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id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="ค้นหาใน วิกิพีเดีย" aria-label="ค้นหาใน วิกิพีเดีย" autocapitalize="sentences" title="ค้นหาวิกิ [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="พิเศษ:ค้นหา"> </div> <button class="cdx-button cdx-search-input__end-button">ค้นหา</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="เครื่องมือส่วนตัว"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="หน้าตา" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">หน้าตา</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_th.wikipedia.org&uselang=th" class=""><span>บริจาคให้วิกิพีเดีย</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ" class=""><span>สร้างบัญชี</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o" class=""><span>เข้าสู่ระบบ</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="ตัวเลือกเพิ่มเติม" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="เครื่องมือส่วนตัว" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">เครื่องมือส่วนตัว</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="เมนูผู้ใช้" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_th.wikipedia.org&uselang=th"><span>บริจาคให้วิกิพีเดีย</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>สร้างบัญชี</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>เข้าสู่ระบบ</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> หน้าสำหรับผู้แก้ไขที่ออกจากระบบ <a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%83%E0%B8%8A%E0%B9%89:%E0%B8%9A%E0%B8%97%E0%B8%99%E0%B8%B3" aria-label="เรียนรู้เพิ่มเกี่ยวกับการแก้ไข"><span>เรียนรู้เพิ่มเติม</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B9%80%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%89%E0%B8%B1%E0%B8%99%E0%B9%80%E0%B8%82%E0%B8%B5%E0%B8%A2%E0%B8%99" title="รายการการแก้ไขจากเลขที่อยู่ไอพีนี้ [y]" accesskey="y"><span>ส่วนร่วม</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%89%E0%B8%B1%E0%B8%99" title="อภิปรายเกี่ยวกับการแก้ไขจากเลขที่อยู่ไอพีนี้ [n]" accesskey="n"><span>คุย</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="ไซต์"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="สารบัญ" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">สารบัญ</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ซ่อน</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">บทนำ</div> </a> </li> <li id="toc-การแทนจำนวนธรรมชาติ_ด้วยผลคูณของจำนวนเฉพาะ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#การแทนจำนวนธรรมชาติ_ด้วยผลคูณของจำนวนเฉพาะ"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>การแทนจำนวนธรรมชาติ ด้วยผลคูณของจำนวนเฉพาะ</span> </div> </a> <ul id="toc-การแทนจำนวนธรรมชาติ_ด้วยผลคูณของจำนวนเฉพาะ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-สมบัติมูลฐาน" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สมบัติมูลฐาน"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>สมบัติมูลฐาน</span> </div> </a> <button aria-controls="toc-สมบัติมูลฐาน-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>Toggle สมบัติมูลฐาน subsection</span> </button> <ul id="toc-สมบัติมูลฐาน-sublist" class="vector-toc-list"> <li id="toc-การแยกตัวประกอบได้อย่างเดียว" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#การแยกตัวประกอบได้อย่างเดียว"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>การแยกตัวประกอบได้อย่างเดียว</span> </div> </a> <ul id="toc-การแยกตัวประกอบได้อย่างเดียว-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-การมีอยู่นับไม่ถ้วน" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#การมีอยู่นับไม่ถ้วน"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>การมีอยู่นับไม่ถ้วน</span> </div> </a> <ul id="toc-การมีอยู่นับไม่ถ้วน-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-การหาจำนวนเฉพาะ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#การหาจำนวนเฉพาะ"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>การหาจำนวนเฉพาะ</span> </div> </a> <ul id="toc-การหาจำนวนเฉพาะ-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-สมบัติเชิงวิเคราะห์" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สมบัติเชิงวิเคราะห์"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>สมบัติเชิงวิเคราะห์</span> </div> </a> <ul id="toc-สมบัติเชิงวิเคราะห์-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-พีชคณิตนามธรรม" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#พีชคณิตนามธรรม"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>พีชคณิตนามธรรม</span> </div> </a> <button aria-controls="toc-พีชคณิตนามธรรม-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>Toggle พีชคณิตนามธรรม subsection</span> </button> <ul id="toc-พีชคณิตนามธรรม-sublist" class="vector-toc-list"> <li id="toc-สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด</span> </div> </a> <ul id="toc-สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-การประยุกต์" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#การประยุกต์"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>การประยุกต์</span> </div> </a> <ul id="toc-การประยุกต์-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ดูเพิ่ม" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ดูเพิ่ม"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>ดูเพิ่ม</span> </div> </a> <ul id="toc-ดูเพิ่ม-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-อ้างอิง" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#อ้างอิง"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>อ้างอิง</span> </div> </a> <ul id="toc-อ้างอิง-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-แหล่งข้อมูลอื่น" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#แหล่งข้อมูลอื่น"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>แหล่งข้อมูลอื่น</span> </div> </a> <button aria-controls="toc-แหล่งข้อมูลอื่น-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>Toggle แหล่งข้อมูลอื่น subsection</span> </button> <ul id="toc-แหล่งข้อมูลอื่น-sublist" class="vector-toc-list"> <li id="toc-คำนวณและสร้างจำนวนเฉพาะ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#คำนวณและสร้างจำนวนเฉพาะ"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>คำนวณและสร้างจำนวนเฉพาะ</span> </div> </a> <ul