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data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inledning</div> </a> </li> <li id="toc-Algoritmer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Algoritmer"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Algoritmer</span> </div> </a> <ul id="toc-Algoritmer-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tillämpbarhet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tillämpbarhet"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tillämpbarhet</span> </div> </a> <ul id="toc-Tillämpbarhet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referenser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referenser"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Referenser</span> </div> </a> <button aria-controls="toc-Referenser-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Växla underavsnittet Referenser</span> </button> <ul id="toc-Referenser-sublist" class="vector-toc-list"> <li id="toc-Noter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Noter"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Noter</span> </div> </a> <ul id="toc-Noter-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tryckta_källor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tryckta_källor"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Tryckta källor</span> </div> </a> <ul id="toc-Tryckta_källor-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Externa_länkar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externa_länkar"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Externa länkar</span> </div> </a> <ul id="toc-Externa_länkar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Innehåll" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Växla innehållsförteckningen" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Växla innehållsförteckningen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Primtalsfaktorisering</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Gå till en artikel på ett annat språk. Tillgänglig på 33 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">33 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Primfaktorzerlegung" title="Primfaktorzerlegung – schweizertyska" lang="gsw" hreflang="gsw" data-title="Primfaktorzerlegung" data-language-autonym="Alemannisch" data-language-local-name="schweizertyska" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%D9%8A%D9%84_%D8%B9%D8%AF%D8%AF_%D8%B5%D8%AD%D9%8A%D8%AD_%D8%A5%D9%84%D9%89_%D8%B9%D9%88%D8%A7%D9%85%D9%84" title="تحليل عدد صحيح إلى عوامل – arabiska" lang="ar" hreflang="ar" data-title="تحليل عدد صحيح إلى عوامل" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Factoritzaci%C3%B3_dels_enters" title="Factorització dels enters – katalanska" lang="ca" hreflang="ca" data-title="Factorització dels enters" data-language-autonym="Català" data-language-local-name="katalanska" 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/Prvo%C4%8D%C3%ADseln%C3%BD_rozklad" title="Prvočíselný rozklad – tjeckiska" lang="cs" hreflang="cs" data-title="Prvočíselný rozklad" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Primtalsopl%C3%B8sning" title="Primtalsopløsning – danska" lang="da" hreflang="da" data-title="Primtalsopløsning" data-language-autonym="Dansk" data-language-local-name="danska" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Primfaktorzerlegung" title="Primfaktorzerlegung – tyska" lang="de" hreflang="de" data-title="Primfaktorzerlegung" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Integer_factorization" title="Integer factorization – engelska" lang="en" hreflang="en" data-title="Integer factorization" data-language-autonym="English" data-language-local-name="engelska" 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/Factorizaci%C3%B3n_de_enteros" title="Factorización de enteros – spanska" lang="es" hreflang="es" data-title="Factorización de enteros" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Faktorado_de_entjero" title="Faktorado de entjero – esperanto" lang="eo" hreflang="eo" data-title="Faktorado de entjero" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_osoen_faktorizazio" title="Zenbaki osoen faktorizazio – baskiska" lang="eu" hreflang="eu" data-title="Zenbaki osoen faktorizazio" data-language-autonym="Euskara" data-language-local-name="baskiska" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%AC%D8%B2%DB%8C%D9%87_%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF_%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C" title="تجزیه اعداد طبیعی – persiska" lang="fa" hreflang="fa" data-title="تجزیه اعداد طبیعی" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/D%C3%A9composition_en_produit_de_facteurs_premiers" title="Décomposition