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title="2147483647 – Czech" lang="cs" hreflang="cs" data-title="2147483647" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/2147483647" title="2147483647 – German" lang="de" hreflang="de" data-title="2147483647" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/2.147.483.647" title="2.147.483.647 – Greek" lang="el" hreflang="el" data-title="2.147.483.647" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/2147483647" title="2147483647 – Spanish" lang="es" hreflang="es" data-title="2147483647" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/2_147_483_647_(nombre)" title="2 147 483 647 (nombre) – French" lang="fr" hreflang="fr" data-title="2 147 483 647 (nombre)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/2,147,483,647" title="2,147,483,647 – Korean" lang="ko" hreflang="ko" data-title="2,147,483,647" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/2147483647" title="2147483647 – Italian" lang="it" hreflang="it" data-title="2147483647" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/2,147,483,647" title="2,147,483,647 – Hebrew" lang="he" hreflang="he" data-title="2,147,483,647" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/2147483647" title="2147483647 – Lithuanian" lang="lt" hreflang="lt" data-title="2147483647" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/2147483647" title="2147483647 – Lombard" lang="lmo" hreflang="lmo" data-title="2147483647" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/2147483647" title="2147483647 – Hungarian" lang="hu" hreflang="hu" data-title="2147483647" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/2.147.483.647_(getal)" title="2.147.483.647 (getal) – Dutch" lang="nl" hreflang="nl" data-title="2.147.483.647 (getal)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/2147483647" title="2147483647 – Portuguese" lang="pt" hreflang="pt" data-title="2147483647" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/2_147_483_647_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="2 147 483 647 (число) – Russian" lang="ru" hreflang="ru" data-title="2 147 483 647 (число)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/2147483647" title="2147483647 – Simple English" lang="en-simple" hreflang="en-simple" data-title="2147483647" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/2_147_483_647" title="2 147 483 647 – Slovak" lang="sk" hreflang="sk" data-title="2 147 483 647" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/2147483647_(tal)" title="2147483647 (tal) – Swedish" lang="sv" hreflang="sv" data-title="2147483647 (tal)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/2147483647_(%D8%B9%D8%AF%D8%AF)" title="2147483647 (عدد) – Urdu" lang="ur" hreflang="ur" data-title="2147483647 (عدد)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/2147483647_(s%E1%BB%91)" title="2147483647 (số) – Vietnamese" lang="vi" hreflang="vi" data-title="2147483647 (số)" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/2147483647" title="2147483647 – Cantonese" lang="yue" hreflang="yue" data-title="2147483647" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/2147483647" title="2147483647 – Chinese" lang="zh" hreflang="zh" data-title="2147483647" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output 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ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><a href="/wiki/List_of_numbers" title="List of numbers">List of numbers</a></li><li><a href="/wiki/Integer" title="Integer">Integers</a></li></ul></div></div><div style="text-align:center;"><a href="/wiki/0" title="0">←</a> <a href="/wiki/1" title="1">10<sup>0</sup></a> <a href="/wiki/10" title="10">10<sup>1</sup></a> <a href="/wiki/100_(number)" class="mw-redirect" title="100 (number)">10<sup>2</sup></a> <a href="/wiki/1000_(number)" title="1000 (number)">10<sup>3</sup></a> <a href="/wiki/10000_(number)" class="mw-redirect" title="10000 (number)">10<sup>4</sup></a> <a href="/wiki/100,000" title="100,000">10<sup>5</sup></a> <a href="/wiki/1,000,000" title="1,000,000">10<sup>6</sup></a> <a href="/wiki/10,000,000" title="10,000,000">10<sup>7</sup></a> <a href="/wiki/100,000,000" title="100,000,000">10<sup>8</sup></a> <a href="/wiki/1,000,000,000" title="1,000,000,000">10<sup>9</sup></a></div></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Cardinal_numeral" title="Cardinal numeral">Cardinal</a></th><td class="infobox-data">two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Ordinal_numeral" title="Ordinal