="/wiki/761_(number)" class="mw-redirect" title="761 (number)">761</a></td> <td><a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a></td> <td><a href="/wiki/773_(number)" class="mw-redirect" title="773 (number)">773</a></td> <td><a href="/wiki/787_(number)" class="mw-redirect" title="787 (number)">787</a></td> <td><a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a></td> <td><a href="/wiki/809_(number)" class="mw-redirect" title="809 (number)">809</a> </td></tr> <tr style="text-align: center;"> <th>141–160 </th> <td><a href="/wiki/811_(number)" class="mw-redirect" title="811 (number)">811</a></td> <td><a href="/wiki/821_(number)" class="mw-redirect" title="821 (number)">821</a></td> <td><a href="/wiki/823_(number)" class="mw-redirect" title="823 (number)">823</a></td> <td><a href="/wiki/827_(number)" class="mw-redirect" title="827 (number)">827</a></td> <td><a href="/wiki/829_(number)" class="mw-redirect" title="829 (number)">829</a></td> <td><a href="/wiki/839_(number)" class="mw-redirect" title="839 (number)">839</a></td> <td><a href="/wiki/853_(number)" class="mw-redirect" title="853 (number)">853</a></td> <td><a href="/wiki/857_(number)" class="mw-redirect" title="857 (number)">857</a></td> <td><a href="/wiki/859_(number)" class="mw-redirect" title="859 (number)">859</a></td> <td><a href="/wiki/863_(number)" class="mw-redirect" title="863 (number)">863</a></td> <td><a href="/wiki/877_(number)" class="mw-redirect" title="877 (number)">877</a></td> <td><a href="/wiki/881_(number)" title="881 (number)">881</a></td> <td><a href="/wiki/883_(number)" class="mw-redirect" title="883 (number)">883</a></td> <td><a href="/wiki/887_(number)" class="mw-redirect" title="887 (number)">887</a></td> <td><a href="/wiki/907_(number)" class="mw-redirect" title="907 (number)">907</a></td> <td><a href="/wiki/911_(number)" title="911 (number)">911</a></td> <td><a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a></td> <td><a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a></td> <td><a href="/wiki/937_(number)" class="mw-redirect" title="937 (number)">937</a></td> <td><a href="/wiki/941_(number)" class="mw-redirect" title="941 (number)">941</a> </td></tr> <tr style="text-align: center;"> <th>161–180 </th> <td><a href="/wiki/947_(number)" class="mw-redirect" title="947 (number)">947</a></td> <td><a href="/wiki/953_(number)" class="mw-redirect" title="953 (number)">953</a></td> <td><a href="/wiki/967_(number)" class="mw-redirect" title="967 (number)">967</a></td> <td><a href="/wiki/971_(number)" title="971 (number)">971</a></td> <td><a href="/wiki/977_(number)" class="mw-redirect" title="977 (number)">977</a></td> <td><a href="/wiki/983_(number)" class="mw-redirect" title="983 (number)">983</a></td> <td><a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a></td> <td><a href="/wiki/997_(number)" class="mw-redirect" title="997 (number)">997</a></td> <td><a href="/wiki/1009_(number)" class="mw-redirect" title="1009 (number)">1009</a></td> <td><a href="/wiki/1013_(number)" class="mw-redirect" title="1013 (number)">1013</a></td> <td><a href="/wiki/1019_(number)" class="mw-redirect" title="1019 (number)">1019</a></td> <td><a href="/wiki/1021_(number)" class="mw-redirect" title="1021 (number)">1021</a></td> <td><a href="/wiki/1031_(number)" class="mw-redirect" title="1031 (number)">1031</a></td> <td><a href="/wiki/1033_(number)" class="mw-redirect" title="1033 (number)">1033</a></td> <td><a href="/wiki/1039_(number)" class="mw-redirect" title="1039 (number)">1039</a></td> <td><a href="/wiki/1049_(number)" class="mw-redirect" title="1049 (number)">1049</a></td> <td><a href="/wiki/1051_(number)" class="mw-redirect" title="1051 (number)">1051</a></td> <td><a href="/wiki/1061_(number)" class="mw-redirect" title="1061 (number)">1061</a></td> <td><a href="/wiki/1063_(number)" class="mw-redirect" title="1063 (number)">1063</a></td> <td><a href="/wiki/1069_(number)" class="mw-redirect" title="1069 (number)">1069</a> </td></tr> <tr style="text-align: center;"> <th>181–200 </th> <td><a href="/wiki/1087_(number)" class="mw-redirect" title="1087 (number)">1087</a></td> <td><a href="/wiki/1091_(number)" class="mw-redirect" title="1091 (number)">1091</a></td> <td><a href="/wiki/1093_(number)" title="1093 (number)">1093</a></td> <td><a href="/wiki/1097_(number)" class="mw-redirect" title="1097 (number)">1097</a></td> <td><a href="/wiki/1103_(number)" class="mw-redirect" title="1103 (number)">1103</a></td> <td><a href="/wiki/1109_(number)" class="mw-redirect" title="1109 (number)">1109</a></td> <td><a href="/wiki/1117_(number)" class="mw-redirect" title="1117 (number)">1117</a></td> <td><a href="/wiki/1123_(number)" class="mw-redirect" title="1123 (number)">1123</a></td> <td><a href="/wiki/1129_(number)" class="mw-redirect" title="1129 (number)">1129</a></td> <td><a href="/wiki/1151_(number)" class="mw-redirect" title="1151 (number)">1151</a></td> <td><a href="/wiki/1153_(number)" class="mw-redirect" title="1153 (number)">1153</a></td> <td><a href="/wiki/1163_(number)" class="mw-redirect" title="1163 (number)">1163</a></td> <td><a href="/wiki/1171_(number)" class="mw-redirect" title="1171 (number)">1171</a></td> <td><a href="/wiki/1181_(number)" class="mw-redirect" title="1181 (number)">1181</a></td> <td><a href="/wiki/1187_(number)" class="mw-redirect" title="1187 (number)">1187</a></td> <td><a href="/wiki/1193_(number)" class="mw-redirect" title="1193 (number)">1193</a></td> <td><a href="/wiki/1201_(number)" class="mw-redirect" title="1201 (number)">1201</a></td> <td><a href="/wiki/1213_(number)" class="mw-redirect" title="1213 (number)">1213</a></td> <td><a href="/wiki/1217_(number)" class="mw-redirect" title="1217 (number)">1217</a></td> <td><a href="/wiki/1223_(number)" class="mw-redirect" title="1223 (number)">1223</a> </td></tr> <tr style="text-align: center;"> <th>201–220 </th> <td><a href="/wiki/1229_(number)" class="mw-redirect" title="1229 (number)">1229</a></td> <td><a href="/wiki/1231_(number)" class="mw-redirect" title="1231 (number)">1231</a></td> <td><a href="/wiki/1237_(number)" class="mw-redirect" title="1237 (number)">1237</a></td> <td><a href="/wiki/1249_(number)" class="mw-redirect" title="1249 (number)">1249</a></td> <td><a href="/wiki/1259_(number)" class="mw-redirect" title="1259 (number)">1259</a></td> <td><a href="/wiki/1277_(number)" class="mw-redirect" title="1277 (number)">1277</a></td> <td><a href="/wiki/1279_(number)" class="mw-redirect" title="1279 (number)">1279</a></td> <td><a href="/wiki/1283_(number)" class="mw-redirect" title="1283 (number)">1283</a></td> <td><a href="/wiki/1289_(number)" title="1289 (number)">1289</a></td> <td><a href="/wiki/1291_(number)" class="mw-redirect" title="1291 (number)">1291</a></td> <td><a href="/wiki/1297_(number)" class="mw-redirect" title="1297 (number)">1297</a></td> <td><a href="/wiki/1301_(number)" class="mw-redirect" title="1301 (number)">1301</a></td> <td><a href="/wiki/1303_(number)" class="mw-redirect" title="1303 (number)">1303</a></td> <td><a href="/wiki/1307_(number)" class="mw-redirect" title="1307 (number)">1307</a></td> <td><a href="/wiki/1319_(number)" class="mw-redirect" title="1319 (number)">1319</a></td> <td><a href="/wiki/1321_(number)" class="mw-redirect" title="1321 (number)">1321</a></td> <td><a href="/wiki/1327_(number)" class="mw-redirect" title="1327 (number)">1327</a></td> <td><a href="/wiki/1361_(number)" class="mw-redirect" title="1361 (number)">1361</a></td> <td><a href="/wiki/1367_(number)" class="mw-redirect" title="1367 (number)">1367</a></td> <td><a href="/wiki/1373_(number)" class="mw-redirect" title="1373 (number)">1373</a> </td></tr> <tr style="text-align: center;"> <th>221–240 </th> <td><a href="/wiki/1381_(number)" class="mw-redirect" title="1381 (number)">1381</a></td> <td><a href="/wiki/1399_(number)" class="mw-redirect" title="1399 (number)">1399</a></td> <td><a href="/wiki/1409_(number)" class="mw-redirect" title="1409 (number)">1409</a></td> <td><a href="/wiki/1423_(number)" class="mw-redirect" title="1423 (number)">1423</a></td> <td><a href="/wiki/1427_(number)" class="mw-redirect" title="1427 (number)">1427</a></td> <td><a href="/wiki/1429_(number)" class="mw-redirect" title="1429 (number)">1429</a></td> <td><a href="/wiki/1433_(number)" class="mw-redirect" title="1433 (number)">1433</a></td> <td><a href="/wiki/1439_(number)" class="mw-redirect" title="1439 (number)">1439</a></td> <td><a href="/wiki/1447_(number)" class="mw-redirect" title="1447 (number)">1447</a></td> <td><a href="/wiki/1451_(number)" class="mw-redirect" title="1451 (number)">1451</a></td> <td><a href="/wiki/1453_(number)" class="mw-redirect" title="1453 (number)">1453</a></td> <td><a href="/wiki/1459_(number)" class="mw-redirect" title="1459 (number)">1459</a></td> <td><a href="/wiki/1471_(number)" class="mw-redirect" title="1471 (number)">1471</a></td> <td><a href="/wiki/1481_(number)" class="mw-redirect" title="1481 (number)">1481</a></td> <td><a href="/wiki/1483_(number)" class="mw-redirect" title="1483 (number)">1483</a></td> <td><a href="/wiki/1487_(number)" class="mw-redirect" title="1487 (number)">1487</a></td> <td><a href="/wiki/1489_(number)" class="mw-redirect" title="1489 (number)">1489</a></td> <td><a href="/wiki/1493_(number)" class="mw-redirect" title="1493 (number)">1493</a></td> <td><a href="/wiki/1499_(number)" class="mw-redirect" title="1499 (number)">1499</a></td> <td><a href="/wiki/1511_(number)" class="mw-redirect" title="1511 (number)">1511</a> </td></tr> <tr style="text-align: center;"> <th>241–260 </th> <td><a href="/wiki/1523_(number)" class="mw-redirect" title="1523 (number)">1523</a></td> <td><a href="/wiki/1531_(number)" class="mw-redirect" title="1531 (number)">1531</a></td> <td><a href="/wiki/1543_(number)" class="mw-redirect" title="1543 (number)">1543</a></td> <td><a href="/wiki/1549_(number)" class="mw-redirect" title="1549 (number)">1549</a></td> <td><a href="/wiki/1553_(number)" class="mw-redirect" title="1553 (number)">1553</a></td> <td><a href="/wiki/1559_(number)" class="mw-redirect" title="1559 (number)">1559</a></td> <td><a href="/wiki/1567_(number)" class="mw-redirect" title="1567 (number)">1567</a></td> <td><a href="/wiki/1571_(number)" class="mw-redirect" title="1571 (number)">1571</a></td> <td><a href="/wiki/1579_(number)" class="mw-redirect" title="1579 (number)">1579</a></td> <td><a href="/wiki/1583_(number)" class="mw-redirect" title="1583 (number)">1583</a></td> <td><a href="/wiki/1597_(number)" class="mw-redirect" title="1597 (number)">1597</a></td> <td><a href="/wiki/1601_(number)" class="mw-redirect" title="1601 (number)">1601</a></td> <td><a href="/wiki/1607_(number)" class="mw-redirect" title="1607 (number)">1607</a></td> <td><a href="/wiki/1609_(number)" class="mw-redirect" title="1609 (number)">1609</a></td> <td><a href="/wiki/1613_(number)" class="mw-redirect" title="1613 (number)">1613</a></td> <td><a href="/wiki/1619_(number)" class="mw-redirect" title="1619 (number)">1619</a></td> <td><a href="/wiki/1621_(number)" class="mw-redirect" title="1621 (number)">1621</a></td> <td><a href="/wiki/1627_(number)" class="mw-redirect" title="1627 (number)">1627</a></td> <td><a href="/wiki/1637_(number)" class="mw-redirect" title="1637 (number)">1637</a></td> <td><a href="/wiki/1657_(number)" class="mw-redirect" title="1657 (number)">1657</a> </td></tr> <tr style="text-align: center;"> <th>261–280 </th> <td><a href="/wiki/1663_(number)" class="mw-redirect" title="1663 (number)">1663</a></td> <td><a href="/wiki/1667_(number)" class="mw-redirect" title="1667 (number)">1667</a></td> <td><a href="/wiki/1669_(number)" class="mw-redirect" title="1669 (number)">1669</a></td> <td><a href="/wiki/1693_(number)" class="mw-redirect" title="1693 (number)">1693</a></td> <td><a href="/wiki/1697_(number)" class="mw-redirect" title="1697 (number)">1697</a></td> <td><a href="/wiki/1699_(number)" class="mw-redirect" title="1699 (number)">1699</a></td> <td><a href="/wiki/1709_(number)" class="mw-redirect" title="1709 (number)">1709</a></td> <td><a href="/wiki/1721_(number)" class="mw-redirect" title="1721 (number)">1721</a></td> <td><a href="/wiki/1723_(number)" class="mw-redirect" title="1723 (number)">1723</a></td> <td><a href="/wiki/1733_(number)" class="mw-redirect" title="1733 (number)">1733</a></td> <td><a href="/wiki/1741_(number)" class="mw-redirect" title="1741 (number)">1741</a></td> <td><a href="/wiki/1747_(number)" class="mw-redirect" title="1747 (number)">1747</a></td> <td><a href="/wiki/1753_(number)" class="mw-redirect" title="1753 (number)">1753</a></td> <td><a href="/wiki/1759_(number)" class="mw-redirect" title="1759 (number)">1759</a></td> <td><a href="/wiki/1777_(number)" class="mw-redirect" title="1777 (number)">1777</a></td> <td><a href="/wiki/1783_(number)" class="mw-redirect" title="1783 (number)">1783</a></td> <td><a href="/wiki/1787_(number)" class="mw-redirect" title="1787 (number)">1787</a></td> <td><a href="/wiki/1789_(number)" class="mw-redirect" title="1789 (number)">1789</a></td> <td><a href="/wiki/1801_(number)" class="mw-redirect" title="1801 (number)">1801</a></td> <td><a href="/wiki/1811_(number)" class="mw-redirect" title="1811 (number)">1811</a> </td></tr> <tr style="text-align: center;"> <th>281–300 </th> <td><a href="/wiki/1823_(number)" class="mw-redirect" title="1823 (number)">1823</a></td> <td><a href="/wiki/1831_(number)" class="mw-redirect" title="1831 (number)">1831</a></td> <td><a href="/wiki/1847_(number)" class="mw-redirect" title="1847 (number)">1847</a></td> <td><a href="/wiki/1861_(number)" class="mw-redirect" title="1861 (number)">1861</a></td> <td><a href="/wiki/1867_(number)" class="mw-redirect" title="1867 (number)">1867</a></td> <td><a href="/wiki/1871_(number)" class="mw-redirect" title="1871 (number)">1871</a></td> <td><a href="/wiki/1873_(number)" class="mw-redirect" title="1873 (number)">1873</a></td> <td><a href="/wiki/1877_(number)" class="mw-redirect" title="1877 (number)">1877</a></td> <td><a href="/wiki/1879_(number)" class="mw-redirect" title="1879 (number)">1879</a></td> <td><a href="/wiki/1889_(number)" class="mw-redirect" title="1889 (number)">1889</a></td> <td><a href="/wiki/1901_(number)" class="mw-redirect" title="1901 (number)">1901</a></td> <td><a href="/wiki/1907_(number)" class="mw-redirect" title="1907 (number)">1907</a></td> <td><a href="/wiki/1913_(number)" class="mw-redirect" title="1913 (number)">1913</a></td> <td><a href="/wiki/1931_(number)" class="mw-redirect" title="1931 (number)">1931</a></td> <td><a href="/wiki/1933_(number)" class="mw-redirect" title="1933 (number)">1933</a></td> <td><a href="/wiki/1949_(number)" class="mw-redirect" title="1949 (number)">1949</a></td> <td><a href="/wiki/1951_(number)" class="mw-redirect" title="1951 (number)">1951</a></td> <td><a href="/wiki/1973_(number)" class="mw-redirect" title="1973 (number)">1973</a></td> <td><a href="/wiki/1000_(number)#1900_to_1999" title="1000 (number)">1979</a></td> <td><a href="/wiki/1987_(number)" title="1987 (number)">1987</a> </td></tr> <tr style="text-align: center;"> <th>301–320 </th> <td><a href="/wiki/1993_(number)" class="mw-redirect" title="1993 (number)">1993</a></td> <td><a href="/wiki/1997_(number)" class="mw-redirect" title="1997 (number)">1997</a></td> <td><a href="/wiki/1999_(number)" class="mw-redirect" title="1999 (number)">1999</a></td> <td><a href="/wiki/2003_(number)" class="mw-redirect" title="2003 (number)">2003</a></td> <td><a href="/wiki/2011_(number)" class="mw-redirect" title="2011 (number)">2011</a></td> <td><a href="/wiki/2017_(number)" class="mw-redirect" title="2017 (number)">2017</a></td> <td><a href="/wiki/2027_(number)" class="mw-redirect" title="2027 (number)">2027</a></td> <td><a href="/wiki/2029_(number)" class="mw-redirect" title="2029 (number)">2029</a></td> <td><a href="/wiki/2039_(number)" class="mw-redirect" title="2039 (number)">2039</a></td> <td><a href="/wiki/2053_(number)" class="mw-redirect" title="2053 (number)">2053</a></td> <td><a href="/wiki/2063_(number)" class="mw-redirect" title="2063 (number)">2063</a></td> <td><a href="/wiki/2069_(number)" class="mw-redirect" title="2069 (number)">2069</a></td> <td><a href="/wiki/2081_(number)" class="mw-redirect" title="2081 (number)">2081</a></td> <td><a href="/wiki/2083_(number)" class="mw-redirect" title="2083 (number)">2083</a></td> <td><a href="/wiki/2087_(number)" class="mw-redirect" title="2087 (number)">2087</a></td> <td><a href="/wiki/2089_(number)" class="mw-redirect" title="2089 (number)">2089</a></td> <td><a href="/wiki/2099_(number)" class="mw-redirect" title="2099 (number)">2099</a></td> <td><a href="/wiki/2111_(number)" class="mw-redirect" title="2111 (number)">2111</a></td> <td><a href="/wiki/2113_(number)" class="mw-redirect" title="2113 (number)">2113</a></td> <td><a href="/wiki/2129_(number)" class="mw-redirect" title="2129 (number)">2129</a> </td></tr> <tr style="text-align: center;"> <th>321–340 </th> <td><a href="/wiki/2131_(number)" class="mw-redirect" title="2131 (number)">2131</a></td> <td><a href="/wiki/2137_(number)" class="mw-redirect" title="2137 (number)">2137</a></td> <td><a href="/wiki/2141_(number)" class="mw-redirect" title="2141 (number)">2141</a></td> <td><a href="/wiki/2143_(number)" class="mw-redirect" title="2143 (number)">2143</a></td> <td><a href="/wiki/2153_(number)" class="mw-redirect" title="2153 (number)">2153</a></td> <td><a href="/wiki/2161_(number)" class="mw-redirect" title="2161 (number)">2161</a></td> <td><a href="/wiki/2179_(number)" class="mw-redirect" title="2179 (number)">2179</a></td> <td><a href="/wiki/2203_(number)" class="mw-redirect" title="2203 (number)">2203</a></td> <td><a href="/wiki/2207_(number)" class="mw-redirect" title="2207 (number)">2207</a></td> <td><a href="/wiki/2213_(number)" class="mw-redirect" title="2213 (number)">2213</a></td> <td><a href="/wiki/2221_(number)" class="mw-redirect" title="2221 (number)">2221</a></td> <td><a href="/wiki/2237_(number)" class="mw-redirect" title="2237 (number)">2237</a></td> <td><a href="/wiki/2239_(number)" class="mw-redirect" title="2239 (number)">2239</a></td> <td><a href="/wiki/2243_(number)" class="mw-redirect" title="2243 (number)">2243</a></td> <td><a href="/wiki/2251_(number)" class="mw-redirect" title="2251 (number)">2251</a></td> <td><a href="/wiki/2267_(number)" class="mw-redirect" title="2267 (number)">2267</a></td> <td><a href="/wiki/2269_(number)" class="mw-redirect" title="2269 (number)">2269</a></td> <td><a href="/wiki/2273_(number)" class="mw-redirect" title="2273 (number)">2273</a></td> <td><a href="/wiki/2281_(number)" class="mw-redirect" title="2281 (number)">2281</a></td> <td><a href="/wiki/2287_(number)" class="mw-redirect" title="2287 (number)">2287</a> </td></tr> <tr style="text-align: center;"> <th>341–360 </th> <td><a href="/wiki/2293_(number)" class="mw-redirect" title="2293 (number)">2293</a></td> <td><a href="/wiki/2297_(number)" class="mw-redirect" title="2297 (number)">2297</a></td> <td><a href="/wiki/2309_(number)" class="mw-redirect" title="2309 (number)">2309</a></td> <td><a href="/wiki/2311_(number)" class="mw-redirect" title="2311 (number)">2311</a></td> <td><a href="/wiki/2333_(number)" class="mw-redirect" title="2333 (number)">2333</a></td> <td><a href="/wiki/2339_(number)" class="mw-redirect" title="2339 (number)">2339</a></td> <td><a href="/wiki/2341_(number)" class="mw-redirect" title="2341 (number)">2341</a></td> <td><a href="/wiki/2347_(number)" class="mw-redirect" title="2347 (number)">2347</a></td> <td><a href="/wiki/2351_(number)" class="mw-redirect" title="2351 (number)">2351</a></td> <td><a href="/wiki/2357_(number)" class="mw-redirect" title="2357 (number)">2357</a></td> <td><a href="/wiki/2371_(number)" class="mw-redirect" title="2371 (number)">2371</a></td> <td><a href="/wiki/2377_(number)" class="mw-redirect" title="2377 (number)">2377</a></td> <td><a href="/wiki/2381_(number)" class="mw-redirect" title="2381 (number)">2381</a></td> <td><a href="/wiki/2383_(number)" class="mw-redirect" title="2383 (number)">2383</a></td> <td><a href="/wiki/2389_(number)" class="mw-redirect" title="2389 (number)">2389</a></td> <td><a href="/wiki/2393_(number)" class="mw-redirect" title="2393 (number)">2393</a></td> <td><a href="/wiki/2399_(number)" class="mw-redirect" title="2399 (number)">2399</a></td> <td><a href="/wiki/2411_(number)" class="mw-redirect" title="2411 (number)">2411</a></td> <td><a href="/wiki/2417_(number)" class="mw-redirect" title="2417 (number)">2417</a></td> <td><a href="/wiki/2423_(number)" class="mw-redirect" title="2423 (number)">2423</a> </td></tr> <tr style="text-align: center;"> <th>361–380 </th> <td><a href="/wiki/2437_(number)" class="mw-redirect" title="2437 (number)">2437</a></td> <td><a href="/wiki/2441_(number)" class="mw-redirect" title="2441 (number)">2441</a></td> <td><a href="/wiki/2447_(number)" class="mw-redirect" title="2447 (number)">2447</a></td> <td><a href="/wiki/2459_(number)" class="mw-redirect" title="2459 (number)">2459</a></td> <td><a href="/wiki/2467_(number)" class="mw-redirect" title="2467 (number)">2467</a></td> <td><a href="/wiki/2473_(number)" class="mw-redirect" title="2473 (number)">2473</a></td> <td><a href="/wiki/2477_(number)" class="mw-redirect" title="2477 (number)">2477</a></td> <td><a href="/wiki/2503_(number)" class="mw-redirect" title="2503 (number)">2503</a></td> <td><a href="/wiki/2521_(number)" class="mw-redirect" title="2521 (number)">2521</a></td> <td><a href="/wiki/2531_(number)" class="mw-redirect" title="2531 (number)">2531</a></td> <td><a href="/wiki/2539_(number)" class="mw-redirect" title="2539 (number)">2539</a></td> <td><a href="/wiki/2543_(number)" class="mw-redirect" title="2543 (number)">2543</a></td> <td><a href="/wiki/2549_(number)" class="mw-redirect" title="2549 (number)">2549</a></td> <td><a href="/wiki/2551_(number)" class="mw-redirect" title="2551 (number)">2551</a></td> <td><a href="/wiki/2557_(number)" class="mw-redirect" title="2557 (number)">2557</a></td> <td><a href="/wiki/2579_(number)" class="mw-redirect" title="2579 (number)">2579</a></td> <td><a href="/wiki/2591_(number)" class="mw-redirect" title="2591 (number)">2591</a></td> <td><a href="/wiki/2593_(number)" class="mw-redirect" title="2593 (number)">2593</a></td> <td><a href="/wiki/2609_(number)" class="mw-redirect" title="2609 (number)">2609</a></td> <td><a href="/wiki/2617_(number)" class="mw-redirect" title="2617 (number)">2617</a> </td></tr> <tr style="text-align: center;"> <th>381–400 </th> <td><a href="/wiki/2621_(number)" class="mw-redirect" title="2621 (number)">2621</a></td> <td><a href="/wiki/2633_(number)" class="mw-redirect" title="2633 (number)">2633</a></td> <td><a href="/wiki/2647_(number)" class="mw-redirect" title="2647 (number)">2647</a></td> <td><a href="/wiki/2657_(number)" class="mw-redirect" title="2657 (number)">2657</a></td> <td><a href="/wiki/2659_(number)" class="mw-redirect" title="2659 (number)">2659</a></td> <td><a href="/wiki/2663_(number)" class="mw-redirect" title="2663 (number)">2663</a></td> <td><a href="/wiki/2671_(number)" class="mw-redirect" title="2671 (number)">2671</a></td> <td><a href="/wiki/2677_(number)" class="mw-redirect" title="2677 (number)">2677</a></td> <td><a href="/wiki/2683_(number)" class="mw-redirect" title="2683 (number)">2683</a></td> <td><a href="/wiki/2687_(number)" class="mw-redirect" title="2687 (number)">2687</a></td> <td><a href="/wiki/2689_(number)" class="mw-redirect" title="2689 (number)">2689</a></td> <td><a href="/wiki/2693_(number)" class="mw-redirect" title="2693 (number)">2693</a></td> <td><a href="/wiki/2699_(number)" class="mw-redirect" title="2699 (number)">2699</a></td> <td><a href="/wiki/2707_(number)" class="mw-redirect" title="2707 (number)">2707</a></td> <td><a href="/wiki/2711_(number)" class="mw-redirect" title="2711 (number)">2711</a></td> <td><a href="/wiki/2713_(number)" class="mw-redirect" title="2713 (number)">2713</a></td> <td><a href="/wiki/2719_(number)" class="mw-redirect" title="2719 (number)">2719</a></td> <td><a href="/wiki/2729_(number)" class="mw-redirect" title="2729 (number)">2729</a></td> <td><a href="/wiki/2731_(number)" class="mw-redirect" title="2731 (number)">2731</a></td> <td><a href="/wiki/2741_(number)" class="mw-redirect" title="2741 (number)">2741</a> </td></tr> <tr style="text-align: center;"> <th>401–420 </th> <td><a href="/wiki/2749_(number)" class="mw-redirect" title="2749 (number)">2749</a></td> <td><a href="/wiki/2753_(number)" class="mw-redirect" title="2753 (number)">2753</a></td> <td><a href="/wiki/2767_(number)" class="mw-redirect" title="2767 (number)">2767</a></td> <td><a href="/wiki/2777_(number)" class="mw-redirect" title="2777 (number)">2777</a></td> <td><a href="/wiki/2789_(number)" class="mw-redirect" title="2789 (number)">2789</a></td> <td><a href="/wiki/2791_(number)" class="mw-redirect" title="2791 (number)">2791</a></td> <td><a href="/wiki/2797_(number)" class="mw-redirect" title="2797 (number)">2797</a></td> <td><a href="/wiki/2801_(number)" class="mw-redirect" title="2801 (number)">2801</a></td> <td><a href="/wiki/2803_(number)" class="mw-redirect" title="2803 (number)">2803</a></td> <td><a href="/wiki/2819_(number)" class="mw-redirect" title="2819 (number)">2819</a></td> <td><a href="/wiki/2833_(number)" class="mw-redirect" title="2833 (number)">2833</a></td> <td><a href="/wiki/2837_(number)" class="mw-redirect" title="2837 (number)">2837</a></td> <td><a href="/wiki/2843_(number)" class="mw-redirect" title="2843 (number)">2843</a></td> <td><a href="/wiki/2851_(number)" class="mw-redirect" title="2851 (number)">2851</a></td> <td><a href="/wiki/2857_(number)" class="mw-redirect" title="2857 (number)">2857</a></td> <td><a href="/wiki/2861_(number)" class="mw-redirect" title="2861 (number)">2861</a></td> <td><a href="/wiki/2879_(number)" class="mw-redirect" title="2879 (number)">2879</a></td> <td><a href="/wiki/2887_(number)" class="mw-redirect" title="2887 (number)">2887</a></td> <td><a href="/wiki/2897_(number)" class="mw-redirect" title="2897 (number)">2897</a></td> <td><a href="/wiki/2903_(number)" class="mw-redirect" title="2903 (number)">2903</a> </td></tr> <tr style="text-align: center;"> <th>421–440 </th> <td><a href="/wiki/2909_(number)" class="mw-redirect" title="2909 (number)">2909</a></td> <td><a href="/wiki/2917_(number)" class="mw-redirect" title="2917 (number)">2917</a></td> <td><a href="/wiki/2927_(number)" class="mw-redirect" title="2927 (number)">2927</a></td> <td><a href="/wiki/2939_(number)" class="mw-redirect" title="2939 (number)">2939</a></td> <td><a href="/wiki/2953_(number)" class="mw-redirect" title="2953 (number)">2953</a></td> <td><a href="/wiki/2957_(number)" class="mw-redirect" title="2957 (number)">2957</a></td> <td><a href="/wiki/2963_(number)" class="mw-redirect" title="2963 (number)">2963</a></td> <td><a href="/wiki/2969_(number)" class="mw-redirect" title="2969 (number)">2969</a></td> <td><a href="/wiki/2971_(number)" class="mw-redirect" title="2971 (number)">2971</a></td> <td><a href="/wiki/2999_(number)" class="mw-redirect" title="2999 (number)">2999</a></td> <td><a href="/wiki/3001_(number)" class="mw-redirect" title="3001 (number)">3001</a></td> <td><a href="/wiki/3011_(number)" class="mw-redirect" title="3011 (number)">3011</a></td> <td><a href="/wiki/3019_(number)" class="mw-redirect" title="3019 (number)">3019</a></td> <td><a href="/wiki/3023_(number)" class="mw-redirect" title="3023 (number)">3023</a></td> <td><a href="/wiki/3037_(number)" class="mw-redirect" title="3037 (number)">3037</a></td> <td><a href="/wiki/3041_(number)" class="mw-redirect" title="3041 (number)">3041</a></td> <td><a href="/wiki/3049_(number)" class="mw-redirect" title="3049 (number)">3049</a></td> <td><a href="/wiki/3061_(number)" class="mw-redirect" title="3061 (number)">3061</a></td> <td><a href="/wiki/3067_(number)" class="mw-redirect" title="3067 (number)">3067</a></td> <td><a href="/wiki/3079_(number)" class="mw-redirect" title="3079 (number)">3079</a> </td></tr> <tr style="text-align: center;"> <th>441–460 </th> <td><a href="/wiki/3083_(number)" class="mw-redirect" title="3083 (number)">3083</a></td> <td><a href="/wiki/3089_(number)" class="mw-redirect" title="3089 (number)">3089</a></td> <td><a href="/wiki/3109_(number)" class="mw-redirect" title="3109 (number)">3109</a></td> <td><a href="/wiki/3119_(number)" class="mw-redirect" title="3119 (number)">3119</a></td> <td><a href="/wiki/3121_(number)" class="mw-redirect" title="3121 (number)">3121</a></td> <td><a href="/wiki/3137_(number)" class="mw-redirect" title="3137 (number)">3137</a></td> <td><a href="/wiki/3163_(number)" class="mw-redirect" title="3163 (number)">3163</a></td> <td><a href="/wiki/3167_(number)" class="mw-redirect" title="3167 (number)">3167</a></td> <td><a href="/wiki/3169_(number)" class="mw-redirect" title="3169 (number)">3169</a></td> <td><a href="/wiki/3181_(number)" class="mw-redirect" title="3181 (number)">3181</a></td> <td><a href="/wiki/3187_(number)" class="mw-redirect" title="3187 (number)">3187</a></td> <td><a href="/wiki/3191_(number)" class="mw-redirect" title="3191 (number)">3191</a></td> <td><a href="/wiki/3203_(number)" class="mw-redirect" title="3203 (number)">3203</a></td> <td><a href="/wiki/3209_(number)" class="mw-redirect" title="3209 (number)">3209</a></td> <td><a href="/wiki/3217_(number)" class="mw-redirect" title="3217 (number)">3217</a></td> <td><a href="/wiki/3221_(number)" class="mw-redirect" title="3221 (number)">3221</a></td> <td><a href="/wiki/3229_(number)" class="mw-redirect" title="3229 (number)">3229</a></td> <td><a href="/wiki/3251_(number)" class="mw-redirect" title="3251 (number)">3251</a></td> <td><a href="/wiki/3253_(number)" class="mw-redirect" title="3253 (number)">3253</a></td> <td><a href="/wiki/3257_(number)" class="mw-redirect" title="3257 (number)">3257</a> </td></tr> <tr style="text-align: center;"> <th>461–480 </th> <td><a href="/wiki/3259_(number)" class="mw-redirect" title="3259 (number)">3259</a></td> <td><a href="/wiki/3271_(number)" class="mw-redirect" title="3271 (number)">3271</a></td> <td><a href="/wiki/3299_(number)" class="mw-redirect" title="3299 (number)">3299</a></td> <td><a href="/wiki/3301_(number)" class="mw-redirect" title="3301 (number)">3301</a></td> <td><a href="/wiki/3307_(number)" class="mw-redirect" title="3307 (number)">3307</a></td> <td><a href="/wiki/3313_(number)" class="mw-redirect" title="3313 (number)">3313</a></td> <td><a href="/wiki/3319_(number)" class="mw-redirect" title="3319 (number)">3319</a></td> <td><a href="/wiki/3323_(number)" class="mw-redirect" title="3323 (number)">3323</a></td> <td><a href="/wiki/3329_(number)" class="mw-redirect" title="3329 (number)">3329</a></td> <td><a href="/wiki/3331_(number)" class="mw-redirect" title="3331 (number)">3331</a></td> <td><a href="/wiki/3343_(number)" class="mw-redirect" title="3343 (number)">3343</a></td> <td><a href="/wiki/3347_(number)" class="mw-redirect" title="3347 (number)">3347</a></td> <td><a href="/wiki/3359_(number)" class="mw-redirect" title="3359 (number)">3359</a></td> <td><a href="/wiki/3361_(number)" class="mw-redirect" title="3361 (number)">3361</a></td> <td><a href="/wiki/3371_(number)" class="mw-redirect" title="3371 (number)">3371</a></td> <td><a href="/wiki/3373_(number)" class="mw-redirect" title="3373 (number)">3373</a></td> <td><a href="/wiki/3389_(number)" class="mw-redirect" title="3389 (number)">3389</a></td> <td><a href="/wiki/3391_(number)" class="mw-redirect" title="3391 (number)">3391</a></td> <td><a href="/wiki/3407_(number)" class="mw-redirect" title="3407 (number)">3407</a></td> <td><a href="/wiki/3413_(number)" class="mw-redirect" title="3413 (number)">3413</a> </td></tr> <tr style="text-align: center;"> <th>481–500 </th> <td><a href="/wiki/3433_(number)" class="mw-redirect" title="3433 (number)">3433</a></td> <td><a href="/wiki/3449_(number)" class="mw-redirect" title="3449 (number)">3449</a></td> <td><a href="/wiki/3457_(number)" class="mw-redirect" title="3457 (number)">3457</a></td> <td><a href="/wiki/3461_(number)" class="mw-redirect" title="3461 (number)">3461</a></td> <td><a href="/wiki/3463_(number)" class="mw-redirect" title="3463 (number)">3463</a></td> <td><a href="/wiki/3467_(number)" class="mw-redirect" title="3467 (number)">3467</a></td> <td><a href="/wiki/3469_(number)" class="mw-redirect" title="3469 (number)">3469</a></td> <td><a href="/wiki/3491_(number)" class="mw-redirect" title="3491 (number)">3491</a></td> <td><a href="/wiki/3499_(number)" class="mw-redirect" title="3499 (number)">3499</a></td> <td><a href="/wiki/3511_(number)" class="mw-redirect" title="3511 (number)">3511</a></td> <td><a href="/wiki/3517_(number)" class="mw-redirect" title="3517 (number)">3517</a></td> <td><a href="/wiki/3527_(number)" class="mw-redirect" title="3527 (number)">3527</a></td> <td><a href="/wiki/3529_(number)" class="mw-redirect" title="3529 (number)">3529</a></td> <td><a href="/wiki/3533_(number)" class="mw-redirect" title="3533 (number)">3533</a></td> <td><a href="/wiki/3539_(number)" class="mw-redirect" title="3539 (number)">3539</a></td> <td><a href="/wiki/3541_(number)" class="mw-redirect" title="3541 (number)">3541</a></td> <td><a href="/wiki/3547_(number)" class="mw-redirect" title="3547 (number)">3547</a></td> <td><a href="/wiki/3557_(number)" class="mw-redirect" title="3557 (number)">3557</a></td> <td><a href="/wiki/3559_(number)" class="mw-redirect" title="3559 (number)">3559</a></td> <td><a href="/wiki/3571_(number)" class="mw-redirect" title="3571 (number)">3571</a> </td></tr> <tr style="text-align: center;"> <th>501–520 </th> <td><a href="/wiki/3581_(number)" class="mw-redirect" title="3581 (number)">3581</a></td> <td><a href="/wiki/3583_(number)" class="mw-redirect" title="3583 (number)">3583</a></td> <td><a href="/wiki/3593_(number)" class="mw-redirect" title="3593 (number)">3593</a></td> <td><a href="/wiki/3607_(number)" class="mw-redirect" title="3607 (number)">3607</a></td> <td><a href="/wiki/3613_(number)" class="mw-redirect" title="3613 (number)">3613</a></td> <td><a href="/wiki/3617_(number)" class="mw-redirect" title="3617 (number)">3617</a></td> <td><a href="/wiki/3623_(number)" class="mw-redirect" title="3623 (number)">3623</a></td> <td><a href="/wiki/3631_(number)" class="mw-redirect" title="3631 (number)">3631</a></td> <td><a href="/wiki/3637_(number)" class="mw-redirect" title="3637 (number)">3637</a></td> <td><a href="/wiki/3643_(number)" class="mw-redirect" title="3643 (number)">3643</a></td> <td><a href="/wiki/3659_(number)" class="mw-redirect" title="3659 (number)">3659</a></td> <td><a href="/wiki/3671_(number)" class="mw-redirect" title="3671 (number)">3671</a></td> <td><a href="/wiki/3673_(number)" class="mw-redirect" title="3673 (number)">3673</a></td> <td><a href="/wiki/3677_(number)" class="mw-redirect" title="3677 (number)">3677</a></td> <td><a href="/wiki/3691_(number)" class="mw-redirect" title="3691 (number)">3691</a></td> <td><a href="/wiki/3697_(number)" class="mw-redirect" title="3697 (number)">3697</a></td> <td><a href="/wiki/3701_(number)" class="mw-redirect" title="3701 (number)">3701</a></td> <td><a href="/wiki/3709_(number)" class="mw-redirect" title="3709 (number)">3709</a></td> <td><a href="/wiki/3719_(number)" class="mw-redirect" title="3719 (number)">3719</a></td> <td><a href="/wiki/3727_(number)" class="mw-redirect" title="3727 (number)">3727</a> </td></tr> <tr style="text-align: center;"> <th>521–540 </th> <td><a href="/wiki/3733_(number)" class="mw-redirect" title="3733 (number)">3733</a></td> <td><a href="/wiki/3739_(number)" class="mw-redirect" title="3739 (number)">3739</a></td> <td><a href="/wiki/3761_(number)" class="mw-redirect" title="3761 (number)">3761</a></td> <td><a href="/wiki/3767_(number)" class="mw-redirect" title="3767 (number)">3767</a></td> <td><a href="/wiki/3769_(number)" class="mw-redirect" title="3769 (number)">3769</a></td> <td><a href="/wiki/3779_(number)" class="mw-redirect" title="3779 (number)">3779</a></td> <td><a href="/wiki/3793_(number)" class="mw-redirect" title="3793 (number)">3793</a></td> <td><a href="/wiki/3797_(number)" class="mw-redirect" title="3797 (number)">3797</a></td> <td><a href="/wiki/3803_(number)" class="mw-redirect" title="3803 (number)">3803</a></td> <td><a href="/wiki/3821_(number)" class="mw-redirect" title="3821 (number)">3821</a></td> <td><a href="/wiki/3823_(number)" class="mw-redirect" title="3823 (number)">3823</a></td> <td><a href="/wiki/3833_(number)" class="mw-redirect" title="3833 (number)">3833</a></td> <td><a href="/wiki/3847_(number)" class="mw-redirect" title="3847 (number)">3847</a></td> <td><a href="/wiki/3851_(number)" class="mw-redirect" title="3851 (number)">3851</a></td> <td><a href="/wiki/3853_(number)" class="mw-redirect" title="3853 (number)">3853</a></td> <td><a href="/wiki/3863_(number)" class="mw-redirect" title="3863 (number)">3863</a></td> <td><a href="/wiki/3877_(number)" class="mw-redirect" title="3877 (number)">3877</a></td> <td><a href="/wiki/3881_(number)" class="mw-redirect" title="3881 (number)">3881</a></td> <td><a href="/wiki/3889_(number)" class="mw-redirect" title="3889 (number)">3889</a></td> <td><a href="/wiki/3907_(number)" class="mw-redirect" title="3907 (number)">3907</a> </td></tr> <tr style="text-align: center;"> <th>541–560 </th> <td><a href="/wiki/3911_(number)" class="mw-redirect" title="3911 (number)">3911</a></td> <td><a href="/wiki/3917_(number)" class="mw-redirect" title="3917 (number)">3917</a></td> <td><a href="/wiki/3919_(number)" class="mw-redirect" title="3919 (number)">3919</a></td> <td><a href="/wiki/3923_(number)" class="mw-redirect" title="3923 (number)">3923</a></td> <td><a href="/wiki/3929_(number)" class="mw-redirect" title="3929 (number)">3929</a></td> <td><a href="/wiki/3931_(number)" class="mw-redirect" title="3931 (number)">3931</a></td> <td><a href="/wiki/3943_(number)" class="mw-redirect" title="3943 (number)">3943</a></td> <td><a href="/wiki/3947_(number)" class="mw-redirect" title="3947 (number)">3947</a></td> <td><a href="/wiki/3967_(number)" class="mw-redirect" title="3967 (number)">3967</a></td> <td><a href="/wiki/3989_(number)" class="mw-redirect" title="3989 (number)">3989</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4001</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4003</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4007</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4013</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4019</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4021</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4027</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4049</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4051</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4057</a> </td></tr> <tr style="text-align: center;"> <th>561–580 </th> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4073</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4079</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4091</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4093</a></td> <td><a href="/wiki/4000_(number)#4001_to_4099" title="4000 (number)">4099</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4111</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4127</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4129</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4133</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4139</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4153</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4157</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4159</a></td> <td><a href="/wiki/4000_(number)#4100_to_4199" title="4000 (number)">4177</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4201</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4211</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4217</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4219</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4229</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4231</a> </td></tr> <tr style="text-align: center;"> <th>581–600 </th> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4241</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4243</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4253</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4259</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4261</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4271</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4273</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4283</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4289</a></td> <td><a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4297</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4327</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4337</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4339</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4349</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4357</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4363</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4373</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4391</a></td> <td><a href="/wiki/4000_(number)#4300_to_4399" title="4000 (number)">4397</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4409</a> </td></tr> <tr style="text-align: center;"> <th>601–620 </th> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4421</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4423</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4441</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4447</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4451</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4457</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4463</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4481</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4483</a></td> <td><a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4493</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4507</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4513</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4517</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4519</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4523</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4547</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4549</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4561</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4567</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4583</a> </td></tr> <tr style="text-align: center;"> <th>621–640 </th> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4591</a></td> <td><a href="/wiki/4000_(number)#4500_to_4599" title="4000 (number)">4597</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4603</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4621</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4637</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4639</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4643</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4649</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4651</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4657</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4663</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4673</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4679</a></td> <td><a href="/wiki/4000_(number)#4600_to_4699" title="4000 (number)">4691</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4703</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4721</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4723</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4729</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4733</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4751</a> </td></tr> <tr style="text-align: center;"> <th>641–660 </th> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4759</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4783</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4787</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4789</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4793</a></td> <td><a href="/wiki/4000_(number)#4700_to_4799" title="4000 (number)">4799</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4801</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4813</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4817</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4831</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4861</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4871</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4877</a></td> <td><a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4889</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4903</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4909</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4919</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4931</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4933</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4937</a> </td></tr> <tr style="text-align: center;"> <th>661–680 </th> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4943</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4951</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4957</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4967</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4969</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4973</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4987</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4993</a></td> <td><a href="/wiki/4000_(number)#4900_to_4999" title="4000 (number)">4999</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5003</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5009</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5011</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5021</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5023</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5039</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5051</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5059</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5077</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5081</a></td> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5087</a> </td></tr> <tr style="text-align: center;"> <th>681–700 </th> <td><a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5099</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5101</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5107</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5113</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5119</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5147</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5153</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5167</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5171</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5179</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5189</a></td> <td><a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5197</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5209</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5227</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5231</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5233</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5237</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5261</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5273</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5279</a> </td></tr> <tr style="text-align: center;"> <th>701–720 </th> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5281</a></td> <td><a href="/wiki/5000_(number)#5200_to_5299" title="5000 (number)">5297</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5303</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5309</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5323</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5333</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5347</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5351</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5381</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5387</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5393</a></td> <td><a href="/wiki/5000_(number)#5300_to_5399" title="5000 (number)">5399</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5407</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5413</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5417</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5419</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5431</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5437</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5441</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5443</a> </td></tr> <tr style="text-align: center;"> <th>721–740 </th> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5449</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5471</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5477</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5479</a></td> <td><a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5483</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5501</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5503</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5507</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5519</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5521</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5527</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5531</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5557</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5563</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5569</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5573</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5581</a></td> <td><a href="/wiki/5000_(number)#5500_to_5599" title="5000 (number)">5591</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5623</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5639</a> </td></tr> <tr style="text-align: center;"> <th>741–760 </th> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5641</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5647</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5651</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5653</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5657</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5659</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5669</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5683</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5689</a></td> <td><a href="/wiki/5000_(number)#5600_to_5699" title="5000 (number)">5693</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5701</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5711</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5717</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5737</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5741</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5743</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5749</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5779</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5783</a></td> <td><a href="/wiki/5000_(number)#5700_to_5799" title="5000 (number)">5791</a> </td></tr> <tr style="text-align: center;"> <th>761–780 </th> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5801</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5807</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5813</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5821</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5827</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5839</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5843</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5849</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5851</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5857</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5861</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5867</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5869</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5879</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5881</a></td> <td><a href="/wiki/5000_(number)#5800_to_5899" title="5000 (number)">5897</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5903</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5923</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5927</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5939</a> </td></tr> <tr style="text-align: center;"> <th>781–800 </th> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5953</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5981</a></td> <td><a href="/wiki/5000_(number)#5900_to_5999" title="5000 (number)">5987</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6007</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6011</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6029</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6037</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6043</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6047</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6053</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6067</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6073</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6079</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6089</a></td> <td><a href="/wiki/6000_(number)#6001_to_6099" title="6000 (number)">6091</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6101</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6113</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6121</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6131</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6133</a> </td></tr> <tr style="text-align: center;"> <th>801–820 </th> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6143</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6151</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6163</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6173</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6197</a></td> <td><a href="/wiki/6000_(number)#6100_to_6199" title="6000 (number)">6199</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6203</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6211</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6217</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6221</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6229</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6247</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6257</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6263</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6269</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6271</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6277</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6287</a></td> <td><a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6299</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6301</a> </td></tr> <tr style="text-align: center;"> <th>821–840 </th> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6311</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6317</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6323</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6329</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6337</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6343</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6353</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6359</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6361</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6367</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6373</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6379</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6389</a></td> <td><a href="/wiki/6000_(number)#6300_to_6399" title="6000 (number)">6397</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6421</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6427</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6449</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6451</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6469</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6473</a> </td></tr> <tr style="text-align: center;"> <th>841–860 </th> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6481</a></td> <td><a href="/wiki/6000_(number)#6400_to_6499" title="6000 (number)">6491</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6521</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6529</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6547</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6551</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6553</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6563</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6569</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6571</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6577</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6581</a></td> <td><a href="/wiki/6000_(number)#6500_to_6599" title="6000 (number)">6599</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6607</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6619</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6637</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6653</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6659</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6661</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6673</a> </td></tr> <tr style="text-align: center;"> <th>861–880 </th> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6679</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6689</a></td> <td><a href="/wiki/6000_(number)#6600_to_6699" title="6000 (number)">6691</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6701</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6703</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6709</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6719</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6733</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6737</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6761</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6763</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6779</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6781</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6791</a></td> <td><a href="/wiki/6000_(number)#6700_to_6799" title="6000 (number)">6793</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6803</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6823</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6827</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6829</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6833</a> </td></tr> <tr style="text-align: center;"> <th>881–900 </th> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6841</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6857</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6863</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6869</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6871</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6883</a></td> <td><a href="/wiki/6000_(number)#6800_to_6899" title="6000 (number)">6899</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6907</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6911</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6917</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6947</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6949</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6959</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6961</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6967</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6971</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6977</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6983</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6991</a></td> <td><a href="/wiki/6000_(number)#6900_to_6999" title="6000 (number)">6997</a> </td></tr> <tr style="text-align: center;"> <th>901–920 </th> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7001</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7013</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7019</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7027</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7039</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7043</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7057</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7069</a></td> <td><a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7079</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7103</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7109</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7121</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7127</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7129</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7151</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7159</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7177</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7187</a></td> <td><a href="/wiki/7000_(number)#7100_to_7199" title="7000 (number)">7193</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7207</a> </td></tr> <tr style="text-align: center;"> <th>921–940 </th> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7211</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7213</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7219</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7229</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7237</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7243</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7247</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7253</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7283</a></td> <td><a href="/wiki/7000_(number)#7200_to_7299" title="7000 (number)">7297</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7307</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7309</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7321</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7331</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7333</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7349</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7351</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7369</a></td> <td><a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7393</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7411</a> </td></tr> <tr style="text-align: center;"> <th>941–960 </th> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7417</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7433</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7451</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7457</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7459</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7477</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7481</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7487</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7489</a></td> <td><a href="/wiki/7000_(number)#7400_to_7499" title="7000 (number)">7499</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7507</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7517</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7523</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7529</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7537</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7541</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7547</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7549</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7559</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7561</a> </td></tr> <tr style="text-align: center;"> <th>961–980 </th> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7573</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7577</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7583</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7589</a></td> <td><a href="/wiki/7000_(number)#7500_to_7599" title="7000 (number)">7591</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7603</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7607</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7621</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7639</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7643</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7649</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7669</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7673</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7681</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7687</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7691</a></td> <td><a href="/wiki/7000_(number)#7600_to_7699" title="7000 (number)">7699</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7703</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7717</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7723</a> </td></tr> <tr style="text-align: center;"> <th>981–1000 </th> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7727</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7741</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7753</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7757</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7759</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7789</a></td> <td><a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7793</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7817</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7823</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7829</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7841</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7853</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7867</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7873</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7877</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7879</a></td> <td><a href="/wiki/7000_(number)#7800_to_7899" title="7000 (number)">7883</a></td> <td><a href="/wiki/7000_(number)#7900_to_7999" title="7000 (number)">7901</a></td> <td><a href="/wiki/7000_(number)#7900_to_7999" title="7000 (number)">7907</a></td> <td><a href="/wiki/7000_(number)#7900_to_7999" title="7000 (number)">7919</a> </td></tr></tbody></table> (sequence <a href="//oeis.org/A000040" class="extiw" title="oeis:A000040">A000040</a> in the <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>). The <a href="/wiki/Goldbach%27s_conjecture" title="Goldbach's conjecture">Goldbach conjecture</a> verification project reports that it has computed all primes smaller than 4×1018.<a href="#cite_note-2">[2]</a> That means 95,676,260,903,887,607 primes<a href="#cite_note-3">[3]</a> (nearly 1017), but they were not stored. There are known formulae to evaluate the <a href="/wiki/Prime-counting_function" title="Prime-counting function">prime-counting function</a> (the number of primes smaller than a given value) faster than computing the primes. This has been used to compute that there are 1,925,320,391,606,803,968,923 primes (roughly 2×1021) smaller than 1023. A different computation found that there are 18,435,599,767,349,200,867,866 primes (roughly 2×1022) smaller than 1024, if the <a href="/wiki/Riemann_hypothesis" title="Riemann hypothesis">Riemann hypothesis</a> is true.<a href="#cite_note-Franke-4">[4]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="Lists_of_primes_by_type">Lists of primes by type</h2> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=2" title="Edit section: Lists of primes by type" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. n is a <a href="/wiki/Natural_number" title="Natural number">natural number</a> (including 0) in the definitions. <div class="mw-heading mw-heading3"><h3 id="Balanced_primes"><a href="/wiki/Balanced_prime" title="Balanced prime">Balanced primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=3" title="Edit section: Balanced primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes with equal-sized <a href="/wiki/Prime_gap" title="Prime gap">prime gaps</a> after and before them, so that they are equal to the <a href="/wiki/Arithmetic_mean" title="Arithmetic mean">arithmetic mean</a> of the nearest primes after and before. <ul><li><a href="/wiki/5_(number)" class="mw-redirect" title="5 (number)">5</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, 157, <a href="/wiki/173_(number)" title="173 (number)">173</a>, 211, <a href="/wiki/257_(number)" title="257 (number)">257</a>, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903, 2963, 3307, 3313, 3637, 3733, 4013, 4409, 4457, 4597, 4657, 4691, 4993, 5107, 5113, 5303, 5387, 5393 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A006562" class="extiw" title="oeis:A006562">A006562</a>).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Bell_primes"><a href="/wiki/Bell_prime" class="mw-redirect" title="Bell prime">Bell primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=4" title="Edit section: Bell primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that are the number of <a href="/wiki/Partition_of_a_set" title="Partition of a set">partitions of a set</a> with n members. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/877_(number)" class="mw-redirect" title="877 (number)">877</a>, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837. The next term has 6,539 digits. (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A051131" class="extiw" title="oeis:A051131">A051131</a>) <div class="mw-heading mw-heading3"><h3 id="Chen_primes"><a href="/wiki/Chen_primes" class="mw-redirect" title="Chen primes">Chen primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=5" title="Edit section: Chen primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Where p is prime and p+2 is either a prime or <a href="/wiki/Semiprime" title="Semiprime">semiprime</a>. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A109611" class="extiw" title="oeis:A109611">A109611</a>) <div class="mw-heading mw-heading3"><h3 id="Circular_primes"><a href="/wiki/Circular_prime" title="Circular prime">Circular primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=6" title="Edit section: Circular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A circular prime number is a number that remains prime on any cyclic rotation of its digits (in base 10). <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/971_(number)" title="971 (number)">971</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a>, <a href="/wiki/1193_(number)" class="mw-redirect" title="1193 (number)">1193</a>, <a href="/wiki/1931_(number)" class="mw-redirect" title="1931 (number)">1931</a>, <a href="/wiki/3119_(number)" class="mw-redirect" title="3119 (number)">3119</a>, <a href="/wiki/3779_(number)" class="mw-redirect" title="3779 (number)">3779</a>, <a href="/wiki/7000_(number)#7700_to_7799" title="7000 (number)">7793</a>, <a href="/wiki/7000_(number)#7900_to_7999" title="7000 (number)">7937</a>, <a href="/wiki/9000_(number)#9300_to_9399" title="9000 (number)">9311</a>, <a href="/wiki/9000_(number)#9300_to_9399" title="9000 (number)">9377</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">11939</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">19391</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">19937</a>, <a href="/wiki/30000_(number)" class="mw-redirect" title="30000 (number)">37199</a>, <a href="/wiki/30000_(number)" class="mw-redirect" title="30000 (number)">39119</a>, <a href="/wiki/70000_(number)" class="mw-redirect" title="70000 (number)">71993</a>, <a href="/wiki/90000_(number)" class="mw-redirect" title="90000 (number)">91193</a>, <a href="/wiki/90000_(number)" class="mw-redirect" title="90000 (number)">93719</a>, <a href="/wiki/90000_(number)" class="mw-redirect" title="90000 (number)">93911</a>, <a href="/wiki/90000_(number)" class="mw-redirect" title="90000 (number)">99371</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">193939</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">199933</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">319993</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">331999</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">391939</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">393919</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">919393</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">933199</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">939193</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">939391</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">993319</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">999331</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A068652" class="extiw" title="oeis:A068652">A068652</a>) Some sources only list the smallest prime in each cycle, for example, listing 13, but omitting 31 (<a href="/wiki/OEIS" class="mw-redirect" title="OEIS">OEIS</a> really calls this sequence circular primes, but not the above sequence): <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/1193_(number)" class="mw-redirect" title="1193 (number)">1193</a>, <a href="/wiki/3779_(number)" class="mw-redirect" title="3779 (number)">3779</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">11939</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">19937</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">193939</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">199933</a>, 1111111111111111111, 11111111111111111111111 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A016114" class="extiw" title="oeis:A016114">A016114</a>) All <a href="/wiki/Repunit" title="Repunit">repunit</a> primes are circular. <div class="mw-heading mw-heading3"><h3 id="Cluster_primes"><a href="/wiki/Cluster_prime" title="Cluster prime">Cluster primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=7" title="Edit section: Cluster primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A cluster prime is a prime p such that every even <a href="/wiki/Natural_number" title="Natural number">natural number</a> k ≤ p − 3 is the difference of two primes not exceeding p. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, ... (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A038134" class="extiw" title="oeis:A038134">A038134</a>) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: <a href="/wiki/2" title="2">2</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>. <div class="mw-heading mw-heading3"><h3 id="Cousin_primes"><a href="/wiki/Cousin_primes" class="mw-redirect" title="Cousin primes">Cousin primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=8" title="Edit section: Cousin primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="#Twin_primes">§ Twin primes</a>, <a href="#Prime_triplets">§ Prime triplets</a>, and <a href="#Prime_quadruplets">§ Prime quadruplets</a></div> Where (p, p + 4) are both prime. (<a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>), (<a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>), (<a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>), (<a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>), (<a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>), (<a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>), (<a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>), (<a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>), (<a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>), (<a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>), (<a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>), (<a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>), (<a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>), (<a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>), (<a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>), (<a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>), (<a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A023200" class="extiw" title="oeis:A023200">A023200</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A046132" class="extiw" title="oeis:A046132">A046132</a>) <div class="mw-heading mw-heading3"><h3 id="Cuban_primes"><a href="/wiki/Cuban_prime" title="Cuban prime">Cuban primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=9" title="Edit section: Cuban primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mi>x</mi> <mo>−</mo> <mi>y</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198e178dc155c09b94b72dbe36915997c89d89fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:5.539ex; height:4.676ex;" alt="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}"></noscript><span class="lazy-image-placeholder" style="width: 5.539ex;height: 4.676ex;vertical-align: -1.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198e178dc155c09b94b72dbe36915997c89d89fb" data-alt="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  where x = y + 1. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/631_(number)" class="mw-redirect" title="631 (number)">631</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/1657_(number)" class="mw-redirect" title="1657 (number)">1657</a>, <a href="/wiki/1801_(number)" class="mw-redirect" title="1801 (number)">1801</a>, <a href="/wiki/1951_(number)" class="mw-redirect" title="1951 (number)">1951</a>, <a href="/wiki/2269_(number)" class="mw-redirect" title="2269 (number)">2269</a>, <a href="/wiki/2437_(number)" class="mw-redirect" title="2437 (number)">2437</a>, <a href="/wiki/2791_(number)" class="mw-redirect" title="2791 (number)">2791</a>, <a href="/wiki/3169_(number)" class="mw-redirect" title="3169 (number)">3169</a>, <a href="/wiki/3571_(number)" class="mw-redirect" title="3571 (number)">3571</a>, <a href="/wiki/4000_(number)#4200_to_4299" title="4000 (number)">4219</a>, <a href="/wiki/4000_(number)#4400_to_4499" title="4000 (number)">4447</a>, <a href="/wiki/5000_(number)#5100_to_5199" title="5000 (number)">5167</a>, <a href="/wiki/5000_(number)#5400_to_5499" title="5000 (number)">5419</a>, <a href="/wiki/6000_(number)#6200_to_6299" title="6000 (number)">6211</a>, <a href="/wiki/7000_(number)#7001_to_7099" title="7000 (number)">7057</a>, <a href="/wiki/7000_(number)#7300_to_7399" title="7000 (number)">7351</a>, <a href="/wiki/8000_(number)#8200_to_8299" title="8000 (number)">8269</a>, <a href="/wiki/9000_(number)#9200_to_9299" title="9000 (number)">9241</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">10267</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">11719</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">12097</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">13267</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">13669</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">16651</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">19441</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">19927</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">22447</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">23497</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">24571</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">25117</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">26227</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">27361</a>, <a href="/wiki/30000_(number)" class="mw-redirect" title="30000 (number)">33391</a>, <a href="/wiki/30000_(number)" class="mw-redirect" title="30000 (number)">35317</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002407" class="extiw" title="oeis:A002407">A002407</a>) Of the form <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mi>x</mi> <mo>−</mo> <mi>y</mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198e178dc155c09b94b72dbe36915997c89d89fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:5.539ex; height:4.676ex;" alt="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}"></noscript><span class="lazy-image-placeholder" style="width: 5.539ex;height: 4.676ex;vertical-align: -1.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198e178dc155c09b94b72dbe36915997c89d89fb" data-alt="{\displaystyle {\tfrac {x^{3}-y^{3}}{x-y}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  where x = y + 2. <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/1201_(number)" class="mw-redirect" title="1201 (number)">1201</a>, <a href="/wiki/1453_(number)" class="mw-redirect" title="1453 (number)">1453</a>, <a href="/wiki/2029_(number)" class="mw-redirect" title="2029 (number)">2029</a>, <a href="/wiki/3469_(number)" class="mw-redirect" title="3469 (number)">3469</a>, <a href="/wiki/3889_(number)" class="mw-redirect" title="3889 (number)">3889</a>, <a href="/wiki/4000_(number)#4800_to_4899" title="4000 (number)">4801</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">10093</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">12289</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">13873</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">18253</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">20173</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">21169</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">22189</a>, <a href="/wiki/20000_(number)" class="mw-redirect" title="20000 (number)">28813</a>, <a href="/wiki/30000_(number)" class="mw-redirect" title="30000 (number)">37633</a>, <a href="/wiki/40000_(number)" class="mw-redirect" title="40000 (number)">43201</a>, <a href="/wiki/40000_(number)" class="mw-redirect" title="40000 (number)">47629</a>, <a href="/wiki/60000_(number)" class="mw-redirect" title="60000 (number)">60493</a>, <a href="/wiki/60000_(number)" class="mw-redirect" title="60000 (number)">63949</a>, <a href="/wiki/60000_(number)" class="mw-redirect" title="60000 (number)">65713</a>, <a href="/wiki/60000_(number)" class="mw-redirect" title="60000 (number)">69313</a>, <a href="/wiki/70000_(number)" class="mw-redirect" title="70000 (number)">73009</a>, <a href="/wiki/70000_(number)" class="mw-redirect" title="70000 (number)">76801</a>, <a href="/wiki/80000_(number)" class="mw-redirect" title="80000 (number)">84673</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">106033</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">108301</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">112909</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">115249</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002648" class="extiw" title="oeis:A002648">A002648</a>) <div class="mw-heading mw-heading3"><h3 id="Cullen_primes"><a href="/wiki/Cullen_number" title="Cullen number">Cullen primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=10" title="Edit section: Cullen primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form n×2n + 1. <a href="/wiki/3" title="3">3</a>, 393050634124102232869567034555427371542904833 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A050920" class="extiw" title="oeis:A050920">A050920</a>) <div class="mw-heading mw-heading3"><h3 id="Delicate_primes"><a href="/wiki/Delicate_prime" title="Delicate prime">Delicate primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=11" title="Edit section: Delicate primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that having any one of their (base 10) digits changed to any other value will always result in a composite number. 294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A050249" class="extiw" title="oeis:A050249">A050249</a>) <div class="mw-heading mw-heading3"><h3 id="Dihedral_primes"><a href="/wiki/Dihedral_prime" title="Dihedral prime">Dihedral primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=12" title="Edit section: Dihedral primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that remain prime when read upside down or mirrored in a <a href="/wiki/Seven-segment_display" title="Seven-segment display">seven-segment display</a>. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/1181_(number)" class="mw-redirect" title="1181 (number)">1181</a>, <a href="/wiki/1000_(number)#1800_to_1899" title="1000 (number)">1811</a>, <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">18181</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">108881</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">110881</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">118081</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">120121</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">121021</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">121151</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">150151</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">151051</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">151121</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">180181</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">180811</a>, <a href="/wiki/100000_(number)" class="mw-redirect" title="100000 (number)">181081</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A134996" class="extiw" title="oeis:A134996">A134996</a>) <div class="mw-heading mw-heading3"><h3 id="Eisenstein_primes_without_imaginary_part"><a href="/wiki/Eisenstein_primes" class="mw-redirect" title="Eisenstein primes">Eisenstein primes</a> without imaginary part</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=13" title="Edit section: Eisenstein primes without imaginary part" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Eisenstein_integer" title="Eisenstein integer">Eisenstein integers</a> that are <a href="/wiki/Irreducible_element" title="Irreducible element">irreducible</a> and real numbers (primes of the form 3n − 1). <a href="/wiki/2" title="2">2</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A003627" class="extiw" title="oeis:A003627">A003627</a>) <div class="mw-heading mw-heading3"><h3 id="Emirps"><a href="/wiki/Emirps" class="mw-redirect" title="Emirps">Emirps</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=14" title="Edit section: Emirps" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that become a different prime when their decimal digits are reversed. The name "emirp" is the reverse of the word "prime". <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/701_(number)" class="mw-redirect" title="701 (number)">701</a>, <a href="/wiki/709_(number)" class="mw-redirect" title="709 (number)">709</a>, <a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/743_(number)" title="743 (number)">743</a>, <a href="/wiki/751_(number)" class="mw-redirect" title="751 (number)">751</a>, <a href="/wiki/761_(number)" class="mw-redirect" title="761 (number)">761</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/907_(number)" class="mw-redirect" title="907 (number)">907</a>, <a href="/wiki/937_(number)" class="mw-redirect" title="937 (number)">937</a>, <a href="/wiki/941_(number)" class="mw-redirect" title="941 (number)">941</a>, <a href="/wiki/953_(number)" class="mw-redirect" title="953 (number)">953</a>, <a href="/wiki/967_(number)" class="mw-redirect" title="967 (number)">967</a>, <a href="/wiki/971_(number)" title="971 (number)">971</a>, <a href="/wiki/983_(number)" class="mw-redirect" title="983 (number)">983</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A006567" class="extiw" title="oeis:A006567">A006567</a>) <div class="mw-heading mw-heading3"><h3 id="Euclid_primes"><a href="/wiki/Euclid_number" title="Euclid number">Euclid primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=15" title="Edit section: Euclid primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form pn# + 1 (a subset of <a href="/wiki/Primorial_prime" title="Primorial prime">primorial primes</a>). <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/2311_(number)" class="mw-redirect" title="2311 (number)">2311</a>, 200560490131 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A018239" class="extiw" title="oeis:A018239">A018239</a><a href="#cite_note-A018239-5">[5]</a>) <div class="mw-heading mw-heading3"><h3 id="Euler_irregular_primes"><a href="/wiki/Regular_prime#Euler_irregular_primes" title="Regular prime">Euler irregular primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=16" title="Edit section: Euler irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A prime <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></noscript><span class="lazy-image-placeholder" style="width: 1.259ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" data-alt="{\displaystyle p}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  that divides <a href="/wiki/Euler_number" class="mw-redirect" title="Euler number">Euler number</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{2n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{2n}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cdf2d8572a17f02edb3dd4e71f9b5e15250948b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.756ex; height:2.509ex;" alt="{\displaystyle E_{2n}}"></noscript><span class="lazy-image-placeholder" style="width: 3.756ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cdf2d8572a17f02edb3dd4e71f9b5e15250948b" data-alt="{\displaystyle E_{2n}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  for some <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq 2n\leq p-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mn>2</mn> <mi>n</mi> <mo>≤</mo> <mi>p</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq 2n\leq p-3}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed755cd663cd984b87468bd71a66c42fa306a21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.089ex; height:2.509ex;" alt="{\displaystyle 0\leq 2n\leq p-3}"></noscript><span class="lazy-image-placeholder" style="width: 15.089ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed755cd663cd984b87468bd71a66c42fa306a21" data-alt="{\displaystyle 0\leq 2n\leq p-3}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a>, <a href="/wiki/571_(number)" class="mw-redirect" title="571 (number)">571</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A120337" class="extiw" title="oeis:A120337">A120337</a>) <div class="mw-heading mw-heading4"><h4 id="Euler_(p,_p_−_3)_irregular_primes"><a href="/wiki/Regular_prime#Irregular_pairs" title="Regular prime">Euler (p, p − 3) irregular primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=17" title="Edit section: Euler (p, p − 3) irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></noscript><span class="lazy-image-placeholder" style="width: 1.259ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" data-alt="{\displaystyle p}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  such that <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (p,p-3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>p</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (p,p-3)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/295415066d02f57efa52aef361f1eb4d14771135" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.185ex; height:2.843ex;" alt="{\displaystyle (p,p-3)}"></noscript><span class="lazy-image-placeholder" style="width: 9.185ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/295415066d02f57efa52aef361f1eb4d14771135" data-alt="{\displaystyle (p,p-3)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is an Euler irregular pair. <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/1000000_(number)" class="mw-redirect" title="1000000 (number)">2946901</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A198245" class="extiw" title="oeis:A198245">A198245</a>) <div class="mw-heading mw-heading3"><h3 id="Factorial_primes"><a href="/wiki/Factorial_prime" title="Factorial prime">Factorial primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=18" title="Edit section: Factorial primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form n<a href="/wiki/Factorial" title="Factorial">!</a> − 1 or n<a href="/wiki/Factorial" title="Factorial">!</a> + 1. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/5000_(number)#5001_to_5099" title="5000 (number)">5039</a>, <a href="/wiki/10000000_(number)" class="mw-redirect" title="10000000 (number)">39916801</a>, <a href="/wiki/100000000_(number)" class="mw-redirect" title="100000000 (number)">479001599</a>, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A088054" class="extiw" title="oeis:A088054">A088054</a>) <div class="mw-heading mw-heading3"><h3 id="Fermat_primes"><a href="/wiki/Fermat_prime" class="mw-redirect" title="Fermat prime">Fermat primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=19" title="Edit section: Fermat primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 22n + 1. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A019434" class="extiw" title="oeis:A019434">A019434</a>) As of June 2024<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a> these are the only known Fermat primes, and conjecturally the only Fermat primes. The probability of the existence of another Fermat prime is less than one in a billion.<a href="#cite_note-6">[6]</a> <div class="mw-heading mw-heading4"><h4 id="Generalized_Fermat_primes">Generalized <a href="/wiki/Fermat_primes" class="mw-redirect" title="Fermat primes">Fermat primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=20" title="Edit section: Generalized Fermat primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form a2n + 1 for fixed integer a. a = 2: <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A019434" class="extiw" title="oeis:A019434">A019434</a>) a = 4: <a href="/wiki/5" title="5">5</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a> a = 6: <a href="/wiki/7" title="7">7</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/1297_(number)" class="mw-redirect" title="1297 (number)">1297</a> a = 8: (does not exist) a = 10: <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a> a = 12: <a href="/wiki/13_(number)" title="13 (number)">13</a> a = 14: <a href="/wiki/197_(number)" title="197 (number)">197</a> a = 16: <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a> a = 18: <a href="/wiki/19_(number)" title="19 (number)">19</a> a = 20: <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, 160001 a = 22: <a href="/wiki/23_(number)" title="23 (number)">23</a> a = 24: <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, 331777 <div class="mw-heading mw-heading3"><h3 id="Fibonacci_primes"><a href="/wiki/Fibonacci_prime" title="Fibonacci prime">Fibonacci primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=21" title="Edit section: Fibonacci primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes in the <a href="/wiki/Fibonacci_sequence" title="Fibonacci sequence">Fibonacci sequence</a> F0 = 0, F1 = 1, Fn = Fn−1 + Fn−2. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/1597_(number)" class="mw-redirect" title="1597 (number)">1597</a>, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A005478" class="extiw" title="oeis:A005478">A005478</a>) <div class="mw-heading mw-heading3"><h3 id="Fortunate_primes"><a href="/wiki/Fortunate_number" title="Fortunate number">Fortunate primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=22" title="Edit section: Fortunate primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Fortunate_number" title="Fortunate number">Fortunate numbers</a> that are prime (it has been conjectured they all are). <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A046066" class="extiw" title="oeis:A046066">A046066</a>) <div class="mw-heading mw-heading3"><h3 id="Gaussian_primes"><a href="/wiki/Gaussian_prime" class="mw-redirect" title="Gaussian prime">Gaussian primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=23" title="Edit section: Gaussian primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Prime_element" title="Prime element">Prime elements</a> of the Gaussian integers; equivalently, primes of the form 4n + 3. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/439_(number)" class="mw-redirect" title="439 (number)">439</a>, <a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a>, <a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002145" class="extiw" title="oeis:A002145">A002145</a>) <div class="mw-heading mw-heading3"><h3 id="Good_primes"><a href="/wiki/Good_prime" title="Good prime">Good primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=24" title="Edit section: Good primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes pn for which pn2 > pn−i pn+i for all 1 ≤ i ≤ n−1, where pn is the nth prime. <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A028388" class="extiw" title="oeis:A028388">A028388</a>) <div class="mw-heading mw-heading3"><h3 id="Happy_primes"><a href="/wiki/Happy_prime" class="mw-redirect" title="Happy prime">Happy primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=25" title="Edit section: Happy primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Happy numbers that are prime. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a>, <a href="/wiki/617_(number)" class="mw-redirect" title="617 (number)">617</a>, <a href="/wiki/653_(number)" class="mw-redirect" title="653 (number)">653</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, <a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a>, <a href="/wiki/709_(number)" class="mw-redirect" title="709 (number)">709</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/761_(number)" class="mw-redirect" title="761 (number)">761</a>, <a href="/wiki/863_(number)" class="mw-redirect" title="863 (number)">863</a>, <a href="/wiki/881_(number)" title="881 (number)">881</a>, <a href="/wiki/907_(number)" class="mw-redirect" title="907 (number)">907</a>, <a href="/wiki/937_(number)" class="mw-redirect" title="937 (number)">937</a>, <a href="/wiki/1009_(number)" class="mw-redirect" title="1009 (number)">1009</a>, <a href="/wiki/1033_(number)" class="mw-redirect" title="1033 (number)">1033</a>, <a href="/wiki/1039_(number)" class="mw-redirect" title="1039 (number)">1039</a>, <a href="/wiki/1093_(number)" title="1093 (number)">1093</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A035497" class="extiw" title="oeis:A035497">A035497</a>) <div class="mw-heading mw-heading3"><h3 id="Harmonic_primes">Harmonic primes</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=26" title="Edit section: Harmonic primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which there are no solutions to Hk ≡ 0 (mod p) and Hk ≡ −ωp (mod p) for 1 ≤ k ≤ p−2, where Hk denotes the k-th <a href="/wiki/Harmonic_number" title="Harmonic number">harmonic number</a> and ωp denotes the <a href="/wiki/Wolstenholme_quotient" class="mw-redirect" title="Wolstenholme quotient">Wolstenholme quotient</a>.<a href="#cite_note-7">[7]</a> <a href="/wiki/5" title="5">5</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A092101" class="extiw" title="oeis:A092101">A092101</a>) <div class="mw-heading mw-heading3"><h3 id="Higgs_primes_for_squares"><a href="/wiki/Higgs_prime" title="Higgs prime">Higgs primes</a> for squares</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=27" title="Edit section: Higgs primes for squares" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which p − 1 divides the square of the product of all earlier terms. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007459" class="extiw" title="oeis:A007459">A007459</a>) <div class="mw-heading mw-heading3"><h3 id="Highly_cototient_primes"><a href="/wiki/Highly_cototient_number" title="Highly cototient number"> Highly cototient primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=28" title="Edit section: Highly cototient primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that are a <a href="/wiki/Cototient" class="mw-redirect" title="Cototient">cototient</a> more often than any integer below it except 1. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/659_(number)" class="mw-redirect" title="659 (number)">659</a>, <a href="/wiki/839_(number)" class="mw-redirect" title="839 (number)">839</a>, <a href="/wiki/1049_(number)" class="mw-redirect" title="1049 (number)">1049</a>, <a href="/wiki/1259_(number)" class="mw-redirect" title="1259 (number)">1259</a>, <a href="/wiki/1889_(number)" class="mw-redirect" title="1889 (number)">1889</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A105440" class="extiw" title="oeis:A105440">A105440</a>) <div class="mw-heading mw-heading3"><h3 id="Home_primes"><a href="/wiki/Home_prime" title="Home prime">Home primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=29" title="Edit section: Home primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> For n ≥ 2, write the prime factorization of n in base 10 and concatenate the factors; iterate until a prime is reached. 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, 31, 241271, 311, 31397, 1129, 71129, 37, 373, 313, 3314192745739, 41, 379, 43, 22815088913, 3411949, 223, 47, 6161791591356884791277 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A037274" class="extiw" title="oeis:A037274">A037274</a>) <div class="mw-heading mw-heading3"><h3 id="Irregular_primes"><a href="/wiki/Irregular_prime" class="mw-redirect" title="Irregular prime">Irregular primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=30" title="Edit section: Irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Odd primes p that divide the <a href="/wiki/Class_number_(number_theory)" class="mw-redirect" title="Class number (number theory)">class number</a> of the p-th <a href="/wiki/Cyclotomic_field" title="Cyclotomic field">cyclotomic field</a>. <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/523_(number)" class="mw-redirect" title="523 (number)">523</a>, <a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/557_(number)" class="mw-redirect" title="557 (number)">557</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a>, <a href="/wiki/607_(number)" class="mw-redirect" title="607 (number)">607</a>, <a href="/wiki/613_(number)" title="613 (number)">613</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000928" class="extiw" title="oeis:A000928">A000928</a>) <div class="mw-heading mw-heading4"><h4 id="(p,_p_−_3)_irregular_primes"><a href="/wiki/Regular_prime#Irregular_pairs" title="Regular prime">(p, p − 3) irregular primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=31" title="Edit section: (p, p − 3) irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> (See <a href="/wiki/Wolstenholme_prime" title="Wolstenholme prime">Wolstenholme prime</a>) <div class="mw-heading mw-heading4"><h4 id="(p,_p_−_5)_irregular_primes"><a href="/wiki/Regular_prime#Irregular_pairs" title="Regular prime">(p, p − 5) irregular primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=32" title="Edit section: (p, p − 5) irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p such that (p, p−5) is an irregular pair.<a href="#cite_note-Johnson-8">[8]</a> <a href="/wiki/37_(number)" title="37 (number)">37</a> <div class="mw-heading mw-heading4"><h4 id="(p,_p_−_9)_irregular_primes"><a href="/wiki/Regular_prime#Irregular_pairs" title="Regular prime">(p, p − 9) irregular primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=33" title="Edit section: (p, p − 9) irregular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p such that (p, p − 9) is an irregular pair.