id="toc-คำนวณและสร้างจำนวนเฉพาะ-sublist" class="vector-toc-list"> </ul> </li> </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="สารบัญ" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">จำนวนเฉพาะ</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="ไปที่บทความในภาษาอื่น ซึ่งมีใน 138 ภาษา" > <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-138" 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">138 ภาษา</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Priemgetal" title="Priemgetal – แอฟริกานส์" lang="af" hreflang="af" data-title="Priemgetal" data-language-autonym="Afrikaans" data-language-local-name="แอฟริกานส์" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Primzahl" title="Primzahl – เยอรมันสวิส" lang="gsw" hreflang="gsw" data-title="Primzahl" data-language-autonym="Alemannisch" data-language-local-name="เยอรมันสวิส" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Numero_primero" title="Numero primero – อารากอน" lang="an" hreflang="an" data-title="Numero primero" data-language-autonym="Aragonés" data-language-local-name="อารากอน" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/Frumt%C3%A6l" title="Frumtæl – อังกฤษโบราณ" lang="ang" hreflang="ang" data-title="Frumtæl" data-language-autonym="Ænglisc" data-language-local-name="อังกฤษโบราณ" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%A3%D9%88%D9%84%D9%8A" title="عدد أولي – อาหรับ" lang="ar" hreflang="ar" data-title="عدد أولي" data-language-autonym="العربية" data-language-local-name="อาหรับ" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B9%D8%A7%D8%AF%D8%A7%D8%AF_%D9%84%D9%88%D9%84%D9%8A" title="عاداد لولي – อาหรับโมร็อกโก" lang="ary" hreflang="ary" data-title="عاداد لولي" data-language-autonym="الدارجة" data-language-local-name="อาหรับโมร็อกโก" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%A7%D9%88%D9%84%D9%89" title="عدد اولى – อาหรับพื้นเมืองอียิปต์" lang="arz" hreflang="arz" data-title="عدد اولى" data-language-autonym="مصرى" data-language-local-name="อาหรับพื้นเมืองอียิปต์" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AE%E0%A7%8C%E0%A6%B2%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="মৌলিক সংখ্যা – อัสสัม" lang="as" hreflang="as" data-title="মৌলিক সংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="อัสสัม" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberu_primu" title="Númberu primu – อัสตูเรียส" lang="ast" hreflang="ast" data-title="Númberu primu" data-language-autonym="Asturianu" data-language-local-name="อัสตูเรียส" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sad%C9%99_%C9%99d%C9%99d" title="Sadə ədəd – อาเซอร์ไบจาน" lang="az" hreflang="az" data-title="Sadə ədəd" data-language-autonym="Azərbaycanca" data-language-local-name="อาเซอร์ไบจาน" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B3%D8%A7%D8%AF%D9%87_%D8%B9%D8%AF%D8%AF" title="ساده عدد – South Azerbaijani" lang="azb" hreflang="azb" data-title="ساده عدد" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%AF%D0%B1%D0%B0%D0%B9_%D2%BB%D0%B0%D0%BD" title="Ябай һан – บัชคีร์" lang="ba" hreflang="ba" data-title="Ябай һан" data-language-autonym="Башҡортса" data-language-local-name="บัชคีร์" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/P%C4%97rm%C4%97nis_skaitlios" title="Pėrmėnis skaitlios – ซาโมจิเตียน" lang="sgs" hreflang="sgs" data-title="Pėrmėnis skaitlios" data-language-autonym="Žemaitėška" data-language-local-name="ซาโมจิเตียน" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%8B_%D0%BB%D1%96%D0%BA" title="Просты лік – เบลารุส" lang="be" hreflang="be" data-title="Просты лік" data-language-autonym="Беларуская" data-language-local-name="เบลารุส" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%8B_%D0%BB%D1%96%D0%BA" title="Просты лік – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Просты лік" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%BE_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Просто число – บัลแกเรีย" lang="bg" hreflang="bg" data-title="Просто число" data-language-autonym="Български" data-language-local-name="บัลแกเรีย" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AE%E0%A7%8C%E0%A6%B2%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="মৌলিক সংখ্যা – บังกลา" lang="bn" hreflang="bn" data-title="মৌলিক সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="บังกลา" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Niver_kentael" title="Niver kentael – เบรตัน" lang="br" hreflang="br" data-title="Niver kentael" data-language-autonym="Brezhoneg" data-language-local-name="เบรตัน" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Prost_broj" title="Prost broj – บอสเนีย" lang="bs" hreflang="bs" data-title="Prost broj" data-language-autonym="Bosanski" data-language-local-name="บอสเนีย" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_primer" title="Nombre primer – คาตาลัน" lang="ca" hreflang="ca" data-title="Nombre primer" data-language-autonym="Català" data-language-local-name="คาตาลัน" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D8%B3%DB%95%D8%B1%DB%95%D8%AA%D8%A7%DB%8C%DB%8C" title="ژمارەی سەرەتایی – เคิร์ดตอนกลาง" lang="ckb" hreflang="ckb" data-title="ژمارەی سەرەتایی" data-language-autonym="کوردی" data-language-local-name="เคิร์ดตอนกลาง" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Prvo%C4%8D%C3%ADslo" title="Prvočíslo – เช็ก" lang="cs" hreflang="cs" data-title="Prvočíslo" data-language-autonym="Čeština" data-language-local-name="เช็ก" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%BD%D1%81%D0%B0%D1%82_%D1%85%D0%B8%D1%81%D0%B5%D0%BF" title="Ансат хисеп – ชูวัช" lang="cv" hreflang="cv" data-title="Ансат хисеп" data-language-autonym="Чӑвашла" data-language-local-name="ชูวัช" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_cysefin" title="Rhif cysefin – เวลส์" lang="cy" hreflang="cy" data-title="Rhif cysefin" data-language-autonym="Cymraeg" data-language-local-name="เวลส์" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Primtal" title="Primtal – เดนมาร์ก" lang="da" hreflang="da" data-title="Primtal" data-language-autonym="Dansk" data-language-local-name="เดนมาร์ก" 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/Primzahl" title="Primzahl – เยอรมัน" lang="de" hreflang="de" data-title="Primzahl" data-language-autonym="Deutsch" data-language-local-name="เยอรมัน" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Amaro_primal" title="Amaro primal – Zazaki" lang="diq" hreflang="diq" data-title="Amaro primal" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CF%8E%CF%84%CE%BF%CF%82_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82" title="Πρώτος αριθμός – กรีก" lang="el" hreflang="el" data-title="Πρώτος αριθμός" data-language-autonym="Ελληνικά" data-language-local-name="กรีก" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/N%C3%B9mer_prim" title="Nùmer prim – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Nùmer prim" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="บทความคุณภาพ"><a href="https://en.wikipedia.org/wiki/Prime_number" title="Prime number – อังกฤษ" lang="en" hreflang="en" data-title="Prime number" data-language-autonym="English" data-language-local-name="อังกฤษ" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Primo" title="Primo – เอสเปรันโต" lang="eo" hreflang="eo" data-title="Primo" data-language-autonym="Esperanto" data-language-local-name="เอสเปรันโต" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es badge-Q17437798 badge-goodarticle mw-list-item" title="บทความคุณภาพ"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_primo" title="Número primo – สเปน" lang="es" hreflang="es" data-title="Número primo" data-language-autonym="Español" data-language-local-name="สเปน" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Algarv" title="Algarv – เอสโตเนีย" lang="et" hreflang="et" data-title="Algarv" data-language-autonym="Eesti" data-language-local-name="เอสโตเนีย" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_lehen" title="Zenbaki lehen – บาสก์" lang="eu" hreflang="eu" data-title="Zenbaki lehen" data-language-autonym="Euskara" data-language-local-name="บาสก์" 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%B9%D8%AF%D8%AF_%D8%A7%D9%88%D9%84" title="عدد اول – เปอร์เซีย" lang="fa" hreflang="fa" data-title="عدد اول" data-language-autonym="فارسی" data-language-local-name="เปอร์เซีย" 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/Alkuluku" title="Alkuluku – ฟินแลนด์" lang="fi" hreflang="fi" data-title="Alkuluku" data-language-autonym="Suomi" data-language-local-name="ฟินแลนด์" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Algarv" title="Algarv – โวโร" lang="vro" hreflang="vro" data-title="Algarv" data-language-autonym="Võro" data-language-local-name="โวโร" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Naba_taumada" title="Naba taumada – ฟิจิ" lang="fj" hreflang="fj" data-title="Naba taumada" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="ฟิจิ" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Primtal" title="Primtal – แฟโร" lang="fo" hreflang="fo" data-title="Primtal" data-language-autonym="Føroyskt" data-language-local-name="แฟโร" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_premier" title="Nombre premier – ฝรั่งเศส" lang="fr" hreflang="fr" data-title="Nombre premier" data-language-autonym="Français" data-language-local-name="ฝรั่งเศส" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Primtaal" title="Primtaal – ฟริเซียนเหนือ" lang="frr" hreflang="frr" data-title="Primtaal" data-language-autonym="Nordfriisk" data-language-local-name="ฟริเซียนเหนือ" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhir_phr%C3%ADomha" title="Uimhir phríomha – ไอริช" lang="ga" hreflang="ga" data-title="Uimhir phríomha" data-language-autonym="Gaeilge" data-language-local-name="ไอริช" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E8%B3%AA%E6%95%B8" title="質數 – จีนกั้น" lang="gan" hreflang="gan" data-title="質數" data-language-autonym="贛語" data-language-local-name="จีนกั้น" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Nonm_pr%C3%A9my%C3%A9" title="Nonm prémyé – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Nonm prémyé" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%BAmero_primo" title="Número primo – กาลิเซีย" lang="gl" hreflang="gl" data-title="Número primo" data-language-autonym="Galego" data-language-local-name="กาลิเซีย" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%B5%E0%AA%BF%E0%AA%AD%E0%AA%BE%E0%AA%9C%E0%AB%8D%E0%AA%AF_%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE" title="અવિભાજ્ય સંખ્યા – คุชราต" lang="gu" hreflang="gu" data-title="અવિભાજ્ય સંખ્યા" data-language-autonym="ગુજરાતી" data-language-local-name="คุชราต" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Helu_kumu" title="Helu kumu – ฮาวาย" lang="haw" hreflang="haw" data-title="Helu kumu" data-language-autonym="Hawaiʻi" data-language-local-name="ฮาวาย" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A8%D7%90%D7%A9%D7%95%D7%A0%D7%99" title="מספר ראשוני – ฮิบรู" lang="he" hreflang="he" data-title="מספר ראשוני" data-language-autonym="עברית" data-language-local-name="ฮิบรู" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%AD%E0%A4%BE%E0%A4%9C%E0%A5%8D%E0%A4%AF_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="अभाज्य संख्या – ฮินดี" lang="hi" hreflang="hi" data-title="अभाज्य संख्या" data-language-autonym="हिन्दी" data-language-local-name="ฮินดี" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Prosti_broj" title="Prosti broj – โครเอเชีย" lang="hr" hreflang="hr" data-title="Prosti broj" data-language-autonym="Hrvatski" data-language-local-name="โครเอเชีย" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Primowa_li%C4%8Dba" title="Primowa ličba – ซอร์เบียตอนบน" lang="hsb" hreflang="hsb" data-title="Primowa ličba" data-language-autonym="Hornjoserbsce" data-language-local-name="ซอร์เบียตอนบน" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Nonm_premye" title="Nonm premye – เฮติครีโอล" lang="ht" hreflang="ht" data-title="Nonm