numeral">Ordinal</a></th><td class="infobox-data">2147483647th<br />(two billion one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seventh)</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Factorization" title="Factorization">Factorization</a></th><td class="infobox-data"><a href="/wiki/Prime_number" title="Prime number">prime</a></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Prime_number" title="Prime number">Prime</a></th><td class="infobox-data">105,097,565th</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Greek_numerals" title="Greek numerals">Greek numeral</a></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\stackrel {\kappa \alpha \delta \psi \mu \eta }{\mathrm {M} }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>κ</mi> <mi>α</mi> <mi>δ</mi> <mi>ψ</mi> <mi>μ</mi> <mi>η</mi> </mrow> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\stackrel {\kappa \alpha \delta \psi \mu \eta }{\mathrm {M} }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ea04359a076d8d7e7d4699a2bfedb2357bd446e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.628ex; height:4.176ex;" alt="{\displaystyle {\stackrel {\kappa \alpha \delta \psi \mu \eta }{\mathrm {M} }}}"></span>͵γχμζ´</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Roman_numerals" title="Roman numerals">Roman numeral</a></th><td class="infobox-data">N/A</td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Binary_number" title="Binary number">Binary</a></th><td class="infobox-data">1111111111111111111111111111111<sub>2</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">Ternary</a></th><td class="infobox-data">12112122212110202101<sub>3</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Senary" title="Senary">Senary</a></th><td class="infobox-data">553032005531<sub>6</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Octal" title="Octal">Octal</a></th><td class="infobox-data">17777777777<sub>8</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Duodecimal" title="Duodecimal">Duodecimal</a></th><td class="infobox-data">4BB2308A7<sub>12</sub></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal"><a href="/wiki/Hexadecimal" title="Hexadecimal">Hexadecimal</a></th><td class="infobox-data">7FFFFFFF<sub>16</sub></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Leonhard_Euler.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/170px-Leonhard_Euler.jpg" decoding="async" width="170" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/255px-Leonhard_Euler.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/340px-Leonhard_Euler.jpg 2x" data-file-width="4672" data-file-height="6040" /></a><figcaption>By 1772, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> had proven that 2,147,483,647 is a <a href="/wiki/Prime_number" title="Prime number">prime</a>.</figcaption></figure> <p>The <a href="/wiki/Number" title="Number">number</a> <b>2,147,483,647</b> is the eighth <a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne prime</a>, equal to 2<sup>31</sup> − 1. It is one of only four known <a href="/wiki/Double_Mersenne_number" title="Double Mersenne number">double Mersenne primes</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Primality_test" title="Primality test">primality</a> of this number was proven by <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, who reported the proof in a letter to <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a> written in 1772.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Euler used <a href="/wiki/Trial_division" title="Trial division">trial division</a>, improving on <a href="/wiki/Pietro_Cataldi" title="Pietro Cataldi">Pietro Cataldi</a>'s method, so that at most 372 divisions were needed.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the <a href="/wiki/Largest_known_prime" class="mw-redirect" title="Largest known prime">largest known prime</a> until 1867.<sup id="cite_ref-The_Largest_Known_Prime_by_Year_4-0" class="reference"><a href="#cite_note-The_Largest_Known_Prime_by_Year-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In computing, this number is the largest value that a <a href="/wiki/Signed_number" class="mw-redirect" title="Signed number">signed</a> <a href="/wiki/32-bit" class="mw-redirect" title="32-bit">32-bit</a> integer field can hold. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Barlow's_prediction"><span id="Barlow.27s_prediction"></span>Barlow's prediction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=2,147,483,647&action=edit&section=1" title="Edit section: Barlow's prediction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the time of its discovery, 2,147,483,647 was the <a href="/wiki/Largest_known_prime_number" title="Largest known prime number">largest known prime number</a>. In 1811, <a href="/wiki/Peter_Barlow_(mathematician)" title="Peter Barlow (mathematician)">Peter Barlow</a>, not anticipating future interest in <a href="/wiki/Perfect_number" title="Perfect number">perfect numbers</a>, wrote (in <i>An Elementary Investigation of the Theory of Numbers</i>): </p> <blockquote><p>Euler ascertained that 2<sup>31</sup> − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above <a href="/wiki/Perfect_number" title="Perfect number">perfect numbers</a> [i.e., 2<sup>30</sup>(2<sup>31</sup> − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one beyond it.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>He repeated this prediction in his work from 1814, <i>A New Mathematical and Philosophical Dictionary</i>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In fact, a larger prime was discovered in 1855 by <a href="/wiki/Thomas_Clausen_(mathematician)" title="Thomas Clausen (mathematician)">Thomas Clausen</a> (67,280,421,310,721), though a proof was not provided. Furthermore, 3,203,431,780,337 was proven to be prime in 1867.<sup id="cite_ref-The_Largest_Known_Prime_by_Year_4-1" class="reference"><a href="#cite_note-The_Largest_Known_Prime_by_Year-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_computing">In computing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=2,147,483,647&action=edit&section=2" title="Edit section: In computing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The number 2,147,483,647 (or <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> 7FFFFFFF<sub>16</sub>) is the maximum positive value for a <a href="/wiki/32-bit" class="mw-redirect" title="32-bit">32-bit</a> <a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">signed binary integer</a> in <a href="/wiki/Computing" title="Computing">computing</a>. It is therefore the maximum value for variables declared as integers (e.g., as <code>int</code>) in many programming languages. </p><p>The data type <a href="/wiki/Time_t" class="mw-redirect" title="Time t">time_t</a>, used on operating systems such as <a href="/wiki/Unix" title="Unix">Unix</a>, is a signed integer counting the number of seconds since the start of the <a href="/wiki/Unix_epoch" class="mw-redirect" title="Unix epoch">Unix epoch</a> (<a href="/wiki/Midnight" title="Midnight">midnight</a> <a href="/wiki/UTC" class="mw-redirect" title="UTC">UTC</a> of 1 January 1970), and is often implemented as a 32-bit integer.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The latest time that can be represented in this form is 03:14:07 UTC on Tuesday, 19 January 2038 (corresponding to 2,147,483,647 seconds since the start of the epoch). This means that systems using a 32-bit <code>time_t</code> type are susceptible to the <a href="/wiki/Year_2038_problem" title="Year 2038 problem">Year 2038 problem</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>On 1 January 2022, a bug was reported for <a href="/wiki/Microsoft_Exchange_Server" title="Microsoft Exchange Server">Microsoft Exchange</a> systems where email delivery would fail. An internal malware scanner (enabled by default since 2013) used the date and time as a signed 32-bit integer. The integer would change during the new year to 2,201,010,001 (with the first two digits representing the year), surpassing the maximum value for this data type.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="In_video_games">In video games</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=2,147,483,647&action=edit&section=3" title="Edit section: In video games"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The number 2,147,483,647 often becomes a hard limit for various statistics in video games, such as points or money, if they are represented by signed 32-bit integers (rather than <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating-point</a>, <a href="/wiki/Double-precision_floating-point_format" title="Double-precision floating-point format">double-precision</a> or <a href="/wiki/Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">arbitrary-precision</a>).