en produit de facteurs premiers – franska" lang="fr" hreflang="fr" data-title="Décomposition en produit de facteurs premiers" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%91%D3%80%D0%B0%D1%80%D1%87%D1%87%D0%B0%D1%87%D0%B0_%D1%82%D0%B0%D1%8C%D1%80%D0%B0%D1%85%D1%8C%D0%B8%D0%B9_%D1%84%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D0%B8" title="БӀарччача таьрахьий факторизаци – ingusjiska" lang="inh" hreflang="inh" data-title="БӀарччача таьрахьий факторизаци" data-language-autonym="ГӀалгӀай" data-language-local-name="ingusjiska" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%86%8C%EC%9D%B8%EC%88%98%EB%B6%84%ED%95%B4" title="소인수분해 – koreanska" lang="ko" hreflang="ko" data-title="소인수분해" data-language-autonym="한국어" data-language-local-name="koreanska" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Faktorisasi_prima" title="Faktorisasi prima – indonesiska" lang="id" hreflang="id" data-title="Faktorisasi prima" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiska" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Frum%C3%BE%C3%A1ttun" title="Frumþáttun – isländska" lang="is" hreflang="is" data-title="Frumþáttun" data-language-autonym="Íslenska" data-language-local-name="isländska" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%99%D7%A8%D7%95%D7%A7_%D7%9C%D7%92%D7%95%D7%A8%D7%9E%D7%99%D7%9D_%D7%A9%D7%9C_%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A9%D7%9C%D7%9D" title="פירוק לגורמים של מספר שלם – hebreiska" lang="he" hreflang="he" data-title="פירוק לגורמים של מספר שלם" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Haaptsaz_vun_der_elementarer_Zuelentheorie" title="Haaptsaz vun der elementarer Zuelentheorie – luxemburgiska" lang="lb" hreflang="lb" data-title="Haaptsaz vun der elementarer Zuelentheorie" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgiska" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pr%C3%ADmfelbont%C3%A1s" title="Prímfelbontás – ungerska" lang="hu" hreflang="hu" data-title="Prímfelbontás" data-language-autonym="Magyar" data-language-local-name="ungerska" 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/Ontbinden_in_priemfactoren" title="Ontbinden in priemfactoren – nederländska" lang="nl" hreflang="nl" data-title="Ontbinden in priemfactoren" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B4%A0%E5%9B%A0%E6%95%B0%E5%88%86%E8%A7%A3" title="素因数分解 – japanska" lang="ja" hreflang="ja" data-title="素因数分解" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fatora%C3%A7%C3%A3o_de_inteiros" title="Fatoração de inteiros – portugisiska" lang="pt" hreflang="pt" data-title="Fatoração de inteiros" data-language-autonym="Português" data-language-local-name="portugisiska" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Descompunerea_%C3%AEn_factori_primi" title="Descompunerea în factori primi – rumänska" lang="ro" hreflang="ro" data-title="Descompunerea în factori primi" data-language-autonym="Română" data-language-local-name="rumänska" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17559452 badge-recommendedarticle mw-list-item" title="rekommenderad artikel"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F_%D1%86%D0%B5%D0%BB%D1%8B%D1%85_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Факторизация целых чисел – ryska" lang="ru" hreflang="ru" data-title="Факторизация целых чисел" data-language-autonym="Русский" data-language-local-name="ryska" 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/Prime_factorization" title="Prime factorization – Simple English" lang="en-simple" hreflang="en-simple" data-title="Prime factorization" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pra%C5%A1tevilski_razcep" title="Praštevilski razcep – slovenska" lang="sl" hreflang="sl" data-title="Praštevilski razcep" data-language-autonym="Slovenščina" data-language-local-name="slovenska" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Rastavljanje_na_faktore" title="Rastavljanje na faktore – serbiska" lang="sr" hreflang="sr" data-title="Rastavljanje na faktore" data-language-autonym="Српски / srpski" data-language-local-name="serbiska" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kokonaislukujen_tekij%C3%B6ihinjako" title="Kokonaislukujen tekijöihinjako – finska" lang="fi" hreflang="fi" data-title="Kokonaislukujen tekijöihinjako" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%A2%E0%B8%81%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%81%E0%B8%AD%E0%B8%9A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="การแยกตัวประกอบจำนวนเต็ม – thailändska" lang="th" hreflang="th" data-title="การแยกตัวประกอบจำนวนเต็ม" data-language-autonym="ไทย" data-language-local-name="thailändska" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Asal_%C3%A7arpanlara_ay%C4%B1rma" title="Asal çarpanlara ayırma – turkiska" lang="tr" hreflang="tr" data-title="Asal çarpanlara ayırma" data-language-autonym="Türkçe" data-language-local-name="turkiska" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D0%B7%D0%B0%D1%86%D1%96%D1%8F_%D1%86%D1%96%D0%BB%D0%B8%D1%85_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Факторизація цілих чисел – ukrainska" lang="uk" hreflang="uk" data-title="Факторизація цілих чисел" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_t%C3%ADch_s%E1%BB%91_nguy%C3%AAn" title="Phân tích số nguyên – vietnamesiska" lang="vi" hreflang="vi" data-title="Phân tích số nguyên" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B4%E6%95%B0%E5%88%86%E8%A7%A3" title="整数分解 – kinesiska" lang="zh" hreflang="zh" data-title="整数分解" data-language-autonym="中文" data-language-local-name="kinesiska" 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 href="https://www.wikidata.org/wiki/Special:EntityPage/Q4846249#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</a></span></div> </div> </div> </div> </header> <div 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data-file-height="170" /></a><figcaption></figcaption></figure> <p><b>Primtalsfaktorisering</b> innebär att ett <a href="/wiki/Heltal" title="Heltal">heltal</a> skrivs som en <a href="/wiki/Produkt_(matematik)" title="Produkt (matematik)">produkt</a> av <a href="/wiki/Primtal" title="Primtal">primtal</a>. Exempelvis har talet 456 faktoriseringen </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 456=2^{3}\cdot 3\cdot 19.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>456</mn> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⋅</mo> <mn>3</mn> <mo>⋅</mo> <mn>19.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 456=2^{3}\cdot 3\cdot 19.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc9ac8bf7a1f736215d10c647382659d8caa68fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.295ex; height:2.676ex;" alt="{\displaystyle 456=2^{3}\cdot 3\cdot 19.}"></span></dd></dl> <p>Enligt <a href="/wiki/Aritmetikens_fundamentalsats" title="Aritmetikens fundamentalsats">aritmetikens fundamentalsats</a> har varje positivt heltal en primtalsfaktorisering som är <i>unik</i> om man bortser från faktorernas inbördes ordning. </p><p><b>Heltalsfaktorisering</b> kallas den allmännare process i vilken ett heltal skrivs som en produkt av mindre men inte nödvändigtvis prima heltal. Till skillnad från primtalsfaktorisering är resultatet av en heltalsfaktorisering inte alltid unikt. Till exempel är både <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 2\cdot 6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>⋅</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\cdot 6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e558ad154a15909f031457c1399ff06d87c6586a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.004ex; height:2.176ex;" alt="{\displaystyle 2\cdot 6}"></span> och <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 3\cdot 4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>⋅</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\cdot 4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/321f91b867c60a4b4d0fbd4dd8b3a5a91c4ab5a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.004ex; height:2.176ex;" alt="{\displaystyle 3\cdot 4}"></span> giltiga heltalsfaktoriseringar av talet 12. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Algoritmer">Algoritmer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=1" title="Redigera avsnitt: Algoritmer" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=1" title="Redigera avsnitts källkod: Algoritmer"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ett flertal <a href="/wiki/Algoritm" title="Algoritm">algoritmer</a> används för primtalsfaktorisering. Den enklaste att förstå är <i><a href="/w/index.php?title=Trial_division&action=edit&redlink=1" class="new" title="Trial division [inte skriven än]">trial division</a></i>, vilken innebär att man för ett tal <i>n</i> testar att dividera <i>n</i> med varje tal upp till och med <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 {\sqrt {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>n</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a2994734eae382ce30100fb17b9447fd8e99f81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.331ex; height:3.009ex;" alt="{\displaystyle {\sqrt {n}}}"></span>.