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href="https://ca.wikipedia.org/wiki/Nombre_de_Proth" title="Nombre de Proth - catalano" lang="ca" hreflang="ca" data-title="Nombre de Proth" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Prothovo_%C4%8D%C3%ADslo" title="Prothovo číslo - ceco" lang="cs" hreflang="cs" data-title="Prothovo číslo" data-language-autonym="Čeština" data-language-local-name="ceco" 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/Prothsche_Primzahl" title="Prothsche Primzahl - tedesco" lang="de" hreflang="de" data-title="Prothsche Primzahl" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Proth_number" title="Proth number - inglese" lang="en" hreflang="en" data-title="Proth number" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_de_Proth" title="Número de Proth - spagnolo" lang="es" hreflang="es" data-title="Número de Proth" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF_%D9%BE%D8%B1%D9%88%D8%AA" title="اعداد پروت - persiano" lang="fa" hreflang="fa" data-title="اعداد پروت" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Prothin_alkuluku" title="Prothin alkuluku - finlandese" lang="fi" hreflang="fi" data-title="Prothin alkuluku" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_de_Proth" title="Nombre de Proth - francese" lang="fr" hreflang="fr" data-title="Nombre de Proth" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Proth-sz%C3%A1mok" title="Proth-számok - ungherese" lang="hu" hreflang="hu" data-title="Proth-számok" data-language-autonym="Magyar" data-language-local-name="ungherese" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%97%E3%83%AD%E3%82%B9%E6%95%B0" title="プロス数 - giapponese" lang="ja" hreflang="ja" data-title="プロス数" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%84%EB%A1%9C%ED%8A%B8_%EC%88%98" title="프로트 수 - coreano" lang="ko" hreflang="ko" data-title="프로트 수" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Prothgetal" title="Prothgetal - olandese" lang="nl" hreflang="nl" data-title="Prothgetal" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/N%C3%BAmero_de_Proth" title="Número de Proth - portoghese" lang="pt" hreflang="pt" data-title="Número de Proth" data-language-autonym="Português" data-language-local-name="portoghese" 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/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%9F%D1%80%D0%BE%D1%82%D0%B0" title="Число Прота - russo" lang="ru" hreflang="ru" data-title="Число Прота" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Prothovo_%C5%A1tevilo" title="Prothovo število - sloveno" lang="sl" hreflang="sl" data-title="Prothovo število" data-language-autonym="Slovenščina" data-language-local-name="sloveno" 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><p>In <a href="/wiki/Teoria_dei_numeri" title="Teoria dei numeri">teoria dei numeri</a>, un <b>numero di Proth</b> è un numero espresso nella forma </p> <dl><dd><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 P=k2^{n}+1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>k</mi> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=k2^{n}+1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe3f4a83642d30d69bd623706f7be8cc52bb0d56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.086ex; height:2.676ex;" alt="{\displaystyle P=k2^{n}+1,}"></span></dd></dl> <p>dove <i>k</i> è <a href="/wiki/Numero_dispari" class="mw-redirect" title="Numero dispari">dispari</a>, <i>n</i> è un <a href="/wiki/Intero" class="mw-redirect" title="Intero">intero</a> positivo, e 2<sup><i>n</i></sup>><i>k</i>. I numeri di Proth sono così chiamati in onore del matematico <a href="/w/index.php?title=Fran%C3%A7ois_Proth&action=edit&redlink=1" class="new" title="François Proth (la pagina non esiste)">François Proth</a>. </p><p>Se un numero di Proth è <a href="/wiki/Numero_primo" title="Numero primo">primo</a>, è chiamato <b>primo di Proth</b>: il <a href="/wiki/Teorema_di_Proth" title="Teorema di Proth">teorema di Proth</a> può essere usato per verificare la primalità di un dato numero di Proth. </p> <div class="mw-heading mw-heading2"><h2 id="Esempi">Esempi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Numero_di_Proth&veaction=edit&section=1" title="Modifica la sezione Esempi" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Numero_di_Proth&action=edit&section=1" title="Edit section's source code: Esempi"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I più piccoli numeri di Proth sono: </p> <dl><dd><i>P</i><sub>0</sub> = 2<sup>1</sup> + 1 = 3;</dd> <dd><i>P</i><sub>1</sub> = 2<sup>2</sup> + 1 = 5;</dd> <dd><i>P</i><sub>2</sub> = 2<sup>3</sup> + 1 = 9;</dd> <dd><i>P</i><sub>3</sub> = 3 × 2<sup>2</sup> + 1 = 13;</dd> <dd><i>P</i><sub>4</sub> = 2<sup>4</sup> + 1 = 17;</dd> <dd><i>P</i><sub>5</sub> = 3 × 2<sup>3</sup> + 1 = 25;</dd> <dd><i>P</i><sub>6</sub> = 2<sup>5</sup> + 1 = 33.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Numero_di_Proth&veaction=edit&section=2" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Numero_di_Proth&action=edit&section=2" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Numero_di_Sierpi%C5%84ski" title="Numero di Sierpiński">Numero di Sierpiński</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Numero_di_Proth&veaction=edit&section=3" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Numero_di_Proth&action=edit&section=3" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://oeis.org/A080075"><span style="font-style:italic;">Sequenza A080075</span></a>, su <span style="font-style:italic;"><a href="/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="On-Line Encyclopedia of Integer Sequences">On-Line Encyclopedia of Integer Sequences</a></span>, The OEIS Foundation.</cite></li> <li class="mw-empty-elt"></li> <li><cite id="CITEREFMathWorld" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/ProthNumber.html"><span style="font-style:italic;">Numero di Proth</span></a>, su <span style="font-style:italic;"><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></span>, Wolfram Research.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q593418#P2812" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li></ul> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-grow: 1"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Crystal128-kmplot.svg" class="mw-file-description" title="Matematica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/25px-Crystal128-kmplot.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/38px-Crystal128-kmplot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Crystal128-kmplot.svg/50px-Crystal128-kmplot.svg.png 2x" data-file-width="245" data-file-height="244" /></a></span> <b><a href="/wiki/Portale:Matematica" title="Portale:Matematica">Portale Matematica</a></b>: accedi alle voci di Wikipedia che trattano di Matematica</div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Estratto da "<a dir="ltr" href="https://it.wikipedia.org/w/index.php?title=Numero_di_Proth&oldid=131228433">https://it.wikipedia.org/w/index.php?title=Numero_di_Proth&oldid=131228433</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categoria:Categorie" title="Categoria:Categorie">Categorie</a>: <ul><li><a href="/wiki/Categoria:Successioni_di_interi" title="Categoria:Successioni di interi">Successioni di interi</a></li><li><a href="/wiki/Categoria:Teoria_dei_numeri" title="Categoria:Teoria dei numeri">Teoria dei numeri</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categoria nascosta: <ul><li><a href="/wiki/Categoria:P2812_letta_da_Wikidata" title="Categoria:P2812 letta da Wikidata">P2812 letta da Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Questa pagina è stata modificata per l'ultima volta il 29 dic 2022 alle 20:41.</li> <li id="footer-info-copyright">Il testo è disponibile secondo la <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.it">licenza Creative Commons Attribuzione-Condividi allo stesso modo</a>; possono applicarsi condizioni ulteriori. 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