<sup id="cite_ref-:0_11-0" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Going over this limit by legitimate means, or by modding or hacking the game, results in many different outcomes caused by <a href="/wiki/Integer_overflow" title="Integer overflow">integer overflow</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The most common outcome is the number "wrapping" into the negatives. Another potential outcome is <i>game crashing</i>, thus meaning there was no failsafe implemented in the event the value exceeds the signed 32-bit limit—generally if the underlying engine has undefined behavior, instead of a wraparound behavior, for integer overflow. A well-known example in video games is that of <i><a href="/wiki/Old_School_RuneScape" title="Old School RuneScape">Old School RuneScape</a> and <a href="/wiki/Grand_Theft_Auto_V" title="Grand Theft Auto V">Grand Theft Auto V</a>,</i> where the number is used as the maximum amount of coins (or any other item) that a player can hold at once with normal methods, known as a "max cash stack".<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In similar cases, where an <a href="/wiki/Unsigned_int" class="mw-redirect" title="Unsigned int">unsigned</a> instead of signed 32-bit integer is used, the limit might be extended to <a href="/wiki/4,294,967,295" title="4,294,967,295">4,294,967,295</a>.<sup id="cite_ref-:0_11-1" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Another well-known example is <i><a href="/wiki/Minecraft" title="Minecraft">Minecraft</a>'</i>s hard limit for travel. The game crashes when trying to travel beyond this point and the game renderer stops ~147 blocks past that point.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=2,147,483,647&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/DoubleMersenneNumber.html">"Double Mersenne Number"</a>. <i>MathWorld</i>. Wolfram Research<span class="reference-accessdate">. Retrieved <span class="nowrap">29 January</span> 2018</span>.</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=Double+Mersenne+Number&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FDoubleMersenneNumber.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunham1999" class="citation book cs1">Dunham, William (1999). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/eulermasterofusa0000dunh"><i>Euler: the master of us all</i></a></span>. The Dolciani mathematical expositions. Washington, D.C.: <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/eulermasterofusa0000dunh/page/4">4</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-88385-328-3" title="Special:BookSources/978-0-88385-328-3"><bdi>978-0-88385-328-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euler%3A+the+master+of+us+all&rft.place=Washington%2C+D.C.&rft.series=The+Dolciani+mathematical+expositions&rft.pages=4&rft.pub=Mathematical+Association+of+America&rft.date=1999&rft.isbn=978-0-88385-328-3&rft.aulast=Dunham&rft.aufirst=William&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Feulermasterofusa0000dunh&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGautschi1994" class="citation book cs1">Gautschi, Walter (1994). Gautschi, Walter (ed.). <i>Mathematics of computation, 1943-1993: a half-century of computational mathematics ; Mathematics of Computation 50th Anniversary Symposium, August 9-13, 1993, Vancouver, British Columbia</i>. Proceedings of symposia in applied mathematics. Vol. 48. Providence, RI: <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. p. 486. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-0291-5" title="Special:BookSources/978-0-8218-0291-5"><bdi>978-0-8218-0291-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+of+computation%2C+1943-1993%3A+a+half-century+of+computational+mathematics+%3B+Mathematics+of+Computation+50th+Anniversary+Symposium%2C+August+9-13%2C+1993%2C+Vancouver%2C+British+Columbia&rft.place=Providence%2C+RI&rft.series=Proceedings+of+symposia+in+applied+mathematics&rft.pages=486&rft.pub=American+Mathematical+Society&rft.date=1994&rft.isbn=978-0-8218-0291-5&rft.aulast=Gautschi&rft.aufirst=Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-The_Largest_Known_Prime_by_Year-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-The_Largest_Known_Prime_by_Year_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-The_Largest_Known_Prime_by_Year_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCaldwell2009" class="citation web cs1">Caldwell, Chris (8 December 2009). <a rel="nofollow" class="external text" href="http://primes.utm.edu/notes/by_year.html">"The Largest Known Prime by Year: A Brief History"</a>. <i>The Prime Pages</i>. University of Tennessee at Martin<span class="reference-accessdate">. Retrieved <span class="nowrap">29 January</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Prime+Pages&rft.atitle=The+Largest+Known+Prime+by+Year%3A+A+Brief+History&rft.date=2009-12-08&rft.aulast=Caldwell&rft.aufirst=Chris&rft_id=http%3A%2F%2Fprimes.utm.edu%2Fnotes%2Fby_year.