premye" data-language-autonym="Kreyòl ayisyen" data-language-local-name="เฮติครีโอล" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pr%C3%ADmsz%C3%A1mok" title="Prímszámok – ฮังการี" lang="hu" hreflang="hu" data-title="Prímszámok" data-language-autonym="Magyar" data-language-local-name="ฮังการี" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%A1%D6%80%D5%A6_%D5%A9%D5%AB%D5%BE" title="Պարզ թիվ – อาร์เมเนีย" lang="hy" hreflang="hy" data-title="Պարզ թիվ" data-language-autonym="Հայերեն" data-language-local-name="อาร์เมเนีย" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%8A%D5%A1%D6%80%D5%A6_%D5%A9%D5%AB%D6%82" title="Պարզ թիւ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Պարզ թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Numero_prime" title="Numero prime – อินเตอร์ลิงกัว" lang="ia" hreflang="ia" data-title="Numero prime" data-language-autonym="Interlingua" data-language-local-name="อินเตอร์ลิงกัว" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_prima" title="Bilangan prima – อินโดนีเซีย" lang="id" hreflang="id" data-title="Bilangan prima" data-language-autonym="Bahasa Indonesia" data-language-local-name="อินโดนีเซีย" 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/Frumtala" title="Frumtala – ไอซ์แลนด์" lang="is" hreflang="is" data-title="Frumtala" data-language-autonym="Íslenska" data-language-local-name="ไอซ์แลนด์" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it badge-Q17437796 badge-featuredarticle mw-list-item" title="บทความคัดสรร"><a href="https://it.wikipedia.org/wiki/Numero_primo" title="Numero primo – อิตาลี" lang="it" hreflang="it" data-title="Numero primo" data-language-autonym="Italiano" data-language-local-name="อิตาลี" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B4%A0%E6%95%B0" title="素数 – ญี่ปุ่น" lang="ja" hreflang="ja" data-title="素数" data-language-autonym="日本語" data-language-local-name="ญี่ปุ่น" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Praim_nomba" title="Praim nomba – อังกฤษคลีโอลจาเมกา" lang="jam" hreflang="jam" data-title="Praim nomba" data-language-autonym="Patois" data-language-local-name="อังกฤษคลีโอลจาเมกา" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/nalfendi_kacna%27u" title="nalfendi kacna'u – โลชบัน" lang="jbo" hreflang="jbo" data-title="nalfendi kacna'u" data-language-autonym="La .lojban." data-language-local-name="โลชบัน" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Wilangan_prima" title="Wilangan prima – ชวา" lang="jv" hreflang="jv" data-title="Wilangan prima" data-language-autonym="Jawa" data-language-local-name="ชวา" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%A0%E1%83%A2%E1%83%98%E1%83%95%E1%83%98_%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%98" title="მარტივი რიცხვი – จอร์เจีย" lang="ka" hreflang="ka" data-title="მარტივი რიცხვი" data-language-autonym="ქართული" data-language-local-name="จอร์เจีย" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D0%B0%D0%B9_%D1%81%D0%B0%D0%BD" title="Жай сан – คาซัค" lang="kk" hreflang="kk" data-title="Жай сан" data-language-autonym="Қазақша" data-language-local-name="คาซัค" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%94%E1%9E%8B%E1%9E%98" title="ចំនួនបឋម – เขมร" lang="km" hreflang="km" data-title="ចំនួនបឋម" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="เขมร" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%B5%E0%B2%BF%E0%B2%AD%E0%B2%BE%E0%B2%9C%E0%B3%8D%E0%B2%AF_%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B3%86" title="ಅವಿಭಾಜ್ಯ ಸಂಖ್ಯೆ – กันนาดา" lang="kn" hreflang="kn" data-title="ಅವಿಭಾಜ್ಯ ಸಂಖ್ಯೆ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="กันนาดา" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%86%8C%EC%88%98_(%EC%88%98%EB%A1%A0)" title="소수 (수론) – เกาหลี" lang="ko" hreflang="ko" data-title="소수 (수론)" data-language-autonym="한국어" data-language-local-name="เกาหลี" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hejmar%C3%AAn_h%C3%AEm%C3%AE" title="Hejmarên hîmî – เคิร์ด" lang="ku" hreflang="ku" data-title="Hejmarên hîmî" data-language-autonym="Kurdî" data-language-local-name="เคิร์ด" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Pennriv" title="Pennriv – คอร์นิช" lang="kw" hreflang="kw" data-title="Pennriv" data-language-autonym="Kernowek" data-language-local-name="คอร์นิช" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%96%D3%A9%D0%BD%D3%A9%D0%BA%D3%A9%D0%B9_%D1%81%D0%B0%D0%BD" title="Жөнөкөй сан – คีร์กีซ" lang="ky" hreflang="ky" data-title="Жөнөкөй сан" data-language-autonym="Кыргызча" data-language-local-name="คีร์กีซ" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numerus_primus" title="Numerus primus – ละติน" lang="la" hreflang="la" data-title="Numerus primus" data-language-autonym="Latina" data-language-local-name="ละติน" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Primzuel" title="Primzuel – ลักเซมเบิร์ก" lang="lb" hreflang="lb" data-title="Primzuel" data-language-autonym="Lëtzebuergesch" data-language-local-name="ลักเซมเบิร์ก" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Priemgetaal" title="Priemgetaal – ลิมเบิร์ก" lang="li" hreflang="li" data-title="Priemgetaal" data-language-autonym="Limburgs" data-language-local-name="ลิมเบิร์ก" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo badge-Q17437796 badge-featuredarticle mw-list-item" title="บทความคัดสรร"><a href="https://lmo.wikipedia.org/wiki/Numer_primm" title="Numer primm – ลอมบาร์ด" lang="lmo" hreflang="lmo" data-title="Numer primm" data-language-autonym="Lombard" data-language-local-name="ลอมบาร์ด" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%95%E0%BA%BB%E0%BA%A7%E0%BB%80%E0%BA%A5%E0%BA%81%E0%BA%AB%E0%BA%BC%E0%BA%B1%E0%BA%81" title="ຕົວເລກຫຼັກ – ลาว" lang="lo" hreflang="lo" data-title="ຕົວເລກຫຼັກ" data-language-autonym="ລາວ" data-language-local-name="ลาว" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Pirminis_skai%C4%8Dius" title="Pirminis skaičius – ลิทัวเนีย" lang="lt" hreflang="lt" data-title="Pirminis