<sup id="cite_ref-Mollin_1-0" class="reference"><a href="#cite_note-Mollin-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup> De tal som ger resten noll är faktorer av <i>n</i>. Trial division är den överlägset effektivaste metoden för att bestämma små faktorer, exempelvis mindre än 10<sup>9</sup>, men oanvändbart för att hitta väsentligt större faktorer. Lyckligtvis är metoden effektiv för slumpmässigt valda tal, eftersom hälften av alla tal har 2 som faktor, en tredjedel har 3 som faktor, och så vidare. Hela 88 % av alla heltal har minst en faktor som är mindre än 100. Trial division kan därför användas för att snabbt röja undan små faktorer varefter en mer avancerad algoritm tar hand om de återstående.<sup id="cite_ref-Crandall_2-0" class="reference"><a href="#cite_note-Crandall-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> </p><p><a href="/wiki/Rationellt_s%C3%A5ll" title="Rationellt såll">Rationellt såll</a> är en generell algoritm för primtalsfaktorisering. Den är ett specialfall av det generella talsållet (general number field sieve, GNFS), och medan den är mindre effektiv än den allmänna algoritmen så är den konceptuellt enklare. </p><p>De enklaste metoderna för att snabbt hitta faktorer något större än cirka 10 siffror är <a href="/w/index.php?title=Pollards_rho-metod&action=edit&redlink=1" class="new" title="Pollards rho-metod [inte skriven än]">Pollards rho-metod</a><sup id="cite_ref-Pollard_3-0" class="reference"><a href="#cite_note-Pollard-3"><span class="cite-reference-link-bracket">[</span>3<span class="cite-reference-link-bracket">]</span></a></sup> och <a href="/w/index.php?title=Pollards_p-1-metod&action=edit&redlink=1" class="new" title="Pollards p-1-metod [inte skriven än]">Pollards p-1-metod</a> samt varianter av dessa. För faktorer i storleksordningen 20–25 siffror är ECM (faktorisering med <a href="/wiki/Elliptisk_kurva" title="Elliptisk kurva">elliptiska kurvor</a>) ytterligare ett alternativ. De enda praktiska algoritmerna för större faktorer än så är varianter av <a href="/wiki/Eratosthenes_s%C3%A5ll" title="Eratosthenes såll">Eratosthenes såll</a>, <a href="/w/index.php?title=Kvadratiskt_s%C3%A5ll&action=edit&redlink=1" class="new" title="Kvadratiskt såll [inte skriven än]">kvadratiska såll</a> och <a href="/w/index.php?title=Talkroppss%C3%A5ll&action=edit&redlink=1" class="new" title="Talkroppssåll [inte skriven än]">talkroppssåll</a>. Effektivast för stora tal är <a href="/w/index.php?title=General_number_field_sieve&action=edit&redlink=1" class="new" title="General number field sieve [inte skriven än]">general number field sieve</a> (GNFS), som används för att faktorisera <a href="/w/index.php?title=RSA-tal&action=edit&redlink=1" class="new" title="RSA-tal [inte skriven än]">RSA-tal</a> med 100-siffriga faktorer.<sup id="cite_ref-Pomerance_4-0" class="reference"><a href="#cite_note-Pomerance-4"><span class="cite-reference-link-bracket">[</span>4<span class="cite-reference-link-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Tillämpbarhet"><span id="Till.C3.A4mpbarhet"></span>Tillämpbarhet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=2" title="Redigera avsnitt: Tillämpbarhet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=2" title="Redigera avsnitts källkod: Tillämpbarhet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Det tycks som om det <a href="/wiki/Ber%C3%A4kningsteori" title="Beräkningsteori">beräkningsmässigt</a> är betydligt svårare att bestämma primtalsfaktorerna till ett givet tal än att multiplicera ihop faktorer. Det är också enklare att med ett <a href="/wiki/Primtalstest" title="Primtalstest">primtalstest</a> avgöra huruvida ett tal kan delas upp i mindre faktorer än att om så är fallet bestämma faktorerna. Datorer kan idag enkelt multiplicera tal med miljontals siffror och utföra primtalstest på tal med tusentals siffror, men att faktorisera ett 100-siffrigt tal är ett utmanande problem. Svårigheten att faktorisera heltal utnyttjas av <a href="/wiki/Krypteringsalgoritm" title="Krypteringsalgoritm">krypteringsalgoritmer</a> som <a href="/wiki/RSA" title="RSA">RSA</a>.<sup id="cite_ref-Brown_5-0" class="reference"><a href="#cite_note-Brown-5"><span class="cite-reference-link-bracket">[</span>5<span class="cite-reference-link-bracket">]</span></a></sup><sup id="cite_ref-Boneh_6-0" class="reference"><a href="#cite_note-Boneh-6"><span class="cite-reference-link-bracket">[</span>6<span class="cite-reference-link-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referenser">Referenser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=3" title="Redigera avsnitt: Referenser" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=3" title="Redigera avsnitts källkod: Referenser"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Noter">Noter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=4" title="Redigera avsnitt: Noter" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=4" title="Redigera avsnitts källkod: Noter"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Mollin-1"><a href="#cite_ref-Mollin_1-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="journal" id="CITEREFMollin2002">Mollin, Richard A. (2002). ”A brief history of factoring and primality testing B. C. (before computers)” (på engelska). <i>Mathematics Magazine</i> 75 (1): sid. 18–29. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.2307%2F3219180">10.2307/3219180</a></span><span class="reference-accessdate">. Läst 26 september 2019</span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+brief+history+of+factoring+and+primality+testing+B.+C.+%28before+computers%29&rft.jtitle=Mathematics+Magazine&rft.aulast=Mollin&rft.aufirst=Richard+A.&rft.au=Mollin%2C+Richard+A.&rft.date=2002&rft.volume=75&rft.issue=1&rft.pages=sid.%26nbsp%3B18%E2%80%9329&rft_id=info:doi/10.2307%2F3219180&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Crandall-2"><a href="#cite_ref-Crandall_2-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFCrandallPomerance2005">Crandall, Richard; Pomerance, Carl (2005) (på engelska). <i><span>Prime numbers. A computational perspective</span></i> (2:a). New York, NY: Springer-Verlag. <a href="/wiki/Special:Bokk%C3%A4llor/0-387-25282-7" title="Special:Bokkällor/0-387-25282-7">ISBN 0-387-25282-7</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Prime+numbers.+A+computational+perspective&rft.aulast=Crandall&rft.aufirst=Richard&rft.au=Crandall%2C+Richard&rft.au=Pomerance%2C+Carl&rft.date=2005&rft.edition=2%3Aa&rft.place=New+York%2C+NY&rft.pub=Springer-Verlag&rft.isbn=0-387-25282-7&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Pollard-3"><a href="#cite_ref-Pollard_3-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="journal" id="CITEREFPollard1975">Pollard, J. M. (1975). ”A Monte Carlo method for factorization” (på engelska). <i>BIT Numerical Mathematics</i> 15 (3): sid. 331–334. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2Fbf01933667">10.1007/bf01933667</a></span><span class="reference-accessdate">. Läst 26 september 2019</span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Monte+Carlo+method+for+factorization&rft.jtitle=BIT+Numerical+Mathematics&rft.aulast=Pollard&rft.aufirst=J.+M.&rft.au=Pollard%2C+J.+M.&rft.date=1975&rft.volume=15&rft.issue=3&rft.pages=sid.%26nbsp%3B331%E2%80%93334&rft_id=info:doi/10.1007%2Fbf01933667&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Pomerance-4"><a href="#cite_ref-Pomerance_4-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="journal" id="CITEREFCarl_Pomerance1982">Carl Pomerance (1982). ”Analysis and Comparison of Some Integer Factoring Algorithms” (på engelska). <i>Mathematical Centre tracts</i> 154: sid. 89-139.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Analysis+and+Comparison+of+Some+Integer+Factoring+Algorithms&rft.jtitle=Mathematical+Centre+tracts&rft.aulast=Carl+Pomerance&rft.au=Carl+Pomerance&rft.date=1982&rft.volume=154&rft.pages=sid.%26nbsp%3B89-139&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Brown-5"><a href="#cite_ref-Brown_5-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="web" id="CITEREFD._Brown2005">D. Brown (2005). <a rel="nofollow" class="external text" href="http://eprint.iacr.org/2005/380">”Breaking RSA may be as difficult as factoring”</a> (på engelska)<span class="printonly">. <a rel="nofollow" class="external free" href="http://eprint.iacr.org/2005/380">http://eprint.iacr.org/2005/380</a></span><span class="reference-accessdate">. Läst 26 september 2019</span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Breaking+RSA+may+be+as+difficult+as+factoring&rft.atitle=&rft.aulast=D.+Brown&rft.au=D.+Brown&rft.date=2005&rft_id=http%3A%2F%2Feprint.iacr.org%2F2005%2F380&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Boneh-6"><a href="#cite_ref-Boneh_6-0">^</a> <span class="reference-text"><cite style="font-style:normal" class="journal" id="CITEREFDan_Boneh,_Ramarathnam_Venkatesan1998">Dan Boneh, Ramarathnam Venkatesan (1998). ”Advances in Cryptology — EUROCRYPT'98” (på engelska). <i>Lecture Notes in Computer Science</i> (Springer) 1403. <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBFb0054117">10.1007/BFb0054117</a></span><span class="reference-accessdate">. Läst 26 september 2019</span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Advances+in+Cryptology+%E2%80%94+EUROCRYPT%2798&rft.jtitle=Lecture+Notes+in+Computer+Science&rft.aulast=Dan+Boneh%2C+Ramarathnam+Venkatesan&rft.au=Dan+Boneh%2C+Ramarathnam+Venkatesan&rft.date=1998&rft.volume=1403&rft.pub=Springer&rft_id=info:doi/10.1007%2FBFb0054117&rfr_id=info:sid/en.wikipedia.org:Primtalsfaktorisering"><span style="display: none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Tryckta_källor"><span id="Tryckta_k.C3.A4llor"></span>Tryckta källor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=5" title="Redigera avsnitt: Tryckta källor" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=5" title="Redigera avsnitts källkod: Tryckta källor"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kodboken" title="Kodboken">Kodboken</a>, Simon Sing. Kryptografins historia där RSA-kryptering nämns.