<a href="#cite_note-Johnson-8">[8]</a> <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/877_(number)" class="mw-redirect" title="877 (number)">877</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A212557" class="extiw" title="oeis:A212557">A212557</a>) <div class="mw-heading mw-heading3"><h3 id="Isolated_primes"><a href="/wiki/Isolated_prime" class="mw-redirect" title="Isolated prime">Isolated primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=34" title="Edit section: Isolated primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p such that neither p − 2 nor p + 2 is prime. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/439_(number)" class="mw-redirect" title="439 (number)">439</a>, <a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a>, <a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a>, <a href="/wiki/457_(number)" class="mw-redirect" title="457 (number)">457</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a>, <a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/557_(number)" class="mw-redirect" title="557 (number)">557</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a>, <a href="/wiki/607_(number)" class="mw-redirect" title="607 (number)">607</a>, <a href="/wiki/613_(number)" title="613 (number)">613</a>, <a href="/wiki/631_(number)" class="mw-redirect" title="631 (number)">631</a>, <a href="/wiki/647_(number)" class="mw-redirect" title="647 (number)">647</a>, <a href="/wiki/653_(number)" class="mw-redirect" title="653 (number)">653</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, <a href="/wiki/677_(number)" class="mw-redirect" title="677 (number)">677</a>, <a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a>, <a href="/wiki/691_(number)" class="mw-redirect" title="691 (number)">691</a>, <a href="/wiki/701_(number)" class="mw-redirect" title="701 (number)">701</a>, <a href="/wiki/709_(number)" class="mw-redirect" title="709 (number)">709</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a>, <a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/743_(number)" title="743 (number)">743</a>, <a href="/wiki/751_(number)" class="mw-redirect" title="751 (number)">751</a>, <a href="/wiki/757_(number)" class="mw-redirect" title="757 (number)">757</a>, <a href="/wiki/761_(number)" class="mw-redirect" title="761 (number)">761</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/773_(number)" class="mw-redirect" title="773 (number)">773</a>, <a href="/wiki/787_(number)" class="mw-redirect" title="787 (number)">787</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/839_(number)" class="mw-redirect" title="839 (number)">839</a>, <a href="/wiki/853_(number)" class="mw-redirect" title="853 (number)">853</a>, <a href="/wiki/863_(number)" class="mw-redirect" title="863 (number)">863</a>, <a href="/wiki/877_(number)" class="mw-redirect" title="877 (number)">877</a>, <a href="/wiki/887_(number)" class="mw-redirect" title="887 (number)">887</a>, <a href="/wiki/907_(number)" class="mw-redirect" title="907 (number)">907</a>, <a href="/wiki/911_(number)" title="911 (number)">911</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a>, <a href="/wiki/937_(number)" class="mw-redirect" title="937 (number)">937</a>, <a href="/wiki/941_(number)" class="mw-redirect" title="941 (number)">941</a>, <a href="/wiki/947_(number)" class="mw-redirect" title="947 (number)">947</a>, <a href="/wiki/953_(number)" class="mw-redirect" title="953 (number)">953</a>, <a href="/wiki/967_(number)" class="mw-redirect" title="967 (number)">967</a>, <a href="/wiki/971_(number)" title="971 (number)">971</a>, <a href="/wiki/977_(number)" class="mw-redirect" title="977 (number)">977</a>, <a href="/wiki/983_(number)" class="mw-redirect" title="983 (number)">983</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a>, <a href="/wiki/997_(number)" class="mw-redirect" title="997 (number)">997</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007510" class="extiw" title="oeis:A007510">A007510</a>) <div class="mw-heading mw-heading3"><h3 id="Leyland_primes"><a href="/wiki/Leyland_number" title="Leyland number">Leyland primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=35" title="Edit section: Leyland primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form xy + yx, with 1 < x < y. <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a>, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A094133" class="extiw" title="oeis:A094133">A094133</a>) <div class="mw-heading mw-heading3"><h3 id="Long_primes"><a href="/wiki/Full_reptend_prime" title="Full reptend prime">Long primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=36" title="Edit section: Long primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which, in a given base b, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {b^{p-1}-1}{p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mi>p</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {b^{p-1}-1}{p}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d34c8fd8cb6da254d26e8066c4a43457908c53f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.996ex; height:6.176ex;" alt="{\displaystyle {\frac {b^{p-1}-1}{p}}}"></noscript><span class="lazy-image-placeholder" style="width: 8.996ex;height: 6.176ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d34c8fd8cb6da254d26e8066c4a43457908c53f" data-alt="{\displaystyle {\frac {b^{p-1}-1}{p}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  gives a <a href="/wiki/Cyclic_number" title="Cyclic number">cyclic number</a>. They are also called full reptend primes. Primes p for base 10: <a href="/wiki/7" title="7">7</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a>, <a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a>, <a href="/wiki/571_(number)" class="mw-redirect" title="571 (number)">571</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A001913" class="extiw" title="oeis:A001913">A001913</a>) <div class="mw-heading mw-heading3"><h3 id="Lucas_primes"><a href="/wiki/Lucas_prime" class="mw-redirect" title="Lucas prime">Lucas primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=37" title="Edit section: Lucas primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes in the Lucas number sequence L0 = 2, L1 = 1, Ln = Ln−1 + Ln−2. <a href="/wiki/2" title="2">2</a>,<a href="#cite_note-9">[9]</a> <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/521_(number)" class="mw-redirect" title="521 (number)">521</a>, <a href="/wiki/2207_(number)" class="mw-redirect" title="2207 (number)">2207</a>, <a href="/wiki/3571_(number)" class="mw-redirect" title="3571 (number)">3571</a>, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A005479" class="extiw" title="oeis:A005479">A005479</a>) <div class="mw-heading mw-heading3"><h3 id="Lucky_primes"><a href="/wiki/Lucky_number" title="Lucky number">Lucky primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=38" title="Edit section: Lucky primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Lucky numbers that are prime. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/541_(number)" class="mw-redirect" title="541 (number)">541</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/601_(number)" class="mw-redirect" title="601 (number)">601</a>, <a href="/wiki/613_(number)" title="613 (number)">613</a>, <a href="/wiki/619_(number)" class="mw-redirect" title="619 (number)">619</a>, <a href="/wiki/631_(number)" class="mw-redirect" title="631 (number)">631</a>, <a href="/wiki/643_(number)" class="mw-redirect" title="643 (number)">643</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, <a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/787_(number)" class="mw-redirect" title="787 (number)">787</a>, <a href="/wiki/823_(number)" class="mw-redirect" title="823 (number)">823</a>, <a href="/wiki/883_(number)" class="mw-redirect" title="883 (number)">883</a>, <a href="/wiki/937_(number)" class="mw-redirect" title="937 (number)">937</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a>, <a href="/wiki/997_(number)" class="mw-redirect" title="997 (number)">997</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A031157" class="extiw" title="oeis:A031157">A031157</a>) <div class="mw-heading mw-heading3"><h3 id="Mersenne_primes"><a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=39" title="Edit section: Mersenne primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 2n − 1. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/8191_(number)" class="mw-redirect" title="8191 (number)">8191</a>, <a href="/wiki/131071_(number)" class="mw-redirect" title="131071 (number)">131071</a>, <a href="/wiki/524287_(number)" class="mw-redirect" title="524287 (number)">524287</a>, <a href="/wiki/2147483647" class="mw-redirect" title="2147483647">2147483647</a>, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000668" class="extiw" title="oeis:A000668">A000668</a>) As of 2024<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, there are 52 known Mersenne primes. The 13th, 14th, and 52nd have respectively 157, 183, and 41,024,320 digits. This includes the largest known prime 2136,279,841-1, which is the 52nd Mersenne prime. <div class="mw-heading mw-heading4"><h4 id="Mersenne_divisors">Mersenne divisors</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=40" title="Edit section: Mersenne divisors" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p that divide 2n − 1, for some prime number n. 3, 7, 23, 31, 47, 89, 127, 167, 223, 233, 263, 359, 383, 431, 439, 479, 503, 719, 839, 863, 887, 983, 1103, 1319, 1367, 1399, 1433, 1439, 1487, 1823, 1913, 2039, 2063, 2089, 2207, 2351, 2383, 2447, 2687, 2767, 2879, 2903, 2999, 3023, 3119, 3167, 3343 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A122094" class="extiw" title="oeis:A122094">A122094</a>) All Mersenne primes are, by definition, members of this sequence. <div class="mw-heading mw-heading4"><h4 id="Mersenne_prime_exponents">Mersenne prime exponents</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=41" title="Edit section: Mersenne prime exponents" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p such that 2p − 1 is prime. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/521_(number)" class="mw-redirect" title="521 (number)">521</a>, <a href="/wiki/607_(number)" class="mw-redirect" title="607 (number)">607</a>, <a href="/wiki/1279_(number)" class="mw-redirect" title="1279 (number)">1279</a>, <a href="/wiki/2203_(number)" class="mw-redirect" title="2203 (number)">2203</a>, <a href="/wiki/2281_(number)" class="mw-redirect" title="2281 (number)">2281</a>, <a href="/wiki/3217_(number)" class="mw-redirect" title="3217 (number)">3217</a>, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, <a href="/wiki/43,112,609_(number)" class="mw-redirect" title="43,112,609 (number)">43112609</a>, 57885161 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000043" class="extiw" title="oeis:A000043">A000043</a>) As of October 2024<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, four more are known to be in the sequence, but it is not known whether they are the next: 74207281, 77232917, 82589933, 136279841 <div class="mw-heading mw-heading4"><h4 id="Double_Mersenne_primes"><a href="/wiki/Double_Mersenne_prime" class="mw-redirect" title="Double Mersenne prime">Double Mersenne primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=42" title="Edit section: Double Mersenne primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A subset of Mersenne primes of the form 22p−1 − 1 for prime p. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/2147483647" class="mw-redirect" title="2147483647">2147483647</a>, 170141183460469231731687303715884105727 (primes in <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A077586" class="extiw" title="oeis:A077586">A077586</a>) <div class="mw-heading mw-heading4"><h4 id="Generalized_repunit_primes">Generalized <a href="/wiki/Repunit#Repunit_primes" title="Repunit">repunit primes</a></h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=43" title="Edit section: Generalized repunit primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form (an − 1) / (a − 1) for fixed integer a. For a = 2, these are the Mersenne primes, while for a = 10 they are the <a href="#Repunit_primes">repunit primes</a>. For other small a, they are given below: a = 3: <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/1093_(number)" title="1093 (number)">1093</a>, 797161, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A076481" class="extiw" title="oeis:A076481">A076481</a>) a = 4: <a href="/wiki/5" title="5">5</a> (the only prime for a = 4) a = 5: <a href="/wiki/31_(number)" title="31 (number)">31</a>, 19531, 12207031, 305175781, 177635683940025046467781066894531, 14693679385278593849609206715278070972733319459651094018859396328480215743184089660644531 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A086122" class="extiw" title="oeis:A086122">A086122</a>) a = 6: <a href="/wiki/7" title="7">7</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, 55987, 7369130657357778596659, 3546245297457217493590449191748546458005595187661976371 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A165210" class="extiw" title="oeis:A165210">A165210</a>) a = 7: 2801, 16148168401, 85053461164796801949539541639542805770666392330682673302530819774105141531698707146930307290253537320447270457 a = 8: <a href="/wiki/73_(number)" title="73 (number)">73</a> (the only prime for a = 8) a = 9: none exist <div class="mw-heading mw-heading4"><h4 id="Other_generalizations_and_variations">Other generalizations and variations</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=44" title="Edit section: Other generalizations and variations" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Many generalizations of Mersenne primes have been defined. This include the following: <ul><li>Primes of the form bn − (b − 1)n,<a href="#cite_note-10">[10]</a><a href="#cite_note-11">[11]</a><a href="#cite_note-12">[12]</a> including the Mersenne primes and the <a href="/wiki/Cuban_prime" title="Cuban prime">cuban primes</a> as special cases</li> <li><a href="/wiki/Williams_prime" class="mw-redirect" title="Williams prime">Williams primes</a>, of the form (b − 1)·bn − 1</li></ul> <div class="mw-heading mw-heading3"><h3 id="Mills_primes"><a href="/wiki/Mills%27_constant" title="Mills' constant">Mills primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=45" title="Edit section: Mills primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form ⌊θ3n⌋, where θ is Mills' constant. This form is prime for all positive integers n. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/1361_(number)" class="mw-redirect" title="1361 (number)">1361</a>, 2521008887, 16022236204009818131831320183 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A051254" class="extiw" title="oeis:A051254">A051254</a>) <div class="mw-heading mw-heading3"><h3 id="Minimal_primes"><a href="/wiki/Minimal_prime_(number_theory)" class="mw-redirect" title="Minimal prime (number theory)">Minimal primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=46" title="Edit section: Minimal primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes for which there is no shorter <a href="/wiki/Subsequence" title="Subsequence">sub-sequence</a> of the decimal digits that form a prime. There are exactly 26 minimal primes: <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a>, <a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a>, <a href="/wiki/881_(number)" title="881 (number)">881</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a>, 6469, 6949, <a href="/wiki/9001_(number)" class="mw-redirect" title="9001 (number)">9001</a>, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A071062" class="extiw" title="oeis:A071062">A071062</a>) <div class="mw-heading mw-heading3"><h3 id="Newman–Shanks–Williams_primes"><a href="/wiki/Newman%E2%80%93Shanks%E2%80%93Williams_prime" title="Newman–Shanks–Williams prime">Newman–Shanks–Williams primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=47" title="Edit section: Newman–Shanks–Williams primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Newman–Shanks–Williams numbers that are prime. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, 9369319, 63018038201, 489133282872437279, 19175002942688032928599 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A088165" class="extiw" title="oeis:A088165">A088165</a>) <div class="mw-heading mw-heading3"><h3 id="Non-generous_primes">Non-generous primes</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=48" title="Edit section: Non-generous primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which the least positive <a href="/wiki/Primitive_root_modulo_n" title="Primitive root modulo n">primitive root</a> is not a primitive root of p2. Three such primes are known; it is not known whether there are more.<a href="#cite_note-13">[13]</a> <a href="/wiki/2" title="2">2</a>, 40487, 6692367337 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A055578" class="extiw" title="oeis:A055578">A055578</a>) <div class="mw-heading mw-heading3"><h3 id="Palindromic_primes"><a href="/wiki/Palindromic_primes" class="mw-redirect" title="Palindromic primes">Palindromic primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=49" title="Edit section: Palindromic primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that remain the same when their decimal digits are read backwards. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a>, <a href="/wiki/757_(number)" class="mw-redirect" title="757 (number)">757</a>, <a href="/wiki/787_(number)" class="mw-redirect" title="787 (number)">787</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a>, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002385" class="extiw" title="oeis:A002385">A002385</a>) <div class="mw-heading mw-heading3"><h3 id="Palindromic_wing_primes">Palindromic wing primes</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=50" title="Edit section: Palindromic wing primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes of the form <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mrow> <mn>9</mn> </mfrac> </mrow> <mo>±</mo> <mi>b</mi> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c9913cc959216f8e52cc938a4602375888a1dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.147ex; height:6.009ex;" alt="{\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}}"></noscript><span class="lazy-image-placeholder" style="width: 25.147ex;height: 6.009ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c9913cc959216f8e52cc938a4602375888a1dc" data-alt="{\displaystyle {\frac {a{\big (}10^{m}-1{\big )}}{9}}\pm b\times 10^{\frac {m-1}{2}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  with <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq a\pm b<10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>a</mi> <mo>±</mo> <mi>b</mi> <mo><</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq a\pm b<10}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82b6af255768db6101ad92d77ba0b89d9bb1645a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:14.752ex; height:2.343ex;" alt="{\displaystyle 0\leq a\pm b<10}"></noscript><span class="lazy-image-placeholder" style="width: 14.752ex;height: 2.343ex;vertical-align: -0.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82b6af255768db6101ad92d77ba0b89d9bb1645a" data-alt="{\displaystyle 0\leq a\pm b<10}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> .<a href="#cite_note-14">[14]</a> This means all digits except the middle digit are equal. <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a>, <a href="/wiki/757_(number)" class="mw-redirect" title="757 (number)">757</a>, <a href="/wiki/787_(number)" class="mw-redirect" title="787 (number)">787</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a>, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A077798" class="extiw" title="oeis:A077798">A077798</a>) <div class="mw-heading mw-heading3"><h3 id="Partition_primes"><a href="/wiki/Partition_function_(number_theory)" title="Partition function (number theory)">Partition primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=51" title="Edit section: Partition primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Partition function values that are prime. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A049575" class="extiw" title="oeis:A049575">A049575</a>) <div class="mw-heading mw-heading3"><h3 id="Pell_primes"><a href="/wiki/Pell_number" title="Pell number">Pell primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=52" title="Edit section: Pell primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes in the Pell number sequence P0 = 0, P1 = 1, Pn = 2Pn−1 + Pn−2. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A086383" class="extiw" title="oeis:A086383">A086383</a>) <div class="mw-heading mw-heading3"><h3 id="Permutable_primes"><a href="/wiki/Permutable_prime" title="Permutable prime">Permutable primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=53" title="Edit section: Permutable primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Any permutation of the decimal digits is a prime. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a>, 1111111111111111111, 11111111111111111111111 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A003459" class="extiw" title="oeis:A003459">A003459</a>) <div class="mw-heading mw-heading3"><h3 id="Perrin_primes"><a href="/wiki/Perrin_number" title="Perrin number">Perrin primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=54" title="Edit section: Perrin primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes in the Perrin number sequence P(0) = 3, P(1) = 0, P(2) = 2, P(n) = P(n−2) + P(n−3). <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/853_(number)" class="mw-redirect" title="853 (number)">853</a>, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A074788" class="extiw" title="oeis:A074788">A074788</a>) <div class="mw-heading mw-heading3"><h3 id="Pierpont_primes"><a href="/wiki/Pierpont_prime" title="Pierpont prime">Pierpont primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=55" title="Edit section: Pierpont primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 2u3v + 1 for some <a href="/wiki/Integer" title="Integer">integers</a> u,v ≥ 0. These are also <a href="/wiki/Prime_number#Classification_of_prime_numbers" title="Prime number">class 1- primes</a>. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/1153_(number)" class="mw-redirect" title="1153 (number)">1153</a>, <a href="/wiki/1297_(number)" class="mw-redirect" title="1297 (number)">1297</a>, <a href="/wiki/1459_(number)" class="mw-redirect" title="1459 (number)">1459</a>, <a href="/wiki/2593_(number)" class="mw-redirect" title="2593 (number)">2593</a>, <a href="/wiki/2917_(number)" class="mw-redirect" title="2917 (number)">2917</a>, <a href="/wiki/3457_(number)" class="mw-redirect" title="3457 (number)">3457</a>, <a href="/wiki/3889_(number)" class="mw-redirect" title="3889 (number)">3889</a>, 10369, 12289, 17497, 18433, 39367, 52489, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a>, 139969, 147457 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A005109" class="extiw" title="oeis:A005109">A005109</a>) <div class="mw-heading mw-heading3"><h3 id="Pillai_primes"><a href="/wiki/Pillai_prime" title="Pillai prime">Pillai primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=56" title="Edit section: Pillai primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which there exist n > 0 such that p divides n! + 1 and n does not divide p − 1. <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a>, <a href="/wiki/499_(number)" class="mw-redirect" title="499 (number)">499</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A063980" class="extiw" title="oeis:A063980">A063980</a>) <div class="mw-heading mw-heading3"><h3 id="Primes_of_the_form_n4_+_1">Primes of the form n4 + 1</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=57" title="Edit section: Primes of the form n4 + 1" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form n4 + 1.<a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a> <a href="/wiki/2" title="2">2</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/1297_(number)" class="mw-redirect" title="1297 (number)">1297</a>, <a href="/wiki/65537_(number)" class="mw-redirect" title="65537 (number)">65537</a>, 160001, 331777, 614657, 1336337, 4477457, 5308417, 8503057, 9834497, 29986577, 40960001, 45212177, 59969537, 65610001, 126247697, 193877777, 303595777, 384160001, 406586897, 562448657, 655360001 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A037896" class="extiw" title="oeis:A037896">A037896</a>) <div class="mw-heading mw-heading3"><h3 id="Primeval_primes"><a href="/wiki/Primeval_prime" class="mw-redirect" title="Primeval prime">Primeval primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=58" title="Edit section: Primeval primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes for which there are more prime permutations of some or all the decimal digits than for any smaller number. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/1013_(number)" class="mw-redirect" title="1013 (number)">1013</a>, <a href="/wiki/1237_(number)" class="mw-redirect" title="1237 (number)">1237</a>, <a href="/wiki/1367_(number)" class="mw-redirect" title="1367 (number)">1367</a>, 10079 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A119535" class="extiw" title="oeis:A119535">A119535</a>) <div class="mw-heading mw-heading3"><h3 id="Primorial_primes"><a href="/wiki/Primorial_prime" title="Primorial prime">Primorial primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=59" title="Edit section: Primorial primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form pn# ± 1. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/2309_(number)" class="mw-redirect" title="2309 (number)">2309</a>, <a href="/wiki/2311_(number)" class="mw-redirect" title="2311 (number)">2311</a>, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 (union of <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A057705" class="extiw" title="oeis:A057705">A057705</a> and <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A018239" class="extiw" title="oeis:A018239">A018239</a><a href="#cite_note-A018239-5">[5]</a>) <div class="mw-heading mw-heading3"><h3 id="Proth_primes"><a href="/wiki/Proth_number" class="mw-redirect" title="Proth number">Proth primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=60" title="Edit section: Proth primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form k×2n + 1, with odd k and k < 2n. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a>, <a href="/wiki/577_(number)" class="mw-redirect" title="577 (number)">577</a>, <a href="/wiki/641_(number)" class="mw-redirect" title="641 (number)">641</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, <a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a>, <a href="/wiki/1153_(number)" class="mw-redirect" title="1153 (number)">1153</a>, <a href="/wiki/1217_(number)" class="mw-redirect" title="1217 (number)">1217</a>, <a href="/wiki/1409_(number)" class="mw-redirect" title="1409 (number)">1409</a>, <a href="/wiki/1601_(number)" class="mw-redirect" title="1601 (number)">1601</a>, <a href="/wiki/2113_(number)" class="mw-redirect" title="2113 (number)">2113</a>, <a href="/wiki/2689_(number)" class="mw-redirect" title="2689 (number)">2689</a>, <a href="/wiki/2753_(number)" class="mw-redirect" title="2753 (number)">2753</a>, <a href="/wiki/3137_(number)" class="mw-redirect" title="3137 (number)">3137</a>, <a href="/wiki/3329_(number)" class="mw-redirect" title="3329 (number)">3329</a>, <a href="/wiki/3457_(number)" class="mw-redirect" title="3457 (number)">3457</a>, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A080076" class="extiw" title="oeis:A080076">A080076</a>) <div class="mw-heading mw-heading3"><h3 id="Pythagorean_primes"><a href="/wiki/Pythagorean_prime" title="Pythagorean prime">Pythagorean primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=61" title="Edit section: Pythagorean primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 4n + 1. <a href="/wiki/5" title="5">5</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/449_(number)" class="mw-redirect" title="449 (number)">449</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002144" class="extiw" title="oeis:A002144">A002144</a>) <div class="mw-heading mw-heading3"><h3 id="Prime_quadruplets"><a href="/wiki/Prime_quadruplet" title="Prime quadruplet">Prime quadruplets</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=62" title="Edit section: Prime quadruplets" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="#Cousin_primes">§ Cousin primes</a>, <a href="#Twin_primes">§ Twin primes</a>, and <a href="#Prime_triplets">§ Prime triplets</a></div> Where (p, p+2, p+6, p+8) are all prime. (<a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>), (11, 13, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>), (<a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>), (<a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>), (<a href="/wiki/821_(number)" class="mw-redirect" title="821 (number)">821</a>, <a href="/wiki/823_(number)" class="mw-redirect" title="823 (number)">823</a>, <a href="/wiki/827_(number)" class="mw-redirect" title="827 (number)">827</a>, <a href="/wiki/829_(number)" class="mw-redirect" title="829 (number)">829</a>), (<a href="/wiki/1481_(number)" class="mw-redirect" title="1481 (number)">1481</a>, <a href="/wiki/1483_(number)" class="mw-redirect" title="1483 (number)">1483</a>, <a href="/wiki/1487_(number)" class="mw-redirect" title="1487 (number)">1487</a>, <a href="/wiki/1489_(number)" class="mw-redirect" title="1489 (number)">1489</a>), (<a href="/wiki/1871_(number)" class="mw-redirect" title="1871 (number)">1871</a>, <a href="/wiki/1873_(number)" class="mw-redirect" title="1873 (number)">1873</a>, <a href="/wiki/1877_(number)" class="mw-redirect" title="1877 (number)">1877</a>, <a href="/wiki/1879_(number)" class="mw-redirect" title="1879 (number)">1879</a>), (<a href="/wiki/2081_(number)" class="mw-redirect" title="2081 (number)">2081</a>, <a href="/wiki/2083_(number)" class="mw-redirect" title="2083 (number)">2083</a>, <a href="/wiki/2087_(number)" class="mw-redirect" title="2087 (number)">2087</a>, <a href="/wiki/2089_(number)" class="mw-redirect" title="2089 (number)">2089</a>), (<a href="/wiki/3251_(number)" class="mw-redirect" title="3251 (number)">3251</a>, <a href="/wiki/3253_(number)" class="mw-redirect" title="3253 (number)">3253</a>, <a href="/wiki/3257_(number)" class="mw-redirect" title="3257 (number)">3257</a>, <a href="/wiki/3259_(number)" class="mw-redirect" title="3259 (number)">3259</a>), (<a href="/wiki/3461_(number)" class="mw-redirect" title="3461 (number)">3461</a>, <a href="/wiki/3463_(number)" class="mw-redirect" title="3463 (number)">3463</a>, <a href="/wiki/3467_(number)" class="mw-redirect" title="3467 (number)">3467</a>, <a href="/wiki/3469_(number)" class="mw-redirect" title="3469 (number)">3469</a>), (5651, 5653, 5657, 5659), (9431, 9433, 9437, 9439) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007530" class="extiw" title="oeis:A007530">A007530</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A136720" class="extiw" title="oeis:A136720">A136720</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A136721" class="extiw" title="oeis:A136721">A136721</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A090258" class="extiw" title="oeis:A090258">A090258</a>) <div class="mw-heading mw-heading3"><h3 id="Quartan_primes"><a href="/wiki/Quartan_prime" title="Quartan prime">Quartan primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=63" title="Edit section: Quartan primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form x4 + y4, where x,y > 0. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/641_(number)" class="mw-redirect" title="641 (number)">641</a>, <a href="/wiki/881_(number)" title="881 (number)">881</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002645" class="extiw" title="oeis:A002645">A002645</a>) <div class="mw-heading mw-heading3"><h3 id="Ramanujan_primes"><a href="/wiki/Ramanujan_prime" title="Ramanujan prime">Ramanujan primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=64" title="Edit section: Ramanujan primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Integers Rn that are the smallest to give at least n primes from x/2 to x for all x ≥ Rn (all such integers are primes). <a href="/wiki/2" title="2">2</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/409_(number)" class="mw-redirect" title="409 (number)">409</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>, <a href="/wiki/439_(number)" class="mw-redirect" title="439 (number)">439</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A104272" class="extiw" title="oeis:A104272">A104272</a>) <div class="mw-heading mw-heading3"><h3 id="Regular_primes"><a href="/wiki/Regular_prime" title="Regular prime">Regular primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=65" title="Edit section: Regular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p that do not divide the <a href="/wiki/Class_number_(number_theory)" class="mw-redirect" title="Class number (number theory)">class number</a> of the p-th <a href="/wiki/Cyclotomic_field" title="Cyclotomic field">cyclotomic field</a>. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007703" class="extiw" title="oeis:A007703">A007703</a>) <div class="mw-heading mw-heading3"><h3 id="Repunit_primes"><a href="/wiki/Repunit#Decimal_repunit_primes" title="Repunit">Repunit primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=66" title="Edit section: Repunit primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes containing only the decimal digit 1. <a href="/wiki/11_(number)" title="11 (number)">11</a>, 1111111111111111111 (19 digits), 11111111111111111111111 (23 digits) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A004022" class="extiw" title="oeis:A004022">A004022</a>) The next have 317, 1031, 49081, 86453, 109297, 270343 digits (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A004023" class="extiw" title="oeis:A004023">A004023</a>) <div class="mw-heading mw-heading3"><h3 id="Residue_classes_of_primes"><a href="/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions" title="Dirichlet's theorem on arithmetic progressions">Residue classes of primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=67" title="Edit section: Residue classes of primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form an + d for fixed integers a and d. Also called primes congruent to d <a href="/wiki/Modular_arithmetic" title="Modular arithmetic">modulo</a> a. The primes of the form 2n+1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4n+1 are Pythagorean primes, 4n+3 are the integer Gaussian primes, and 6n+5 are the Eisenstein primes (with 2 omitted). The classes 10n+d (d = 1, 3, 7, 9) are primes ending in the decimal digit d. 2n+1: <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A065091" class="extiw" title="oeis:A065091">A065091</a>) 4n+1: 5, 13, 17, 29, 37, 41, 53, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002144" class="extiw" title="oeis:A002144">A002144</a>) 4n+3: 3, 7, 11, 19, 23, 31, 43, 47, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002145" class="extiw" title="oeis:A002145">A002145</a>) 6n+1: 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002476" class="extiw" title="oeis:A002476">A002476</a>) 6n+5: 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007528" class="extiw" title="oeis:A007528">A007528</a>) 8n+1: 17, 41, 73, 89, 97, 113, 137, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/257_(number)" title="257 (number)">257</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007519" class="extiw" title="oeis:A007519">A007519</a>) 8n+3: 3, 11, 19, 43, 59, 67, 83, 107, <a href="/wiki/131_(number)" title="131 (number)">131</a>, 139, <a href="/wiki/163_(number)" title="163 (number)">163</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007520" class="extiw" title="oeis:A007520">A007520</a>) 8n+5: 5, 13, 29, 37, 53, 61, 101, 109, <a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>, <a href="/wiki/269_(number)" title="269 (number)">269</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007521" class="extiw" title="oeis:A007521">A007521</a>) 8n+7: 7, 23, 31, 47, 71, 79, 103, 127, <a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007522" class="extiw" title="oeis:A007522">A007522</a>) 10n+1: 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, <a href="/wiki/271_(number)" title="271 (number)">271</a>, 281 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A030430" class="extiw" title="oeis:A030430">A030430</a>) 10n+3: 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A030431" class="extiw" title="oeis:A030431">A030431</a>) 10n+7: 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, <a href="/wiki/277_(number)" title="277 (number)">277</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A030432" class="extiw" title="oeis:A030432">A030432</a>) 10n+9: 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A030433" class="extiw" title="oeis:A030433">A030433</a>) 12n+1: 13, 37, 61, 73, 97, 109, 157, 181, 193, 229, 241, 277, 313, 337, 349 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A068228" class="extiw" title="oeis:A068228">A068228</a>) 12n+5: 5, 17, 29, 41, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A040117" class="extiw" title="oeis:A040117">A040117</a>) 12n+7: 7, 19, 31, 43, 67, 79, 103, 127, 139, 151, 163, 199, 211, 223, 271 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A068229" class="extiw" title="oeis:A068229">A068229</a>) 12n+11: 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A068231" class="extiw" title="oeis:A068231">A068231</a>) <div class="mw-heading mw-heading3"><h3 id="Safe_primes"><a href="/wiki/Safe_prime" class="mw-redirect" title="Safe prime">Safe primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=68" title="Edit section: Safe primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Where p and (p−1) / 2 are both prime. <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/263_(number)" title="263 (number)">263</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a>, <a href="/wiki/503_(number)" class="mw-redirect" title="503 (number)">503</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a>, <a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/839_(number)" class="mw-redirect" title="839 (number)">839</a>, <a href="/wiki/863_(number)" class="mw-redirect" title="863 (number)">863</a>, <a href="/wiki/887_(number)" class="mw-redirect" title="887 (number)">887</a>, <a href="/wiki/983_(number)" class="mw-redirect" title="983 (number)">983</a>, <a href="/wiki/1019_(number)" class="mw-redirect" title="1019 (number)">1019</a>, <a href="/wiki/1187_(number)" class="mw-redirect" title="1187 (number)">1187</a>, <a href="/wiki/1283_(number)" class="mw-redirect" title="1283 (number)">1283</a>, <a href="/wiki/1307_(number)" class="mw-redirect" title="1307 (number)">1307</a>, <a href="/wiki/1319_(number)" class="mw-redirect" title="1319 (number)">1319</a>, <a href="/wiki/1367_(number)" class="mw-redirect" title="1367 (number)">1367</a>, <a href="/wiki/1439_(number)" class="mw-redirect" title="1439 (number)">1439</a>, <a href="/wiki/1487_(number)" class="mw-redirect" title="1487 (number)">1487</a>, <a href="/wiki/1523_(number)" class="mw-redirect" title="1523 (number)">1523</a>, <a href="/wiki/1619_(number)" class="mw-redirect" title="1619 (number)">1619</a>, <a href="/wiki/1823_(number)" class="mw-redirect" title="1823 (number)">1823</a>, <a href="/wiki/1907_(number)" class="mw-redirect" title="1907 (number)">1907</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A005385" class="extiw" title="oeis:A005385">A005385</a>) <div class="mw-heading mw-heading3"><h3 id="Self_primes_in_base_10"><a href="/wiki/Self_number" title="Self number">Self primes</a> in base 10</h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=69" title="Edit section: Self primes in base 10" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that cannot be generated by any integer added to the sum of its decimal digits. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/389_(number)" class="mw-redirect" title="389 (number)">389</a>, <a href="/wiki/457_(number)" class="mw-redirect" title="457 (number)">457</a>, <a href="/wiki/479_(number)" class="mw-redirect" title="479 (number)">479</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/569_(number)" class="mw-redirect" title="569 (number)">569</a>, <a href="/wiki/613_(number)" title="613 (number)">613</a>, <a href="/wiki/659_(number)" class="mw-redirect" title="659 (number)">659</a>, <a href="/wiki/727_(number)" class="mw-redirect" title="727 (number)">727</a>, <a href="/wiki/839_(number)" class="mw-redirect" title="839 (number)">839</a>, <a href="/wiki/883_(number)" class="mw-redirect" title="883 (number)">883</a>, <a href="/wiki/929_(number)" class="mw-redirect" title="929 (number)">929</a>, <a href="/wiki/1021_(number)" class="mw-redirect" title="1021 (number)">1021</a>, <a href="/wiki/1087_(number)" class="mw-redirect" title="1087 (number)">1087</a>, <a href="/wiki/1109_(number)" class="mw-redirect" title="1109 (number)">1109</a>, <a href="/wiki/1223_(number)" class="mw-redirect" title="1223 (number)">1223</a>, <a href="/wiki/1289_(number)" title="1289 (number)">1289</a>, <a href="/wiki/1447_(number)" class="mw-redirect" title="1447 (number)">1447</a>, <a href="/wiki/1559_(number)" class="mw-redirect" title="1559 (number)">1559</a>, <a href="/wiki/1627_(number)" class="mw-redirect" title="1627 (number)">1627</a>, <a href="/wiki/1693_(number)" class="mw-redirect" title="1693 (number)">1693</a>, <a href="/wiki/1783_(number)" class="mw-redirect" title="1783 (number)">1783</a>, <a href="/wiki/1873_(number)" class="mw-redirect" title="1873 (number)">1873</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A006378" class="extiw" title="oeis:A006378">A006378</a>) <div class="mw-heading mw-heading3"><h3 id="Sexy_primes"><a href="/wiki/Sexy_prime" title="Sexy prime">Sexy primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=70" title="Edit section: Sexy primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Where (p, p + 6) are both prime. (<a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>), (<a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>), (11, <a href="/wiki/17_(number)" title="17 (number)">17</a>), (13, <a href="/wiki/19_(number)" title="19 (number)">19</a>), (17, <a href="/wiki/23_(number)" title="23 (number)">23</a>), (23, <a href="/wiki/29_(number)" title="29 (number)">29</a>), (<a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>), (37, <a href="/wiki/43_(number)" title="43 (number)">43</a>), (<a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>), (47, <a href="/wiki/53_(number)" title="53 (number)">53</a>), (53, <a href="/wiki/59_(number)" title="59 (number)">59</a>), (<a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>), (67, <a href="/wiki/73_(number)" title="73 (number)">73</a>), (73, <a href="/wiki/79_(number)" title="79 (number)">79</a>), (<a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>), (<a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>), (<a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/107_(number)" title="107 (number)">107</a>), (103, <a href="/wiki/109_(number)" title="109 (number)">109</a>), (107, <a href="/wiki/113_(number)" title="113 (number)">113</a>), (<a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>), (<a href="/wiki/151_(number)" title="151 (number)">151</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>), (157, <a href="/wiki/163_(number)" title="163 (number)">163</a>), (<a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>), (173, <a href="/wiki/179_(number)" title="179 (number)">179</a>), (<a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>), (<a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A023201" class="extiw" title="oeis:A023201">A023201</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A046117" class="extiw" title="oeis:A046117">A046117</a>) <div class="mw-heading mw-heading3"><h3 id="Smarandache–Wellin_primes"><a href="/wiki/Smarandache%E2%80%93Wellin_number" title="Smarandache–Wellin number">Smarandache–Wellin primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=71" title="Edit section: Smarandache–Wellin primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that are the concatenation of the first n primes written in decimal. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/2357_(number)" class="mw-redirect" title="2357 (number)">2357</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A069151" class="extiw" title="oeis:A069151">A069151</a>) The fourth Smarandache-Wellin prime is the 355-digit concatenation of the first 128 primes that end with 719. <div class="mw-heading mw-heading3"><h3 id="Solinas_primes"><a href="/wiki/Solinas_prime" title="Solinas prime">Solinas primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=72" title="Edit section: Solinas primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 2a ± 2b ± 1, where 0 < b < a. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A165255" class="extiw" title="oeis:A165255">A165255</a>) <div class="mw-heading mw-heading3"><h3 id="Sophie_Germain_primes"><a href="/wiki/Sophie_Germain_prime" class="mw-redirect" title="Sophie Germain prime">Sophie Germain primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=73" title="Edit section: Sophie Germain primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Where p and 2p + 1 are both prime. A Sophie Germain prime has a corresponding <a href="#Safe_primes">safe prime</a>. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/89_(number)" title="89 (number)">89</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/131_(number)" title="131 (number)">131</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/251_(number)" title="251 (number)">251</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/359_(number)" title="359 (number)">359</a>, <a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a>, <a href="/wiki/491_(number)" class="mw-redirect" title="491 (number)">491</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a>, <a href="/wiki/641_(number)" class="mw-redirect" title="641 (number)">641</a>, <a href="/wiki/653_(number)" class="mw-redirect" title="653 (number)">653</a>, <a href="/wiki/659_(number)" class="mw-redirect" title="659 (number)">659</a>, <a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/743_(number)" title="743 (number)">743</a>, <a href="/wiki/761_(number)" class="mw-redirect" title="761 (number)">761</a>, <a href="/wiki/809_(number)" class="mw-redirect" title="809 (number)">809</a>, <a href="/wiki/911_(number)" title="911 (number)">911</a>, <a href="/wiki/953_(number)" class="mw-redirect" title="953 (number)">953</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A005384" class="extiw" title="oeis:A005384">A005384</a>) <div class="mw-heading mw-heading3"><h3 id="Stern_primes"><a href="/wiki/Stern_prime" title="Stern prime">Stern primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=74" title="Edit section: Stern primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that are not the sum of a smaller prime and twice the square of a nonzero integer. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/977_(number)" class="mw-redirect" title="977 (number)">977</a>, <a href="/wiki/1187_(number)" class="mw-redirect" title="1187 (number)">1187</a>, <a href="/wiki/1493_(number)" class="mw-redirect" title="1493 (number)">1493</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A042978" class="extiw" title="oeis:A042978">A042978</a>) As of 2011<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, these are the only known Stern primes, and possibly the only existing. <div class="mw-heading mw-heading3"><h3 id="Super-primes"><a href="/wiki/Super-prime" title="Super-prime">Super-primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=75" title="Edit section: Super-primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes with prime-numbered indexes in the sequence of prime numbers (the 2nd, 3rd, 5th, ... prime). <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/157_(number)" title="157 (number)">157</a>, <a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/211_(number)" title="211 (number)">211</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>, <a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/401_(number)" class="mw-redirect" title="401 (number)">401</a>, <a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/509_(number)" class="mw-redirect" title="509 (number)">509</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a>, <a href="/wiki/587_(number)" class="mw-redirect" title="587 (number)">587</a>, <a href="/wiki/599_(number)" class="mw-redirect" title="599 (number)">599</a>, <a href="/wiki/617_(number)" class="mw-redirect" title="617 (number)">617</a>, <a href="/wiki/709_(number)" class="mw-redirect" title="709 (number)">709</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/773_(number)" class="mw-redirect" title="773 (number)">773</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/859_(number)" class="mw-redirect" title="859 (number)">859</a>, <a href="/wiki/877_(number)" class="mw-redirect" title="877 (number)">877</a>, <a href="/wiki/919_(number)" class="mw-redirect" title="919 (number)">919</a>, <a href="/wiki/967_(number)" class="mw-redirect" title="967 (number)">967</a>, <a href="/wiki/991_(number)" class="mw-redirect" title="991 (number)">991</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A006450" class="extiw" title="oeis:A006450">A006450</a>) <div class="mw-heading mw-heading3"><h3 id="Supersingular_primes"><a href="/wiki/Supersingular_prime_(moonshine_theory)" title="Supersingular prime (moonshine theory)">Supersingular primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=76" title="Edit section: Supersingular primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> There are exactly fifteen supersingular primes: <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A002267" class="extiw" title="oeis:A002267">A002267</a>) <div class="mw-heading mw-heading3"><h3 id="Thabit_primes"><a href="/wiki/Thabit_prime" class="mw-redirect" title="Thabit prime">Thabit primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=77" title="Edit section: Thabit primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form 3×2n − 1. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007505" class="extiw" title="oeis:A007505">A007505</a>) The primes of the form 3×2n + 1 are related. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/769_(number)" class="mw-redirect" title="769 (number)">769</a>, 12289, 786433, 3221225473, 206158430209, 6597069766657 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A039687" class="extiw" title="oeis:A039687">A039687</a>) <div class="mw-heading mw-heading3"><h3 id="Prime_triplets"><a href="/wiki/Prime_triplet" title="Prime triplet">Prime triplets</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=78" title="Edit section: Prime triplets" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="#Cousin_primes">§ Cousin primes</a>, <a href="#Twin_primes">§ Twin primes</a>, and <a href="#Prime_quadruplets">§ Prime quadruplets</a></div> Where (p, p+2, p+6) or (p, p+4, p+6) are all prime. (<a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>), (7, 11, <a href="/wiki/13_(number)" title="13 (number)">13</a>), (11, 13, <a href="/wiki/17_(number)" title="17 (number)">17</a>), (13, 17, <a href="/wiki/19_(number)" title="19 (number)">19</a>), (17, 19, <a href="/wiki/23_(number)" title="23 (number)">23</a>), (<a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>), (41, 43, <a href="/wiki/47_(number)" title="47 (number)">47</a>), (<a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>), (<a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>), (101, 103, <a href="/wiki/107_(number)" title="107 (number)">107</a>), (103, 107, <a href="/wiki/109_(number)" title="109 (number)">109</a>), (107, 109, <a href="/wiki/113_(number)" title="113 (number)">113</a>), (<a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>), (193, 197, <a href="/wiki/199_(number)" title="199 (number)">199</a>), (<a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>), (227, 229, <a href="/wiki/233_(number)" title="233 (number)">233</a>), (<a href="/wiki/277_(number)" title="277 (number)">277</a>, <a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>), (<a href="/wiki/307_(number)" title="307 (number)">307</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>), (311, 313, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>), (<a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007529" class="extiw" title="oeis:A007529">A007529</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A098414" class="extiw" title="oeis:A098414">A098414</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A098415" class="extiw" title="oeis:A098415">A098415</a>) <div class="mw-heading mw-heading3"><h3 id="Truncatable_prime"><a href="/wiki/Truncatable_prime" title="Truncatable prime">Truncatable prime</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=79" title="Edit section: Truncatable prime" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <div class="mw-heading mw-heading4"><h4 id="Left-truncatable">Left-truncatable</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=80" title="Edit section: Left-truncatable" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that remain prime when the leading decimal digit is successively removed. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/47_(number)" title="47 (number)">47</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/67_(number)" title="67 (number)">67</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/83_(number)" title="83 (number)">83</a>, <a href="/wiki/97_(number)" title="97 (number)">97</a>, <a href="/wiki/113_(number)" title="113 (number)">113</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/173_(number)" title="173 (number)">173</a>, <a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/223_(number)" title="223 (number)">223</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, <a href="/wiki/367_(number)" class="mw-redirect" title="367 (number)">367</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, <a href="/wiki/397_(number)" class="mw-redirect" title="397 (number)">397</a>, <a href="/wiki/443_(number)" class="mw-redirect" title="443 (number)">443</a>, <a href="/wiki/467_(number)" class="mw-redirect" title="467 (number)">467</a>, <a href="/wiki/523_(number)" class="mw-redirect" title="523 (number)">523</a>, <a href="/wiki/547_(number)" class="mw-redirect" title="547 (number)">547</a>, <a href="/wiki/613_(number)" title="613 (number)">613</a>, <a href="/wiki/617_(number)" class="mw-redirect" title="617 (number)">617</a>, <a href="/wiki/643_(number)" class="mw-redirect" title="643 (number)">643</a>, <a href="/wiki/647_(number)" class="mw-redirect" title="647 (number)">647</a>, <a href="/wiki/653_(number)" class="mw-redirect" title="653 (number)">653</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, <a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A024785" class="extiw" title="oeis:A024785">A024785</a>) <div class="mw-heading mw-heading4"><h4 id="Right-truncatable">Right-truncatable</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=81" title="Edit section: Right-truncatable" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that remain prime when the least significant decimal digit is successively removed. <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/233_(number)" title="233 (number)">233</a>, <a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/293_(number)" title="293 (number)">293</a>, <a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/379_(number)" class="mw-redirect" title="379 (number)">379</a>, <a href="/wiki/593_(number)" class="mw-redirect" title="593 (number)">593</a>, <a href="/wiki/599_(number)" class="mw-redirect" title="599 (number)">599</a>, <a href="/wiki/719_(number)" class="mw-redirect" title="719 (number)">719</a>, <a href="/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>, <a href="/wiki/739_(number)" class="mw-redirect" title="739 (number)">739</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/2333_(number)" class="mw-redirect" title="2333 (number)">2333</a>, <a href="/wiki/2339_(number)" class="mw-redirect" title="2339 (number)">2339</a>, <a href="/wiki/2393_(number)" class="mw-redirect" title="2393 (number)">2393</a>, <a href="/wiki/2399_(number)" class="mw-redirect" title="2399 (number)">2399</a>, <a href="/wiki/2939_(number)" class="mw-redirect" title="2939 (number)">2939</a>, <a href="/wiki/3119_(number)" class="mw-redirect" title="3119 (number)">3119</a>, <a href="/wiki/3137_(number)" class="mw-redirect" title="3137 (number)">3137</a>, <a href="/wiki/3733_(number)" class="mw-redirect" title="3733 (number)">3733</a>, <a href="/wiki/3739_(number)" class="mw-redirect" title="3739 (number)">3739</a>, <a href="/wiki/3793_(number)" class="mw-redirect" title="3793 (number)">3793</a>, <a href="/wiki/3797_(number)" class="mw-redirect" title="3797 (number)">3797</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A024770" class="extiw" title="oeis:A024770">A024770</a>) <div class="mw-heading mw-heading4"><h4 id="Two-sided">Two-sided</h4> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=82" title="Edit section: Two-sided" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes that are both left-truncatable and right-truncatable. There are exactly fifteen two-sided primes: <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/53_(number)" title="53 (number)">53</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/317_(number)" class="mw-redirect" title="317 (number)">317</a>, <a href="/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, <a href="/wiki/797_(number)" class="mw-redirect" title="797 (number)">797</a>, <a href="/wiki/3137_(number)" class="mw-redirect" title="3137 (number)">3137</a>, <a href="/wiki/3797_(number)" class="mw-redirect" title="3797 (number)">3797</a>, 739397 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A020994" class="extiw" title="oeis:A020994">A020994</a>) <div class="mw-heading mw-heading3"><h3 id="Twin_primes"><a href="/wiki/Twin_prime" title="Twin prime">Twin primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=83" title="Edit section: Twin primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="#Cousin_primes">§ Cousin primes</a>, <a href="#Prime_triplets">§ Prime triplets</a>, and <a href="#Prime_quadruplets">§ Prime quadruplets</a></div> Where (p, p+2) are both prime. (<a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>), (5, <a href="/wiki/7" title="7">7</a>), (<a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>), (<a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>), (<a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>), (<a href="/wiki/41_(number)" title="41 (number)">41</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>), (<a href="/wiki/59_(number)" title="59 (number)">59</a>, <a href="/wiki/61_(number)" title="61 (number)">61</a>), (<a href="/wiki/71_(number)" title="71 (number)">71</a>, <a href="/wiki/73_(number)" title="73 (number)">73</a>), (<a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/103_(number)" title="103 (number)">103</a>), (<a href="/wiki/107_(number)" title="107 (number)">107</a>, <a href="/wiki/109_(number)" title="109 (number)">109</a>), (<a href="/wiki/137_(number)" title="137 (number)">137</a>, <a href="/wiki/139_(number)" title="139 (number)">139</a>), (<a href="/wiki/149_(number)" title="149 (number)">149</a>, <a href="/wiki/151_(number)" title="151 (number)">151</a>), (<a href="/wiki/179_(number)" title="179 (number)">179</a>, <a href="/wiki/181_(number)" title="181 (number)">181</a>), (<a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/193_(number)" title="193 (number)">193</a>), (<a href="/wiki/197_(number)" title="197 (number)">197</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>), (<a href="/wiki/227_(number)" title="227 (number)">227</a>, <a href="/wiki/229_(number)" title="229 (number)">229</a>), (<a href="/wiki/239_(number)" title="239 (number)">239</a>, <a href="/wiki/241_(number)" title="241 (number)">241</a>), (<a href="/wiki/269_(number)" title="269 (number)">269</a>, <a href="/wiki/271_(number)" title="271 (number)">271</a>), (<a href="/wiki/281_(number)" title="281 (number)">281</a>, <a href="/wiki/283_(number)" title="283 (number)">283</a>), (<a href="/wiki/311_(number)" title="311 (number)">311</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>), (<a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/349_(number)" class="mw-redirect" title="349 (number)">349</a>), (<a href="/wiki/419_(number)" class="mw-redirect" title="419 (number)">419</a>, <a href="/wiki/421_(number)" class="mw-redirect" title="421 (number)">421</a>), (<a href="/wiki/431_(number)" class="mw-redirect" title="431 (number)">431</a>, <a href="/wiki/433_(number)" class="mw-redirect" title="433 (number)">433</a>), (<a href="/wiki/461_(number)" class="mw-redirect" title="461 (number)">461</a>, <a href="/wiki/463_(number)" class="mw-redirect" title="463 (number)">463</a>) (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A001359" class="extiw" title="oeis:A001359">A001359</a>, <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A006512" class="extiw" title="oeis:A006512">A006512</a>) <div class="mw-heading mw-heading3"><h3 id="Unique_primes"><a href="/wiki/Unique_prime" class="mw-redirect" title="Unique prime">Unique primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=84" title="Edit section: Unique primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> The list of primes p for which the <a href="/wiki/Period_length" class="mw-redirect" title="Period length">period length</a> of the decimal expansion of 1/p is unique (no other prime gives the same period). <a href="/wiki/3" title="3">3</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A040017" class="extiw" title="oeis:A040017">A040017</a>) <div class="mw-heading mw-heading3"><h3 id="Wagstaff_primes"><a href="/wiki/Wagstaff_prime" title="Wagstaff prime">Wagstaff primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=85" title="Edit section: Wagstaff primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form (2n + 1) / 3. <a href="/wiki/3" title="3">3</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/683_(number)" class="mw-redirect" title="683 (number)">683</a>, <a href="/wiki/2731_(number)" class="mw-redirect" title="2731 (number)">2731</a>, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000979" class="extiw" title="oeis:A000979">A000979</a>) Values of n: 3, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, 11, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/17_(number)" title="17 (number)">17</a>, <a href="/wiki/19_(number)" title="19 (number)">19</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/31_(number)" title="31 (number)">31</a>, 43, <a href="/wiki/61_(number)" title="61 (number)">61</a>, <a href="/wiki/79_(number)" title="79 (number)">79</a>, <a href="/wiki/101_(number)" title="101 (number)">101</a>, <a href="/wiki/127_(number)" title="127 (number)">127</a>, <a href="/wiki/167_(number)" title="167 (number)">167</a>, <a href="/wiki/191_(number)" title="191 (number)">191</a>, <a href="/wiki/199_(number)" title="199 (number)">199</a>, <a href="/wiki/313_(number)" title="313 (number)">313</a>, <a href="/wiki/347_(number)" class="mw-redirect" title="347 (number)">347</a>, <a href="/wiki/701_(number)" class="mw-redirect" title="701 (number)">701</a>, <a href="/wiki/1709_(number)" class="mw-redirect" title="1709 (number)">1709</a>, <a href="/wiki/2617_(number)" class="mw-redirect" title="2617 (number)">2617</a>, <a href="/wiki/3539_(number)" class="mw-redirect" title="3539 (number)">3539</a>, <a href="/wiki/5807_(number)" class="mw-redirect" title="5807 (number)">5807</a>, <a href="/wiki/10501_(number)" class="mw-redirect" title="10501 (number)">10501</a>, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A000978" class="extiw" title="oeis:A000978">A000978</a>) <div class="mw-heading mw-heading3"><h3 id="Wall–Sun–Sun_primes"><a href="/wiki/Wall%E2%80%93Sun%E2%80%93Sun_prime" title="Wall–Sun–Sun prime">Wall–Sun–Sun primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=86" title="Edit section: Wall–Sun–Sun primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A prime p > 5, if p2 divides the <a href="/wiki/Fibonacci_number" class="mw-redirect" title="Fibonacci number">Fibonacci number</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F_{p-\left({\frac {p}{5}}\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mn>5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{p-\left({\frac {p}{5}}\right)}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/966c07b341b72613573a8e208730e595c5368ef0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.302ex; height:4.176ex;" alt="{\displaystyle F_{p-\left({\frac {p}{5}}\right)}}"></noscript><span class="lazy-image-placeholder" style="width: 7.302ex;height: 4.176ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/966c07b341b72613573a8e208730e595c5368ef0" data-alt="{\displaystyle F_{p-\left({\frac {p}{5}}\right)}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , where the <a href="/wiki/Legendre_symbol" title="Legendre symbol">Legendre symbol</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {p}{5}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mn>5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {p}{5}}\right)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe8e481a09e455d04b82d1d7dfddd04c6193d38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.781ex; height:4.843ex;" alt="{\displaystyle \left({\frac {p}{5}}\right)}"></noscript><span class="lazy-image-placeholder" style="width: 4.781ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe8e481a09e455d04b82d1d7dfddd04c6193d38" data-alt="{\displaystyle \left({\frac {p}{5}}\right)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is defined as <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {p}{5}}\right)={\begin{cases}1&{\textrm {if}}\;p\equiv \pm 1{\pmod {5}}\\-1&{\textrm {if}}\;p\equiv \pm 2{\pmod {5}}.\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mn>5</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>if</mtext> </mrow> </mrow> <mspace width="thickmathspace"></mspace> <mi>p</mi> <mo>≡</mo> <mo>±</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0.444em"></mspace> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em"></mspace> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mn>1</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>if</mtext> </mrow> </mrow> <mspace width="thickmathspace"></mspace> <mi>p</mi> <mo>≡</mo> <mo>±</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0.444em"></mspace> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em"></mspace> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {p}{5}}\right)={\begin{cases}1&{\textrm {if}}\;p\equiv \pm 1{\pmod {5}}\\-1&{\textrm {if}}\;p\equiv \pm 2{\pmod {5}}.\end{cases}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29ec64c65cf6c164aa6a4d1860543e95a45a9171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.113ex; height:6.176ex;" alt="{\displaystyle \left({\frac {p}{5}}\right)={\begin{cases}1&{\textrm {if}}\;p\equiv \pm 1{\pmod {5}}\\-1&{\textrm {if}}\;p\equiv \pm 2{\pmod {5}}.\end{cases}}}"></noscript><span class="lazy-image-placeholder" style="width: 35.113ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29ec64c65cf6c164aa6a4d1860543e95a45a9171" data-alt="{\displaystyle \left({\frac {p}{5}}\right)={\begin{cases}1&{\textrm {if}}\;p\equiv \pm 1{\pmod {5}}\\-1&{\textrm {if}}\;p\equiv \pm 2{\pmod {5}}.\end{cases}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> As of 2018<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, no Wall-Sun-Sun primes are known. <div class="mw-heading mw-heading3"><h3 id="Wieferich_primes"><a href="/wiki/Wieferich_prime" title="Wieferich prime">Wieferich primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=87" title="Edit section: Wieferich primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p such that ap − 1 ≡ 1 (mod p2) for fixed integer a > 1. 2p − 1 ≡ 1 (mod p2): <a href="/wiki/1093_(number)" title="1093 (number)">1093</a>, <a href="/wiki/3511_(number)" class="mw-redirect" title="3511 (number)">3511</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A001220" class="extiw" title="oeis:A001220">A001220</a>) 3p − 1 ≡ 1 (mod p2): <a href="/wiki/11_(number)" title="11 (number)">11</a>, 1006003 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A014127" class="extiw" title="oeis:A014127">A014127</a>)<a href="#cite_note-17">[17]</a><a href="#cite_note-18">[18]</a><a href="#cite_note-19">[19]</a> 4p − 1 ≡ 1 (mod p2): <a href="/wiki/1093_(number)" title="1093 (number)">1093</a>, <a href="/wiki/3511_(number)" class="mw-redirect" title="3511 (number)">3511</a> 5p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a>, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A123692" class="extiw" title="oeis:A123692">A123692</a>) 6p − 1 ≡ 1 (mod p2): 66161, 534851, 3152573 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A212583" class="extiw" title="oeis:A212583">A212583</a>) 7p − 1 ≡ 1 (mod p2): <a href="/wiki/5" title="5">5</a>, 491531 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A123693" class="extiw" title="oeis:A123693">A123693</a>) 8p − 1 ≡ 1 (mod p2): <a href="/wiki/3" title="3">3</a>, <a href="/wiki/1093_(number)" title="1093 (number)">1093</a>, <a href="/wiki/3511_(number)" class="mw-redirect" title="3511 (number)">3511</a> 9p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a>, <a href="/wiki/11_(number)" title="11 (number)">11</a>, 1006003 10p − 1 ≡ 1 (mod p2): <a href="/wiki/3" title="3">3</a>, <a href="/wiki/487_(number)" class="mw-redirect" title="487 (number)">487</a>, 56598313 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A045616" class="extiw" title="oeis:A045616">A045616</a>) 11p − 1 ≡ 1 (mod p2): <a href="/wiki/71_(number)" title="71 (number)">71</a><a href="#cite_note-RibenboimWelt-20">[20]</a> 12p − 1 ≡ 1 (mod p2): <a href="/wiki/2693_(number)" class="mw-redirect" title="2693 (number)">2693</a>, 123653 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A111027" class="extiw" title="oeis:A111027">A111027</a>) 13p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a>, <a href="/wiki/863_(number)" class="mw-redirect" title="863 (number)">863</a>, 1747591 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A128667" class="extiw" title="oeis:A128667">A128667</a>)<a href="#cite_note-RibenboimWelt-20">[20]</a> 14p − 1 ≡ 1 (mod p2): <a href="/wiki/29_(number)" title="29 (number)">29</a>, <a href="/wiki/353_(number)" title="353 (number)">353</a>, 7596952219 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A234810" class="extiw" title="oeis:A234810">A234810</a>) 15p − 1 ≡ 1 (mod p2): 29131, 119327070011 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A242741" class="extiw" title="oeis:A242741">A242741</a>) 16p − 1 ≡ 1 (mod p2): <a href="/wiki/1093_(number)" title="1093 (number)">1093</a>, <a href="/wiki/3511_(number)" class="mw-redirect" title="3511 (number)">3511</a> 17p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, 46021, 48947 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A128668" class="extiw" title="oeis:A128668">A128668</a>)<a href="#cite_note-RibenboimWelt-20">[20]</a> 18p − 1 ≡ 1 (mod p2): <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/37_(number)" title="37 (number)">37</a>, <a href="/wiki/331_(number)" class="mw-redirect" title="331 (number)">331</a>, 33923, 1284043 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A244260" class="extiw" title="oeis:A244260">A244260</a>) 19p − 1 ≡ 1 (mod p2): <a href="/wiki/3" title="3">3</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/43_(number)" title="43 (number)">43</a>, <a href="/wiki/137_(number)" title="137 (number)">137</a>, 63061489 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A090968" class="extiw" title="oeis:A090968">A090968</a>)<a href="#cite_note-RibenboimWelt-20">[20]</a> 20p − 1 ≡ 1 (mod p2): <a href="/wiki/281_(number)" title="281 (number)">281</a>, 46457, 9377747, 122959073 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A242982" class="extiw" title="oeis:A242982">A242982</a>) 21p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a> 22p − 1 ≡ 1 (mod p2): <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/673_(number)" class="mw-redirect" title="673 (number)">673</a>, 1595813, 492366587, 9809862296159 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A298951" class="extiw" title="oeis:A298951">A298951</a>) 23p − 1 ≡ 1 (mod p2): <a href="/wiki/13_(number)" title="13 (number)">13</a>, 2481757, 13703077, 15546404183, 2549536629329 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A128669" class="extiw" title="oeis:A128669">A128669</a>) 24p − 1 ≡ 1 (mod p2): <a href="/wiki/5" title="5">5</a>, 25633 25p − 1 ≡ 1 (mod p2): <a href="/wiki/2" title="2">2</a>, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 As of 2018<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, these are all known Wieferich primes with a ≤ 25. <div class="mw-heading mw-heading3"><h3 id="Wilson_primes"><a href="/wiki/Wilson_prime" title="Wilson prime">Wilson primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=88" title="Edit section: Wilson primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which p2 divides (p−1)! + 1. <a href="/wiki/5" title="5">5</a>, <a href="/wiki/13_(number)" title="13 (number)">13</a>, <a href="/wiki/563_(number)" class="mw-redirect" title="563 (number)">563</a> (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A007540" class="extiw" title="oeis:A007540">A007540</a>) As of 2018<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, these are the only known Wilson primes. <div class="mw-heading mw-heading3"><h3 id="Wolstenholme_primes"><a href="/wiki/Wolstenholme_prime" title="Wolstenholme prime">Wolstenholme primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=89" title="Edit section: Wolstenholme primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Primes p for which the <a href="/wiki/Binomial_coefficient" title="Binomial coefficient">binomial coefficient</a> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mo>≡</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em"></mspace> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em"></mspace> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2511f4d35103fd2b8d9128de1494539626a465ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.571ex; height:6.176ex;" alt="{\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}"></noscript><span class="lazy-image-placeholder" style="width: 26.571ex;height: 6.176ex;vertical-align: -2.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2511f4d35103fd2b8d9128de1494539626a465ef" data-alt="{\displaystyle {{2p-1} \choose {p-1}}\equiv 1{\pmod {p^{4}}}.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  <a href="/wiki/16843_(number)" class="mw-redirect" title="16843 (number)">16843</a>, 2124679 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A088164" class="extiw" title="oeis:A088164">A088164</a>) As of 2018<a class="external text" href="https://en.wikipedia.org/w/index.php?title=List_of_prime_numbers&action=edit">[update]</a>, these are the only known Wolstenholme primes. <div class="mw-heading mw-heading3"><h3 id="Woodall_primes"><a href="/wiki/Woodall_number" title="Woodall number">Woodall primes</a></h3> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=90" title="Edit section: Woodall primes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Of the form n×2n − 1. <a href="/wiki/7" title="7">7</a>, <a href="/wiki/23_(number)" title="23 (number)">23</a>, <a href="/wiki/383_(number)" class="mw-redirect" title="383 (number)">383</a>, 32212254719, 2833419889721787128217599, 195845982777569926302400511, 4776913109852041418248056622882488319 (<a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A050918" class="extiw" title="oeis:A050918">A050918</a>) </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="See_also">See also</h2> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=91" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><noscript><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" data-file-width="128" data-file-height="128"></noscript><span class="lazy-image-placeholder" style="width: 28px;height: 28px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" data-alt="icon" data-width="28" data-height="28" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-class="mw-file-element"> </a><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col div-col-small" style="column-width: 20em;"> <ul><li><a href="/wiki/Illegal_prime" class="mw-redirect" title="Illegal prime">Illegal prime</a> – Number representing illegal informationPages displaying short descriptions of redirect targets</li> <li><a href="/wiki/Largest_known_prime_number" title="Largest known prime number">Largest known prime number</a></li> <li><a href="/wiki/List_of_largest_known_primes_and_probable_primes" title="List of largest known primes and probable primes">List of largest known primes and probable primes</a></li> <li><a href="/wiki/List_of_numbers" title="List of numbers">List of numbers</a> – Notable numbers</li> <li><a href="/wiki/Prime_gap" title="Prime gap">Prime gap</a> – Difference between two successive prime numbers</li> <li><a href="/wiki/Prime_number_theorem" title="Prime number theorem">Prime number theorem</a> – Characterization of how many integers are prime</li> <li><a href="/wiki/Probable_prime" title="Probable prime">Probable prime</a> – Integers that satisfy a specific condition</li> <li><a href="/wiki/Pseudoprime" title="Pseudoprime">Pseudoprime</a> – Probable prime that is composite</li> <li><a href="/wiki/Strong_prime" title="Strong prime">Strong prime</a></li> <li><a href="/wiki/Table_of_prime_factors" title="Table of prime factors">Table of prime factors</a></li> <li><a href="/wiki/Wieferich_pair" title="Wieferich pair">Wieferich pair</a></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="References">References</h2> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=92" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFLehmer1982" class="citation book cs1"><a href="/wiki/Derrick_Norman_Lehmer" title="Derrick Norman Lehmer">Lehmer, D. N.