skaičius" data-language-autonym="Lietuvių" data-language-local-name="ลิทัวเนีย" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Pirmskaitlis" title="Pirmskaitlis – ลัตเวีย" lang="lv" hreflang="lv" data-title="Pirmskaitlis" data-language-autonym="Latviešu" data-language-local-name="ลัตเวีย" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Isa_tsy_azo_tsinjaraina" title="Isa tsy azo tsinjaraina – มาลากาซี" lang="mg" hreflang="mg" data-title="Isa tsy azo tsinjaraina" data-language-autonym="Malagasy" data-language-local-name="มาลากาซี" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82_%D0%B1%D1%80%D0%BE%D1%98" title="Прост број – มาซิโดเนีย" lang="mk" hreflang="mk" data-title="Прост број" data-language-autonym="Македонски" data-language-local-name="มาซิโดเนีย" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%AD%E0%B4%BE%E0%B4%9C%E0%B5%8D%E0%B4%AF%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF" title="അഭാജ്യസംഖ്യ – มาลายาลัม" lang="ml" hreflang="ml" data-title="അഭാജ്യസംഖ്യ" data-language-autonym="മലയാളം" data-language-local-name="มาลายาลัม" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D0%BD%D1%85%D0%BD%D1%8B_%D1%82%D0%BE%D0%BE" title="Анхны тоо – มองโกเลีย" lang="mn" hreflang="mn" data-title="Анхны тоо" data-language-autonym="Монгол" data-language-local-name="มองโกเลีย" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AE%E0%A5%82%E0%A4%B3_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="मूळ संख्या – มราฐี" lang="mr" hreflang="mr" data-title="मूळ संख्या" data-language-autonym="मराठी" data-language-local-name="มราฐี" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Nombor_perdana" title="Nombor perdana – มาเลย์" lang="ms" hreflang="ms" data-title="Nombor perdana" data-language-autonym="Bahasa Melayu" data-language-local-name="มาเลย์" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Numru_l-ewwel" title="Numru l-ewwel – มอลตา" lang="mt" hreflang="mt" data-title="Numru l-ewwel" data-language-autonym="Malti" data-language-local-name="มอลตา" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%AF%E1%80%92%E1%80%B9%E1%80%93%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8" title="သုဒ္ဓကိန်း – พม่า" lang="my" hreflang="my" data-title="သုဒ္ဓကိန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="พม่า" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Primtall" title="Primtall – เยอรมันต่ำ" lang="nds" hreflang="nds" data-title="Primtall" data-language-autonym="Plattdüütsch" data-language-local-name="เยอรมันต่ำ" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%87%E0%A4%AE_%E0%A4%B8%E0%A4%99%E0%A5%8D%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="प्राइम सङ्ख्या – เนปาล" lang="ne" hreflang="ne" data-title="प्राइम सङ्ख्या" data-language-autonym="नेपाली" data-language-local-name="เนปาล" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Priemgetal" title="Priemgetal – ดัตช์" lang="nl" hreflang="nl" data-title="Priemgetal" data-language-autonym="Nederlands" data-language-local-name="ดัตช์" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Primtal" title="Primtal – นอร์เวย์นีนอสก์" lang="nn" hreflang="nn" data-title="Primtal" data-language-autonym="Norsk nynorsk" data-language-local-name="นอร์เวย์นีนอสก์" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Primtall" title="Primtall – นอร์เวย์บุคมอล" lang="nb" hreflang="nb" data-title="Primtall" data-language-autonym="Norsk bokmål" data-language-local-name="นอร์เวย์บุคมอล" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nombre_primi%C3%A8r" title="Nombre primièr – อ็อกซิตัน" lang="oc" hreflang="oc" data-title="Nombre primièr" data-language-autonym="Occitan" data-language-local-name="อ็อกซิตัน" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AE%E0%AD%8C%E0%AC%B3%E0%AC%BF%E0%AC%95_%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE" title="ମୌଳିକ ସଂଖ୍ୟା – โอดิยา" lang="or" hreflang="or" data-title="ମୌଳିକ ସଂଖ୍ୟା" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="โอดิยา" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%AD%E0%A8%BE%E0%A8%9C_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86" title="ਅਭਾਜ ਸੰਖਿਆ – ปัญจาบ" lang="pa" hreflang="pa" data-title="ਅਭਾਜ ਸੰਖਿਆ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="ปัญจาบ" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_pierwsze" title="Liczby pierwsze – โปแลนด์" lang="pl" hreflang="pl" data-title="Liczby pierwsze" data-language-autonym="Polski" data-language-local-name="โปแลนด์" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/N%C3%B9mer_prim" title="Nùmer prim – พีดมอนต์" lang="pms" hreflang="pms" data-title="Nùmer prim" data-language-autonym="Piemontèis" data-language-local-name="พีดมอนต์" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%BE%D8%B1%D8%A7%D8%A6%D9%85_%D9%86%D9%85%D8%A8%D8%B1" title="پرائم نمبر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="پرائم نمبر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_primo" title="Número primo – โปรตุเกส" lang="pt" hreflang="pt" data-title="Número primo" data-language-autonym="Português" data-language-local-name="โปรตุเกส" 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/Num%C4%83r_prim" title="Număr prim – โรมาเนีย" lang="ro" hreflang="ro" data-title="Număr prim" data-language-autonym="Română" data-language-local-name="โรมาเนีย" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Простое число – รัสเซีย" lang="ru" hreflang="ru" data-title="Простое число" data-language-autonym="Русский" data-language-local-name="รัสเซีย" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Простое число – ซาคา" lang="sah" hreflang="sah" data-title="Простое число" data-language-autonym="Саха тыла" data-language-local-name="ซาคา" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmuru_primu" title="Nùmmuru primu – ซิซิลี" lang="scn" hreflang="scn" data-title="Nùmmuru primu" data-language-autonym="Sicilianu" data-language-local-name="ซิซิลี" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Prost_broj" title="Prost broj – เซอร์โบ-โครเอเชีย" lang="sh" hreflang="sh" data-title="Prost