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarlow1811" class="citation book cs1"><a href="/wiki/Peter_Barlow_(mathematician)" title="Peter Barlow (mathematician)">Barlow, Peter</a> (1811). <a rel="nofollow" class="external text" href="https://archive.org/details/anelementaryinv00barlgoog"><i>An Elementary Investigation of the Theory of Numbers</i></a>. London: J. Johnson & Co. p. <a rel="nofollow" class="external text" href="https://archive.org/details/anelementaryinv00barlgoog/page/n65">43</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1191003275">1191003275</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Elementary+Investigation+of+the+Theory+of+Numbers&rft.place=London&rft.pages=43&rft.pub=J.+Johnson+%26+Co.&rft.date=1811&rft_id=info%3Aoclcnum%2F1191003275&rft.aulast=Barlow&rft.aufirst=Peter&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fanelementaryinv00barlgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarlow1814" class="citation book cs1"><a href="/wiki/Peter_Barlow_(mathematician)" title="Peter Barlow (mathematician)">Barlow, Peter</a> (1814). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Y-csAAAAYAAJ&q=2147483647&pg=PT544"><i>A New Mathematical and Philosophical Dictionary: Comprising an Explanation of Terms and Principles of Pure and Mixed Mathematics, and Such Branches of Natural Philosophy as Are Susceptible of Mathematical Investigation</i></a>. London: G. and S. Robinson. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/889473251">889473251</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+New+Mathematical+and+Philosophical+Dictionary%3A+Comprising+an+Explanation+of+Terms+and+Principles+of+Pure+and+Mixed+Mathematics%2C+and+Such+Branches+of+Natural+Philosophy+as+Are+Susceptible+of+Mathematical+Investigation&rft.place=London&rft.pub=G.+and+S.+Robinson&rft.date=1814&rft_id=info%3Aoclcnum%2F889473251&rft.aulast=Barlow&rft.aufirst=Peter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DY-csAAAAYAAJ%26q%3D2147483647%26pg%3DPT544&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShanks2001" class="citation book cs1">Shanks, Daniel (2001). <i>Solved and Unsolved Problems in Number Theory</i> (4th ed.). Providence, Rhode Island: <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. p. 495. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-2824-3" title="Special:BookSources/978-0-8218-2824-3"><bdi>978-0-8218-2824-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Solved+and+Unsolved+Problems+in+Number+Theory&rft.place=Providence%2C+Rhode+Island&rft.pages=495&rft.edition=4th&rft.pub=American+Mathematical+Society&rft.date=2001&rft.isbn=978-0-8218-2824-3&rft.aulast=Shanks&rft.aufirst=Daniel&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.opengroup.org/onlinepubs/000095399/">"The Open Group Base Specifications Issue 6 IEEE Std 1003.1, 2004 Edition (definition of epoch)"</a>. <i><a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a> and <a href="/wiki/The_Open_Group" title="The Open Group">The Open Group</a></i>. <a href="/wiki/The_Open_Group" title="The Open Group">The Open Group</a>. 2004. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081219153936/http://www.opengroup.org/onlinepubs/000095399/">Archived</a> from the original on 19 December 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">7 March</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=IEEE+and+The+Open+Group&rft.atitle=The+Open+Group+Base+Specifications+Issue+6+IEEE+Std+1003.1%2C+2004+Edition+%28definition+of+epoch%29&rft.date=2004&rft_id=http%3A%2F%2Fwww.opengroup.org%2Fonlinepubs%2F000095399%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.2038bug.com/">"The Year-2038 Bug"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090318084855/http://www.2038bug.com/">Archived</a> from the original on 18 March 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">9 April</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Year-2038+Bug&rft_id=http%3A%2F%2Fwww.2038bug.com%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAbrams2022" class="citation