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Externa_länkar"><span id="Externa_l.C3.A4nkar"></span>Externa länkar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Primtalsfaktorisering&veaction=edit&section=6" title="Redigera avsnitt: Externa länkar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Primtalsfaktorisering&action=edit&section=6" title="Redigera avsnitts källkod: Externa länkar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Wikimedia Commons har media som rör <a href="https://commons.wikimedia.org/wiki/Category:Prime_factorization" class="extiw" title="commons:Category:Prime factorization">Primtalsfaktorisering</a>.<div class="interProject commons" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Prime_factorization" class="extiw" title="commons:Category:Prime factorization">Bilder & media</a></div></li></ul> <style data-mw-deduplicate="TemplateStyles:r56287950">.mw-parser-output table.navbox{border:#aaa 1px solid;width:100%;margin:auto;margin-top:1em;clear:both;font-size:88%;text-align:center;padding:1px}.mw-parser-output link+table.navbox{margin-top:-1px}.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow,.mw-parser-output table.navbox th{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-thlinkcolor .navbox-title button,.mw-parser-output .navbox-thlinkcolor .navbox-title .mw-collapsible-text,.mw-parser-output .navbox-thlinkcolor .navbox-title a{color:inherit}.mw-parser-output .nowraplinks a,.mw-parser-output .nowraplinks .selflink{white-space:nowrap}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right;font-weight:bold;padding-left:1em;padding-right:1em}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-title,.mw-parser-output table.navbox th{background:#b0c4de}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background:#d0e0f5}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background:#deeafa}.mw-parser-output .navbox-even{background:#f7f7f7}.mw-parser-output .navbox-odd{background:transparent}</style><table class="navbox" style="border-spacing:0; ;"><tbody><tr><td style="padding:2px;"><table class="collapsible autocollapse" style="width:100%;border-spacing:0;background:transparent;color:inherit;;"><tbody><tr><th style=";" colspan="3" class="navbox-title"><div style="float:left; width:3em;text-align:left;"><div class="noprint plainlinks" style="background-color:transparent; padding:0; white-space:nowrap; font-weight:normal; font-size:80%; border:none;; color: inherit;"><a href="/wiki/Mall:Delbarhetsklasser" title="Mall:Delbarhetsklasser"><span title="Visa denna mall" style="border:none;;">v</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://sv.wikipedia.org/w/index.php?title=Mall:Delbarhetsklasser&action=edit"><span style="border:none;;" title="Redigera den här mallen">r</span></a></div></div><span style="font-size:110%;">Delbarhetsbaserade heltalsmängder</span></th></tr><tr style="height:2px;"><td></td></tr><tr><td class="navbox-group" style=";;">Översikt</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a class="mw-selflink selflink">Primtalsfaktorisering</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Delbarhet" title="Delbarhet">Delbarhet</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Unit%C3%A4r_delare" title="Unitär delare">Unitär delare</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Sigmafunktionen" title="Sigmafunktionen">Sigmafunktionen</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Primtalsfaktor" title="Primtalsfaktor">Primtalsfaktor</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Aritmetikens_fundamentalsats" title="Aritmetikens fundamentalsats">Aritmetikens fundamentalsats</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Aritmetiskt_tal" title="Aritmetiskt tal">Aritmetiskt tal</a></div></td><td style="width:0%;padding:0px 0px 0px 2px;" rowspan="11"><span typeof="mw:File"><a href="/wiki/Fil:Lattice_of_the_divisibility_of_60.svg" class="mw-file-description" title="Delbarheten av 60"><img alt="Delbarheten av 60" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/200px-Lattice_of_the_divisibility_of_60.svg.png" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/300px-Lattice_of_the_divisibility_of_60.