broj" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="เซอร์โบ-โครเอเชีย" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Am%E1%B8%8Dan_amnzu" title="Amḍan amnzu – ทาเชลีห์ท" lang="shi" hreflang="shi" data-title="Amḍan amnzu" data-language-autonym="Taclḥit" data-language-local-name="ทาเชลีห์ท" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%AE%E0%B6%B8%E0%B6%9A_%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F" title="ප්‍රථමක සංඛ්‍යා – สิงหล" lang="si" hreflang="si" data-title="ප්‍රථමක සංඛ්‍යා" data-language-autonym="සිංහල" data-language-local-name="สิงหล" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Prime_number" title="Prime number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Prime number" 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/Prvo%C4%8D%C3%ADslo" title="Prvočíslo – สโลวัก" lang="sk" hreflang="sk" data-title="Prvočíslo" data-language-autonym="Slovenčina" data-language-local-name="สโลวัก" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pra%C5%A1tevilo" title="Praštevilo – สโลวีเนีย" lang="sl" hreflang="sl" data-title="Praštevilo" data-language-autonym="Slovenščina" data-language-local-name="สโลวีเนีย" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Thiin_mutuxan" title="Thiin mutuxan – โซมาลี" lang="so" hreflang="so" data-title="Thiin mutuxan" data-language-autonym="Soomaaliga" data-language-local-name="โซมาลี" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numri_i_thjesht%C3%AB" title="Numri i thjeshtë – แอลเบเนีย" lang="sq" hreflang="sq" data-title="Numri i thjeshtë" data-language-autonym="Shqip" data-language-local-name="แอลเบเนีย" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82_%D0%B1%D1%80%D0%BE%D1%98" title="Прост број – เซอร์เบีย" lang="sr" hreflang="sr" data-title="Прост број" data-language-autonym="Српски / srpski" data-language-local-name="เซอร์เบีย" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Primtal" title="Primtal – สวีเดน" lang="sv" hreflang="sv" data-title="Primtal" data-language-autonym="Svenska" data-language-local-name="สวีเดน" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Namba_tasa" title="Namba tasa – สวาฮีลี" lang="sw" hreflang="sw" data-title="Namba tasa" data-language-autonym="Kiswahili" data-language-local-name="สวาฮีลี" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Pjyrszo_n%C5%AFmera" title="Pjyrszo nůmera – ไซลีเซีย" lang="szl" hreflang="szl" data-title="Pjyrszo nůmera" data-language-autonym="Ślůnski" data-language-local-name="ไซลีเซีย" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%95%E0%AE%BE_%E0%AE%8E%E0%AE%A3%E0%AF%8D" title="பகா எண் – ทมิฬ" lang="ta" hreflang="ta" data-title="பகா எண்" data-language-autonym="தமிழ்" data-language-local-name="ทมิฬ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B1%8D%E0%B0%B0%E0%B0%A7%E0%B0%BE%E0%B0%A8_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF" title="ప్రధాన సంఖ్య – เตลูกู" lang="te" hreflang="te" data-title="ప్రధాన సంఖ్య" data-language-autonym="తెలుగు" data-language-local-name="เตลูกู" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%B4%D2%B3%D0%BE%D0%B8_%D1%81%D0%BE%D0%B4%D0%B0" title="Ададҳои сода – ทาจิก" lang="tg" hreflang="tg" data-title="Ададҳои сода" data-language-autonym="Тоҷикӣ" data-language-local-name="ทาจิก" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pangunahing_bilang" title="Pangunahing bilang – ตากาล็อก" lang="tl" hreflang="tl" data-title="Pangunahing bilang" data-language-autonym="Tagalog" data-language-local-name="ตากาล็อก" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Asal_say%C4%B1" title="Asal sayı – ตุรกี" lang="tr" hreflang="tr" data-title="Asal sayı" data-language-autonym="Türkçe" data-language-local-name="ตุรกี" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%AA%DB%88%D9%BE_%D8%B3%D8%A7%D9%86" title="تۈپ سان – อุยกูร์" lang="ug" hreflang="ug" data-title="تۈپ سان" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="อุยกูร์" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Просте число – ยูเครน" lang="uk" hreflang="uk" data-title="Просте число" data-language-autonym="Українська" data-language-local-name="ยูเครน" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%81%D8%B1%D8%AF_%D8%B9%D8%AF%D8%AF" title="مفرد عدد – อูรดู" lang="ur" hreflang="ur" data-title="مفرد عدد" data-language-autonym="اردو" data-language-local-name="อูรดู" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tub_son" title="Tub son – อุซเบก" lang="uz" hreflang="uz" data-title="Tub son" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="อุซเบก" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/N%C3%B9maro_primo" title="Nùmaro primo – เวเนโต้" lang="vec" hreflang="vec" data-title="Nùmaro primo" data-language-autonym="Vèneto" data-language-local-name="เวเนโต้" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Palatoi_lugu" title="Palatoi lugu – เวปส์" lang="vep" hreflang="vep" data-title="Palatoi lugu" data-language-autonym="Vepsän kel’" data-language-local-name="เวปส์" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437798 badge-goodarticle mw-list-item" title="บทความคุณภาพ"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_nguy%C3%AAn_t%E1%BB%91" title="Số nguyên tố – เวียดนาม" lang="vi" hreflang="vi" data-title="Số nguyên tố" data-language-autonym="Tiếng Việt" data-language-local-name="เวียดนาม" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Priemgetal" title="Priemgetal – เฟลมิชตะวันตก" lang="vls" hreflang="vls" data-title="Priemgetal" data-language-autonym="West-Vlams" data-language-local-name="เฟลมิชตะวันตก" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Nombe_prum%C3%AE" title="Nombe prumî – วอลลูน" lang="wa" hreflang="wa" data-title="Nombe prumî" data-language-autonym="Walon" data-language-local-name="วอลลูน" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Panguna_nga_ihap" title="Panguna nga ihap – วาเรย์" lang="war" hreflang="war" data-title="Panguna nga ihap" data-language-autonym="Winaray" data-language-local-name="วาเรย์" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B4%A8%E6%95%B0" title="质数 – จีนอู๋" lang="wuu" hreflang="wuu" data-title="质数" data-language-autonym="吴语" data-language-local-name="จีนอู๋" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%AD%D0%BA%D0%BD_%D1%82%D0%BE%D0%B9%D0%B3" title="Экн тойг – คัลมืยค์" lang="xal" hreflang="xal" data-title="Экн тойг" data-language-autonym="Хальмг" data-language-local-name="คัลมืยค์" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%A8%D7%99%D7%9E%D7%A6%D7%90%D7%9C" title="פרימצאל – ยิดดิช" lang="yi" hreflang="yi" data-title="פרימצאל" data-language-autonym="ייִדיש" data-language-local-name="ยิดดิช" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/N%E1%BB%8D%CC%81mb%C3%A0_%C3%A0k%E1%BB%8D%CC%81k%E1%BB%8D%CC%81" title="Nọ́mbà àkọ́kọ́ – โยรูบา" lang="yo" hreflang="yo" data-title="Nọ́mbà àkọ́kọ́" data-language-autonym="Yorùbá" data-language-local-name="โยรูบา" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B4%B0%E2%B5%8E%E2%B4%B9%E2%B4%B0%E2%B5%8F_%E2%B4%B0%E2%B5%8E%E2%B5%8F%E2%B5%A3%E2%B5%93" title="ⴰⵎⴹⴰⵏ ⴰⵎⵏⵣⵓ – ทามาไซต์โมร็อกโกมาตรฐาน" lang="zgh" hreflang="zgh" data-title="ⴰⵎⴹⴰⵏ ⴰⵎⵏⵣⵓ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="ทามาไซต์โมร็อกโกมาตรฐาน" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B4%A8%E6%95%B0" title="质数 – จีน" lang="zh" hreflang="zh" data-title="质数" data-language-autonym="中文" data-language-local-name="จีน" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%B3%AA%E6%95%B8" title="質數 – จีนคลาสสิก" lang="lzh" hreflang="lzh" data-title="質數" data-language-autonym="文言" data-language-local-name="จีนคลาสสิก" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C3%B2%CD%98-s%C3%B2%CD%98" title="Sò͘-sò͘ – จีนมินหนาน" lang="nan" hreflang="nan" data-title="Sò͘-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="จีนมินหนาน" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%B3%AA%E6%95%B8" title="質數 – กวางตุ้ง" lang="yue" hreflang="yue" data-title="質數" data-language-autonym="粵語" data-language-local-name="กวางตุ้ง" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span 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class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">เครื่องมือ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ซ่อน</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="ตัวเลือกเพิ่มเติม" > <div 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class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="รายการหน้าวิกิทุกหน้าที่ลิงก์มาที่นี่ [j]" accesskey="j"><span>หน้าที่ลิงก์มา</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9B%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" rel="nofollow" title="รายการเปลี่ยนแปลงล่าสุดในหน้าที่ลิงก์จากหน้านี้ [k]" accesskey="k"><span>การเปลี่ยนแปลงที่เกี่ยวโยง</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%AD%E0%B8%B1%E0%B8%9B%E0%B9%82%E0%B8%AB%E0%B8%A5%E0%B8%94" title="อัปโหลดไฟล์ [u]" accesskey="u"><span>อัปโหลดไฟล์</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9" title="รายการหน้าพิเศษทั้งหมด [q]" accesskey="q"><span>หน้าพิเศษ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&oldid=11910676" title="ลิงก์ถาวรมารุ่นนี้ของหน้านี้"><span>ลิงก์ถาวร</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=info" title="ข้อมูลเพิ่มเติมเกี่ยวกับหน้านี้"><span>สารสนเทศหน้า</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87&page=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&id=11910676&wpFormIdentifier=titleform" title="สารสนเทศเกี่ยวกับวิธีการอ้างอิงหน้านี้"><span>อ้างอิงบทความนี้</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:UrlShortener&url=https%3A%2F%2Fth.wikipedia.org%2Fwiki%2F%25E0%25B8%2588%25E0%25B8%25B3%25E0%25B8%2599%25E0%25B8%25A7%25E0%25B8%2599%25E0%25B9%2580%25E0%25B8%2589%25E0%25B8%259E%25E0%25B8%25B2%25E0%25B8%25B0"><span>รับยูอาร์แอลแบบสั้น</span></a></li><li id="t-urlshortener-qrcode" 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href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:DownloadAsPdf&page=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=show-download-screen"><span>ดาวน์โหลดเป็น PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&printable=yes" title="รุ่นที่พร้อมพิมพ์ของหน้านี้ [p]" accesskey="p"><span>รุ่นพร้อมพิมพ์</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> ในโครงการอื่น </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Prime_numbers" hreflang="en"><span>วิกิมีเดียคอมมอนส์</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q49008" title="ลิงก์ไปยังสิ่งนี้ในคลังซึ่งเชื่อมโยงข้อมูลต่าง ๆ เข้าด้วยกัน [g]" accesskey="g"><span>สิ่งนี้ในวิกิสนเทศ</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="หน้าเครื่องมือ"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">หน้าตา</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ซ่อน</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">จากวิกิพีเดีย สารานุกรมเสรี</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="th" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Primes-vs-composites.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Primes-vs-composites.svg/220px-Primes-vs-composites.svg.png" decoding="async" width="220" height="309" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Primes-vs-composites.svg/330px-Primes-vs-composites.