</a> (1982). List of prime numbers from 1 to 10,006,721. Vol. 165. Washington D.C.: Carnegie Institution of Washington. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL16553580M">16553580M</a>. OL16553580M.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=List+of+prime+numbers+from+1+to+10%2C006%2C721&rft.place=Washington+D.C.&rft.pub=Carnegie+Institution+of+Washington&rft.date=1982&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL16553580M%23id-name%3DOL&rft.aulast=Lehmer&rft.aufirst=D.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> Tomás Oliveira e Silva, <a rel="nofollow" class="external text" href="http://www.ieeta.pt/~tos/goldbach.html">Goldbach conjecture verification</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110524084452/http://www.ieeta.pt/~tos/goldbach.html">Archived</a> 24 May 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Retrieved 16 July 2013 </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> (sequence <a href="//oeis.org/A080127" class="extiw" title="oeis:A080127">A080127</a> in the <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>) </li> <li id="cite_note-Franke-4"><a href="#cite_ref-Franke_4-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJens_Franke2010" class="citation web cs1">Jens Franke (29 July 2010). <a rel="nofollow" class="external text" href="http://primes.utm.edu/notes/pi(10%5E24).html">"Conditional Calculation of pi(1024)"</a>. <a rel="nofollow" class="external text" href="http://archive.wikiwix.com/cache/20140824032441/http://primes.utm.edu/notes/pi(10%5E24).html">Archived</a> from the original on 24 August 2014. Retrieved 17 May 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Conditional+Calculation+of+pi%2810%3Csup%3E24%3C%2Fsup%3E%29&rft.date=2010-07-29&rft.au=Jens+Franke&rft_id=http%3A%2F%2Fprimes.utm.edu%2Fnotes%2Fpi%2810%255E24%29.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-A018239-5">^ <a href="#cite_ref-A018239_5-0">a</a> <a href="#cite_ref-A018239_5-1">b</a> <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>: <a href="//oeis.org/A018239" class="extiw" title="oeis:A018239">A018239</a> includes 2 = <a href="/wiki/Empty_product" title="Empty product">empty product</a> of first 0 primes plus 1, but 2 is excluded in this list. </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoklanConway2016" class="citation arxiv cs1">Boklan, Kent D.; Conway, John H. (2016). "Expect at most one billionth of a new Fermat Prime!". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1605.01371">1605.01371</a> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/math.NT">math.NT</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Expect+at+most+one+billionth+of+a+new+Fermat+Prime%21&rft.date=2016&rft_id=info%3Aarxiv%2F1605.01371&rft.aulast=Boklan&rft.aufirst=Kent+D.&rft.au=Conway%2C+John+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyd1994" class="citation journal cs1">Boyd, D. W. (1994). <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.em/1048515811">"A p-adic Study of the Partial Sums of the Harmonic Series"</a>. <a href="/wiki/Experimental_Mathematics_(journal)" title="Experimental Mathematics (journal)">Experimental Mathematics</a>. 3 (4): 287–302. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F10586458.1994.10504298">10.1080/10586458.1994.10504298</a>. <a href="/wiki/Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:0838.11015">0838.11015</a>. <a href="/wiki/CiteSeerX" title="CiteSeerX">CiteSeerX</a>: <a rel="nofollow" class="external text" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.7026">10.1.1.56.7026</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160127080246/http://projecteuclid.org/euclid.em/1048515811">Archived</a> from the original on 27 January 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Experimental+Mathematics&rft.atitle=A+p-adic+Study+of+the+Partial+Sums+of+the+Harmonic+Series&rft.volume=3&rft.issue=4&rft.pages=287-302&rft.date=1994&rft_id=https%3A%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0838.11015%23id-name%3DZbl&rft_id=info%3Adoi%2F10.1080%2F10586458.1994.10504298&rft.aulast=Boyd&rft.aufirst=D.+W.&rft_id=http%3A%2F%2Fprojecteuclid.org%2Feuclid.em%2F1048515811&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-Johnson-8">^ <a href="#cite_ref-Johnson_8-0">a</a> <a href="#cite_ref-Johnson_8-1">b</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnson1975" class="citation journal cs1">Johnson, W. (1975). <a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2005468">"Irregular Primes and Cyclotomic Invariants"</a>. <a href="/wiki/Mathematics_of_Computation" title="Mathematics of Computation">Mathematics of Computation</a>. 29 (129). <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">AMS</a>: 113–120. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2005468">10.2307/2005468</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2005468">2005468</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+of+Computation&rft.atitle=Irregular+Primes+and+Cyclotomic+Invariants&rft.volume=29&rft.issue=129&rft.pages=113-120&rft.date=1975&rft_id=info%3Adoi%2F10.2307%2F2005468&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2005468%23id-name%3DJSTOR&rft.aulast=Johnson&rft.aufirst=W.&rft_id=https%3A%2F%2Fdoi.org%2F10.2307%252F2005468&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> It varies whether L0 = 2 is included in the Lucas numbers. </li> <li id="cite_note-10"><a href="#cite_ref-10">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id='CITEREFSloane_"A121091"' class="citation web cs1"><a href="/wiki/Neil_Sloane" title="Neil Sloane">Sloane, N. J. A.</a> (ed.). <a rel="nofollow" class="external text" href="https://oeis.org/A121091">"Sequence A121091 (Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime)"</a>. The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a>. OEIS Foundation.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+On-Line+Encyclopedia+of+Integer+Sequences&rft.atitle=Sequence%26%23x20%3BA121091%26%23x20%3B%28Smallest+nexus+prime+of+the+form+n%5Ep+-+%28n-1%29%5Ep%2C+where+p+is+an+odd+prime%29&rft_id=https%3A%2F%2Foeis.org%2FA121091&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-11"><a href="#cite_ref-11">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id='CITEREFSloane_"A121616"' class="citation web cs1"><a href="/wiki/Neil_Sloane" title="Neil Sloane">Sloane, N. J. A.</a> (ed.). <a rel="nofollow" class="external text" href="https://oeis.org/A121616">"Sequence A121616 (Primes of form (n+1)^5 - n^5)"</a>. The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a>. OEIS Foundation.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+On-Line+Encyclopedia+of+Integer+Sequences&rft.atitle=Sequence%26%23x20%3BA121616%26%23x20%3B%28Primes+of+form+%28n%2B1%29%5E5+-+n%5E5%29&rft_id=https%3A%2F%2Foeis.org%2FA121616&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id='CITEREFSloane_"A121618"' class="citation web cs1"><a href="/wiki/Neil_Sloane" title="Neil Sloane">Sloane, N. J. A.</a> (ed.). <a rel="nofollow" class="external text" href="https://oeis.org/A121618">"Sequence A121618 (Nexus primes of order 7 or primes of form n^7 - (n-1)^7)"</a>. The <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a>. OEIS Foundation.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+On-Line+Encyclopedia+of+Integer+Sequences&rft.atitle=Sequence%26%23x20%3BA121618%26%23x20%3B%28Nexus+primes+of+order+7+or+primes+of+form+n%5E7+-+%28n-1%29%5E7%29&rft_id=https%3A%2F%2Foeis.org%2FA121618&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-13"><a href="#cite_ref-13">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPaszkiewicz2009" class="citation journal cs1">Paszkiewicz, Andrzej (2009). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02090-5/S0025-5718-08-02090-5.pdf">"A new prime <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></noscript><span class="lazy-image-placeholder" style="width: 1.259ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" data-alt="{\displaystyle p}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  for which the least primitive root <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\textrm {mod}}p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>mod</mtext> </mrow> </mrow> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\textrm {mod}}p)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25e6d58c64c381a65c0282879fc728c3d974ea66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.37ex; height:2.843ex;" alt="{\displaystyle ({\textrm {mod}}p)}"></noscript><span class="lazy-image-placeholder" style="width: 7.37ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25e6d58c64c381a65c0282879fc728c3d974ea66" data-alt="{\displaystyle ({\textrm {mod}}p)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and the least primitive root <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({\textrm {mod}}p^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>mod</mtext> </mrow> </mrow> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\textrm {mod}}p^{2})}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d801b105a09e28a76fab50734c43c147f367e3a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.424ex; height:3.176ex;" alt="{\displaystyle ({\textrm {mod}}p^{2})}"></noscript><span class="lazy-image-placeholder" style="width: 8.424ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d801b105a09e28a76fab50734c43c147f367e3a5" data-alt="{\displaystyle ({\textrm {mod}}p^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  are not equal"</a> (PDF). Math. Comp. 78 (266). American Mathematical Society: 1193–1195. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009MaCom..78.1193P">2009MaCom..78.1193P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0025-5718-08-02090-5">10.1090/S0025-5718-08-02090-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Math.+Comp.&rft.atitle=A+new+prime+MATH+RENDER+ERROR+for+which+the+least+primitive+root+MATH+RENDER+ERROR+and+the+least+primitive+root+MATH+RENDER+ERROR+are+not+equal&rft.volume=78&rft.issue=266&rft.pages=1193-1195&rft.date=2009&rft_id=info%3Adoi%2F10.1090%2FS0025-5718-08-02090-5&rft_id=info%3Abibcode%2F2009MaCom..78.1193P&rft.aulast=Paszkiewicz&rft.aufirst=Andrzej&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fmcom%2F2009-78-266%2FS0025-5718-08-02090-5%2FS0025-5718-08-02090-5.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCaldwellDubner1996–97" class="citation journal cs1 cs1-prop-year-range-abbreviated"><a href="/wiki/Chris_Caldwell_(mathematician)" class="mw-redirect" title="Chris Caldwell (mathematician)">Caldwell, C.</a>; <a href="/wiki/Harvey_Dubner" title="Harvey Dubner">Dubner, H.</a> (1996–97). "The near repdigit primes <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{n-k-1}B_{1}A_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{n-k-1}B_{1}A_{k}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2de11a3a8c7548020e6ee41223d3afa233211448" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.847ex; height:2.509ex;" alt="{\displaystyle A_{n-k-1}B_{1}A_{k}}"></noscript><span class="lazy-image-placeholder" style="width: 12.847ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2de11a3a8c7548020e6ee41223d3afa233211448" data-alt="{\displaystyle A_{n-k-1}B_{1}A_{k}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , especially <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 9_{n-k-1}8_{1}9_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mn>9</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <msub> <mn>8</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mn>9</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 9_{n-k-1}8_{1}9_{k}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc41cf72d4a10aaec0c28e6e77d4967a68e4d5f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.084ex; height:2.509ex;" alt="{\displaystyle 9_{n-k-1}8_{1}9_{k}}"></noscript><span class="lazy-image-placeholder" style="width: 11.084ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc41cf72d4a10aaec0c28e6e77d4967a68e4d5f8" data-alt="{\displaystyle 9_{n-k-1}8_{1}9_{k}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> ". <a href="/wiki/Journal_of_Recreational_Mathematics" title="Journal of Recreational Mathematics">Journal of Recreational Mathematics</a>. 28 (1): 1–9.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Recreational+Mathematics&rft.atitle=The+near+repdigit+primes+MATH+RENDER+ERROR%2C+especially+MATH+RENDER+ERROR&rft.volume=28&rft.issue=1&rft.pages=1-9&rft.date=1996%2F1997&rft.aulast=Caldwell&rft.aufirst=C.&rft.au=Dubner%2C+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLal1967" class="citation journal cs1">Lal, M. 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Retrieved 26 January 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Mirimanoff%27s+Congruence%3A+Other+Congruences&rft_id=http%3A%2F%2Fwww.museumstuff.com%2Flearn%2Ftopics%2FMirimanoff%2527s_congruence%3A%3Asub%3A%3AOther_Congruences&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-19"><a href="#cite_ref-19">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGallotMoreeZudilin2011" class="citation journal cs1">Gallot, Y.; Moree, P.; Zudilin, W. (2011). <a rel="nofollow" class="external text" href="http://www.mpim-bonn.mpg.de/preprints/send?bid=4053">"The Erdös-Moser equation 1k + 2k +...+ (m−1)k = mk revisited using continued fractions"</a>. Mathematics of Computation. 80. American Mathematical Society: 1221–1237. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0907.1356">0907.1356</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0025-5718-2010-02439-1">10.1090/S0025-5718-2010-02439-1</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16305654">16305654</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+of+Computation&rft.atitle=The+Erd%C3%B6s-Moser+equation+1%3Csup%3Ek%3C%2Fsup%3E+%2B+2%3Csup%3Ek%3C%2Fsup%3E+%2B...%2B+%28m%E2%88%921%29%3Csup%3Ek%3C%2Fsup%3E+%3D+m%3Csup%3Ek%3C%2Fsup%3E+revisited+using+continued+fractions&rft.volume=80&rft.pages=1221-1237&rft.date=2011&rft_id=info%3Aarxiv%2F0907.1356&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16305654%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1090%2FS0025-5718-2010-02439-1&rft.aulast=Gallot&rft.aufirst=Y.&rft.au=Moree%2C+P.&rft.au=Zudilin%2C+W.&rft_id=http%3A%2F%2Fwww.mpim-bonn.mpg.de%2Fpreprints%2Fsend%3Fbid%3D4053&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> <li id="cite_note-RibenboimWelt-20">^ <a href="#cite_ref-RibenboimWelt_20-0">a</a> <a href="#cite_ref-RibenboimWelt_20-1">b</a> <a href="#cite_ref-RibenboimWelt_20-2">c</a> <a href="#cite_ref-RibenboimWelt_20-3">d</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRibenboim2006" class="citation book cs1"><a href="/wiki/Paulo_Ribenboim" title="Paulo Ribenboim">Ribenboim, P.</a> (2006). <a rel="nofollow" class="external text" href="https://www.gbv.de/dms/bs/toc/495799599.pdf">Die Welt der Primzahlen</a> (PDF). Berlin: Springer. p. 240. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-540-34283-4" title="Special:BookSources/3-540-34283-4"><bdi>3-540-34283-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Die+Welt+der+Primzahlen&rft.place=Berlin&rft.pages=240&rft.pub=Springer&rft.date=2006&rft.isbn=3-540-34283-4&rft.aulast=Ribenboim&rft.aufirst=P.&rft_id=https%3A%2F%2Fwww.gbv.de%2Fdms%2Fbs%2Ftoc%2F495799599.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"> </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="External_links">External links</h2> <a role="button" href="/w/index.php?title=List_of_prime_numbers&action=edit&section=93" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <ul><li><a rel="nofollow" class="external autonumber" href="https://prime-numbers.de">[1]</a> All prime numbers from 31 to 6,469,693,189 for free download.</li> <li><a rel="nofollow" class="external text" href="http://primes.utm.edu/lists/">Lists of Primes</a> at the Prime Pages.</li> <li><a rel="nofollow" class="external text" href="http://primes.utm.edu/nthprime/">The Nth Prime Page</a> Nth prime through n=10^12, pi(x) through x=3*10^13, Random primes in same range.</li> <li><a rel="nofollow" class="external text" href="http://www.rsok.com/~jrm/printprimes.html">Interface to a list of the first 98 million primes</a> (primes less than 2,000,000,000)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/topics/PrimeNumberSequences.html">"Prime Number Sequences"</a>. <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Prime+Number+Sequences&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2Ftopics%2FPrimeNumberSequences.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"></li> <li><a rel="nofollow" class="external text" href="http://oeis.org/wiki/Index_to_OEIS:_Section_Pri">Selected prime related sequences</a> in <a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">OEIS</a>.</li> <li>Fischer, R. <a rel="nofollow" class="external text" href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort.txt">Thema: Fermatquotient B^(P−1) == 1 (mod P^2)</a> (in German) (Lists Wieferich primes in all bases up to 1052)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1">Padilla, Tony (7 February 2013). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=QSEKzFGpCQs">"New Largest Known Prime Number"</a>. Numberphile. <a href="/wiki/Brady_Haran" title="Brady Haran">Brady Haran</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211102/QSEKzFGpCQs">Archived</a> from the original on 2 November 2021.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Numberphile&rft.atitle=New+Largest+Known+Prime+Number&rft.date=2013-02-07&rft.aulast=Padilla&rft.aufirst=Tony&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DQSEKzFGpCQs&rfr_id=info%3Asid%2Fen.wikipedia.org%3AList+of+prime+numbers" class="Z3988"></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output 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class="post-content last-modified-bar__content"> Last edited on 3 November 2024, at 00:08 </div> </a> <div class="post-content footer-content"> <div id='mw-data-after-content'> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Languages</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%A7%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF_%D8%A7%D9%84%D8%A3%D9%88%D9%84%D9%8A%D8%A9" title="قائمة الأعداد الأولية – Arabic" lang="ar" hreflang="ar" data-title="قائمة الأعداد الأولية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Lista_de_numeros_primers_de_l%271_dica_o_100000" title="Lista de numeros primers de l'1 dica o 100000 – Aragonese" lang="an" hreflang="an" data-title="Lista de numeros primers de l'1 dica o 100000" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target">Aragonés</a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Spisak_1000_prostih_brojeva" title="Spisak 1000 prostih brojeva – Bosnian" lang="bs" hreflang="bs" data-title="Spisak 1000 prostih brojeva" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target">Bosanski</a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Seznam_prvo%C4%8D%C3%ADsel" title="Seznam prvočísel – Czech" lang="cs" hreflang="cs" data-title="Seznam prvočísel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target">Čeština</a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhestr_rhifau_cysefin" title="Rhestr rhifau cysefin – Welsh" lang="cy" hreflang="cy" data-title="Rhestr rhifau cysefin" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target">Cymraeg</a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/El%C3%A8inc_ed_n%C3%B9mer_pr%C3%ACm" title="Elèinc ed nùmer prìm – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Elèinc ed nùmer prìm" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target">Emiliàn e rumagnòl</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Anexo:N%C3%BAmeros_primos" title="Anexo:Números primos – Spanish" lang="es" hreflang="es" data-title="Anexo:Números primos" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D9%87%D8%B1%D8%B3%D8%AA_%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF_%D8%A7%D9%88%D9%84" title="فهرست اعداد اول – Persian" lang="fa" hreflang="fa" data-title="فهرست اعداد اول" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Liste_de_nombres_premiers" title="Liste de nombres premiers – French" lang="fr" hreflang="fr" data-title="Liste de nombres premiers" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Lista_de_n%C3%BAmeros_primos" title="Lista de números primos – Galician" lang="gl" hreflang="gl" data-title="Lista de números primos" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%86%8C%EC%88%98_%EB%AA%A9%EB%A1%9D" title="소수 목록 – Korean" lang="ko" hreflang="ko" data-title="소수 목록" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%A1%D6%80%D5%A6_%D5%A9%D5%BE%D5%A5%D6%80%D5%AB_%D6%81%D5%A1%D5%B6%D5%AF" title="Պարզ թվերի ցանկ – Armenian" lang="hy" hreflang="hy" data-title="Պարզ թվերի ցանկ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Daftar_bilangan_prima" title="Daftar bilangan prima – Indonesian" lang="id" hreflang="id" data-title="Daftar bilangan prima" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Lista_di_numeri_primi" title="Lista di numeri primi – Italian" lang="it" hreflang="it" data-title="Lista di numeri primi" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pr%C3%ADmsz%C3%A1mok_list%C3%A1ja" title="Prímszámok listája – Hungarian" lang="hu" hreflang="hu" data-title="Prímszámok listája" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BD%D0%B0_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%B8_%D0%B1%D1%80%D0%BE%D0%B5%D0%B2%D0%B8" title="Список на прости броеви – Macedonian" lang="mk" hreflang="mk" data-title="Список на прости броеви" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lijst_van_priemgetallen" title="Lijst van priemgetallen – Dutch" lang="nl" hreflang="nl" data-title="Lijst van priemgetallen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B4%A0%E6%95%B0%E3%81%AE%E4%B8%80%E8%A6%A7" title="素数の一覧 – Japanese" lang="ja" hreflang="ja" data-title="素数の一覧" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Liste_over_primtal" title="Liste over primtal – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Liste over primtal" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tub_sonlar_ro%CA%BByxati" title="Tub sonlar roʻyxati – Uzbek" lang="uz" hreflang="uz" data-title="Tub sonlar roʻyxati" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target">Oʻzbekcha / ўзбекча</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Lista_de_n%C3%BAmeros_primos" title="Lista de números primos – Portuguese" lang="pt" hreflang="pt" data-title="Lista de números primos" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/List%C4%83_de_numere_prime" title="Listă de numere prime – Romanian" lang="ro" hreflang="ro" data-title="Listă de numere prime" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%8B%D1%85_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Список простых чисел – Russian" lang="ru" hreflang="ru" data-title="Список простых чисел" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/List_of_prime_numbers" title="List of prime numbers – Simple English" lang="en-simple" hreflang="en-simple" data-title="List of prime numbers" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Zoznam_prvo%C4%8D%C3%ADsel" title="Zoznam prvočísel – Slovak" lang="sk" hreflang="sk" data-title="Zoznam prvočísel" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%B0%D0%BA_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%B8%D1%85_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Списак простих бројева – Serbian" lang="sr" hreflang="sr" data-title="Списак простих бројева" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Lista_%C3%B6ver_primtal" title="Lista över primtal – Swedish" lang="sv" hreflang="sv" data-title="Lista över primtal" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%95%E0%AE%BE_%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%B3%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%AA%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="பகா எண்களின் பட்டியல் – Tamil" lang="ta" hreflang="ta" data-title="பகா எண்களின் பட்டியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B2%E0%B8%A2%E0%B8%8A%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="รายชื่อจำนวนเฉพาะ – Thai" lang="th" hreflang="th" data-title="รายชื่อจำนวนเฉพาะ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Asal_say%C4%B1lar%C4%B1n_listesi" title="Asal sayıların listesi – Turkish" lang="tr" hreflang="tr" data-title="Asal sayıların listesi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%B8%D1%85_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Список простих чисел – Ukrainian" lang="uk" hreflang="uk" data-title="Список простих чисел" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Danh_s%C3%A1ch_s%E1%BB%91_nguy%C3%AAn_t%E1%BB%91" title="Danh sách số nguyên tố – Vietnamese" lang="vi" hreflang="vi" data-title="Danh sách số nguyên tố" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target">Tiếng Việt</a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B3%AA%E6%95%B8%E5%88%97%E8%A1%A8" title="質數列表 – Chinese" lang="zh" hreflang="zh" data-title="質數列表" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target">中文</a></li></ul> </section> </div> <div class="minerva-footer-logo"><img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" 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