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/400px-Lattice_of_the_divisibility_of_60.svg.png 2x" data-file-width="313" data-file-height="250" /></a></span></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Faktoriserade former</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Primtal" title="Primtal">Primtal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Sammansatt_tal" title="Sammansatt tal">Sammansatt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Semiprimtal" title="Semiprimtal">Semiprimtal</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Rektangeltal" title="Rektangeltal">Rektangel</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Sfeniskt_tal" title="Sfeniskt tal">Sfeniskt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Kvadratfritt_tal" title="Kvadratfritt tal">Kvadratfritt</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Potensrikt_tal&action=edit&redlink=1" class="new" title="Potensrikt tal [inte skriven än]">Potensrikt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Perfekt_potens" title="Perfekt potens">Perfekt potens</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Akillestal" title="Akillestal">Akilles</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Sl%C3%A4tt_tal&action=edit&redlink=1" class="new" title="Slätt tal [inte skriven än]">Slätt</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Regelbundet_tal&action=edit&redlink=1" class="new" title="Regelbundet tal [inte skriven än]">Regelbundet</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Grovt_tal&action=edit&redlink=1" class="new" title="Grovt tal [inte skriven än]">Grovt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Extraordin%C3%A4rt_tal" title="Extraordinärt tal">Extraordinärt</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Begränsade <a href="/wiki/Delarsumma" title="Delarsumma">delarsummor</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Perfekt_tal" title="Perfekt tal">Perfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/N%C3%A4stan-perfekt_tal" title="Nästan-perfekt tal">Nästan-perfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Kvasiperfekt_tal" title="Kvasiperfekt tal">Kvasiperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Multiperfekt_tal" title="Multiperfekt tal">Multiperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Hemiperfekt_tal" title="Hemiperfekt tal">Hemiperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Hyperperfekt_tal" title="Hyperperfekt tal">Hyperperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Superperfekt_tal" title="Superperfekt tal">Superperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Unit%C3%A4rt_perfekt_tal" title="Unitärt perfekt tal">Unitärt perfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Semiperfekt_tal" title="Semiperfekt tal">Semiperfekt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Praktiskt_tal" title="Praktiskt tal">Praktiskt</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Erd%C5%91s%E2%80%93Nicolas-tal&action=edit&redlink=1" class="new" title="Erdős–Nicolas-tal [inte skriven än]">Erdős–Nicolas</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Med många delare</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/wiki/Ymnigt_tal" title="Ymnigt tal">Ymnigt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Primitivt_ymnigt_tal" title="Primitivt ymnigt tal">Primitivt ymnigt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Mycket_ymnigt_tal" title="Mycket ymnigt tal">Mycket ymnigt</a><span 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class="new" title="Alikvotföljd [inte skriven än]">Alikvotföljdsrelaterade</a></td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" class="navbox-list navbox-"><div style="padding:0em 0.25em"><a href="/w/index.php?title=Ober%C3%B6rbart_tal&action=edit&redlink=1" class="new" title="Oberörbart tal [inte skriven än]">Oberörbart</a><span style="font-weight:bold;"> · </span> <a href="/wiki/V%C3%A4nskapligt_tal" title="Vänskapligt tal">Vänskapligt</a><span style="font-weight:bold;"> · </span> <a href="/w/index.php?title=Sociabelt_tal&action=edit&redlink=1" class="new" title="Sociabelt tal [inte skriven än]">Sociabelt</a><span style="font-weight:bold;"> · </span> <a href="/wiki/Kvasiv%C3%A4nskapligt_tal" title="Kvasivänskapligt tal">Kvasivänskapligt</a></div></td></tr><tr style="height:2px"><td></td></tr><tr><td class="navbox-group" style=";;">Andra mängder</td><td style="text-align:left;border-left:2px solid #fdfdfd;width:100%;padding:0px;;;" 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