web cs1">Abrams, Lawrence (1 January 2022). <a rel="nofollow" class="external text" href="https://www.bleepingcomputer.com/news/microsoft/microsoft-exchange-year-2022-bug-in-fip-fs-breaks-email-delivery/">"Microsoft Exchange year 2022 bug in FIP-FS breaks email delivery"</a>. <i><a href="/wiki/Bleeping_Computer" title="Bleeping Computer">Bleeping Computer</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">2 January</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bleeping+Computer&rft.atitle=Microsoft+Exchange+year+2022+bug+in+FIP-FS+breaks+email+delivery&rft.date=2022-01-01&rft.aulast=Abrams&rft.aufirst=Lawrence&rft_id=https%3A%2F%2Fwww.bleepingcomputer.com%2Fnews%2Fmicrosoft%2Fmicrosoft-exchange-year-2022-bug-in-fip-fs-breaks-email-delivery%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-:0-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLever2012" class="citation book cs1">Lever, Nik (6 August 2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eV0My6PR9xIC&pg=PA149"><i>Director MX 2004 Games: Game Development with Director</i></a>. Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-136-14525-4" title="Special:BookSources/978-1-136-14525-4"><bdi>978-1-136-14525-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Director+MX+2004+Games%3A+Game+Development+with+Director&rft.pub=Taylor+%26+Francis&rft.date=2012-08-06&rft.isbn=978-1-136-14525-4&rft.aulast=Lever&rft.aufirst=Nik&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeV0My6PR9xIC%26pg%3DPA149&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCockfield2018" class="citation web cs1">Cockfield, Bryan (19 September 2018). <a rel="nofollow" class="external text" href="https://hackaday.com/2018/09/19/final-fantasy-exploit-teaches-32-bit-integer-math/">"Final Fantasy Exploit Teaches 32-bit Integer Math"</a>. <i>Hackaday</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hackaday&rft.atitle=Final+Fantasy+Exploit+Teaches+32-bit+Integer+Math&rft.date=2018-09-19&rft.aulast=Cockfield&rft.aufirst=Bryan&rft_id=https%3A%2F%2Fhackaday.com%2F2018%2F09%2F19%2Ffinal-fantasy-exploit-teaches-32-bit-integer-math%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFByrne2015" class="citation web cs1">Byrne, Michael (12 April 2015). <a rel="nofollow" class="external text" href="https://www.vice.com/en/article/ae39e4/32-bit-integers-and-why-old-computers-matter">"32-Bit Integers and Why Old Computers Matter"</a>. <i><a href="/wiki/Vice_(magazine)" title="Vice (magazine)">Vice</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Vice&rft.atitle=32-Bit+Integers+and+Why+Old+Computers+Matter&rft.date=2015-04-12&rft.aulast=Byrne&rft.aufirst=Michael&rft_id=https%3A%2F%2Fwww.vice.com%2Fen%2Farticle%2Fae39e4%2F32-bit-integers-and-why-old-computers-matter&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://runescape.wiki/w/Coins">"Coins"</a>. <i>Runescape Official Wiki</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Runescape+Official+Wiki&rft.atitle=Coins&rft_id=https%3A%2F%2Frunescape.wiki%2Fw%2FCoins&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWood2018" class="citation news cs1">Wood, Austin (12 July 2018). <a rel="nofollow" class="external text" href="https://www.pcgamer.com/old-school-runescape-pulled-offline-as-billions-of-gold-appear-out-of-nowhere/">"Old School Runescape pulled offline as billions of gold appear out of nowhere"</a>. <i>PC Gamer</i><span class="reference-accessdate">. Retrieved <span class="nowrap">25 September</span> 2022</span>. <q>it's appropriate to check that the calculation doesn't overflow the max integer limit of the game's language (2.1 billion). Unfortunately, the logic used for this calculation was incorrect, and when executed on stacks of other items (not the pouch itself) the result was to convert the stack to 2.1b coins.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PC+Gamer&rft.atitle=Old+School+Runescape+pulled+offline+as+billions+of+gold+appear+out+of+nowhere&rft.date=2018-07-12&rft.aulast=Wood&rft.aufirst=Austin&rft_id=https%3A%2F%2Fwww.pcgamer.com%2Fold-school-runescape-pulled-offline-as-billions-of-gold-appear-out-of-nowhere%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3A2%2C147%2C483%2C647" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://minecraft.wiki/w/Java_Edition_hard_limits#32-bit_limit_(X/Z:_%3E%C2%B12,147,483,647)">"Java Edition hard limits"</a>. <i>Minecraft Wiki</i><span class="reference-accessdate">. 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