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Primes-vs-composites.svg/440px-Primes-vs-composites.svg.png 2x" data-file-width="468" data-file-height="658" /></a><figcaption><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%81%E0%B8%AD%E0%B8%9A" title="จำนวนประกอบ">จำนวนประกอบ</a>สามารถสร้างเป็นสี่เหลี่ยมผืนผ้าที่ทุกด้านยาวมากกว่า 1 ได้ แต่<a class="mw-selflink selflink">จำนวนเฉพาะ</a>ทำไม่ได้</figcaption></figure> <p>ใน<a href="/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="คณิตศาสตร์">คณิตศาสตร์</a> <b>จำนวนเฉพาะ</b> (<a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%AD%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B8%A4%E0%B8%A9" title="ภาษาอังกฤษ">อังกฤษ</a>: <span lang="en">prime number</span>) คือ <a href="/wiki/%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%E0%B8%9A%E0%B8%A7%E0%B8%81" class="mw-redirect" title="จำนวนเต็มบวก">จำนวนเต็มบวก</a>ที่มากกว่า 1 และมี<a href="/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%AB%E0%B8%B2%E0%B8%A3" title="ตัวหาร">ตัวหาร</a>ที่เป็นบวกอยู่ 2 ตัว คือ 1 กับตัวมันเอง ตรงข้ามกับ<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%81%E0%B8%AD%E0%B8%9A" title="จำนวนประกอบ">จำนวนประกอบ</a> </p><p>ลำดับของจำนวนเฉพาะเริ่มต้นด้วย </p> <dl><dd><dl><dd><a href="/wiki/2" title="2">2</a>, <a href="/wiki/3" title="3">3</a>, <a href="/wiki/5" title="5">5</a>, <a href="/wiki/7" title="7">7</a>, <a href="/wiki/11" title="11">11</a>, <a href="/wiki/13" title="13">13</a>, <a href="/wiki/17" title="17">17</a>, <a href="/wiki/19" title="19">19</a>, <a href="/wiki/23" title="23">23</a>, <a href="/wiki/29" title="29">29</a>, <a href="/wiki/31" title="31">31</a>, <a href="/wiki/37" title="37">37</a>, <a href="/wiki/41" title="41">41</a>, <a href="/wiki/43" title="43">43</a>, <a href="/wiki/47" title="47">47</a>, <a href="/wiki/53" title="53">53</a>, <a href="/wiki/59" title="59">59</a>, <a href="/wiki/61" title="61">61</a>, <a href="/wiki/67" title="67">67</a>, <a href="/wiki/71" title="71">71</a>, <a href="/wiki/73" title="73">73</a>, <a href="/wiki/79" title="79">79</a>, <a href="/wiki/83" title="83">83</a>, <a href="/wiki/89" title="89">89</a>, <a href="/wiki/97" title="97">97</a>, <a href="/wiki/101" title="101">101</a>, <a href="/wiki/103" title="103">103</a>, <a href="/wiki/107" title="107">107</a>, <a href="/wiki/109" title="109">109</a>, <a href="/wiki/113" title="113">113</a>, <a href="/w/index.php?title=127_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="127 ตัวเลข (ไม่มีหน้านี้)">127</a>, <a href="/w/index.php?title=131_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="131 ตัวเลข (ไม่มีหน้านี้)">131</a>, <a href="/w/index.php?title=137_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="137 ตัวเลข (ไม่มีหน้านี้)">137</a>, <a href="/w/index.php?title=139_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="139 ตัวเลข (ไม่มีหน้านี้)">139</a>, <a href="/w/index.php?title=149_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="149 ตัวเลข (ไม่มีหน้านี้)">149</a>, <a href="/w/index.php?title=151_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="151 ตัวเลข (ไม่มีหน้านี้)">151</a>, <a href="/w/index.php?title=157_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="157 ตัวเลข (ไม่มีหน้านี้)">157</a>, <a href="/w/index.php?title=163_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="163 ตัวเลข (ไม่มีหน้านี้)">163</a>, <a href="/w/index.php?title=167_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="167 ตัวเลข (ไม่มีหน้านี้)">167</a>, <a href="/w/index.php?title=173_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="173 ตัวเลข (ไม่มีหน้านี้)">173</a>, <a href="/w/index.php?title=179_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="179 ตัวเลข (ไม่มีหน้านี้)">179</a>, <a href="/w/index.php?title=181_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="181 ตัวเลข (ไม่มีหน้านี้)">181</a>, <a href="/w/index.php?title=191_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="191 ตัวเลข (ไม่มีหน้านี้)">191</a>, <a href="/w/index.php?title=193_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="193 ตัวเลข (ไม่มีหน้านี้)">193</a>, <a href="/w/index.php?title=197_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="197 ตัวเลข (ไม่มีหน้านี้)">197</a>, <a href="/w/index.php?title=199_%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82&action=edit&redlink=1" class="new" title="199 ตัวเลข (ไม่มีหน้านี้)">199</a>, ... (ลำดับ <span class="nowrap"><span typeof="mw:File"><a href="/wiki/%E0%B8%AA%E0%B8%B2%E0%B8%A3%E0%B8%B2%E0%B8%99%E0%B8%B8%E0%B8%81%E0%B8%A3%E0%B8%A1%E0%B8%AD%E0%B8%AD%E0%B8%99%E0%B9%84%E0%B8%A5%E0%B8%99%E0%B9%8C%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A5%E0%B8%B3%E0%B8%94%E0%B8%B1%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="OEIS"><img alt="OEIS" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556" /></a></span> <a href="//oeis.org/A000040" class="extiw" title="oeis:A000040">A000040</a>)</span></dd></dl></dd></dl> <style data-mw-deduplicate="TemplateStyles:r9751016">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">บทความหลัก: <a href="/wiki/%E0%B8%A3%E0%B8%B2%E0%B8%A2%E0%B8%8A%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="รายชื่อจำนวนเฉพาะ">รายชื่อจำนวนเฉพาะ</a></div> <p>ในเดือนธันวาคม พ.ศ. 2561 มีข่าว<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B2%E0%B8%81%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%AA%E0%B8%B8%E0%B8%94%E0%B9%80%E0%B8%97%E0%B9%88%E0%B8%B2%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%A1%E0%B8%B5%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%84%E0%B9%89%E0%B8%99%E0%B8%9E%E0%B8%9A" title="จำนวนเฉพาะที่มากที่สุดเท่าที่มีการค้นพบ">จำนวนเฉพาะที่มากที่สุดเท่าที่มีการค้นพบ</a> ซึ่งมีความยาว 24,862,048 หลัก<sup id="cite_ref-GIMPS-2018_1-0" class="reference"><a href="#cite_note-GIMPS-2018-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="การแทนจำนวนธรรมชาติ_ด้วยผลคูณของจำนวนเฉพาะ"><span id=".E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B9.81.E0.B8.97.E0.B8.99.E0.B8.88.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.99.E0.B8.98.E0.B8.A3.E0.B8.A3.E0.B8.A1.E0.B8.8A.E0.B8.B2.E0.B8.95.E0.B8.B4_.E0.B8.94.E0.B9.89.E0.B8.A7.E0.B8.A2.E0.B8.9C.E0.B8.A5.E0.B8.84.E0.B8.B9.E0.B8.93.E0.B8.82.E0.B8.AD.E0.B8.87.E0.B8.88.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.99.E0.B9.80.E0.B8.89.E0.B8.9E.E0.B8.B2.E0.B8.B0"></span>การแทนจำนวนธรรมชาติ ด้วยผลคูณของจำนวนเฉพาะ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=1" title="แก้ไขส่วน: การแทนจำนวนธรรมชาติ ด้วยผลคูณของจำนวนเฉพาะ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%A1%E0%B8%B9%E0%B8%A5%E0%B8%90%E0%B8%B2%E0%B8%99%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="ทฤษฎีบทมูลฐานของเลขคณิต">ทฤษฎีบทมูลฐานของเลขคณิต</a>กล่าวว่า จำนวนเต็มบวกทุกตัวสามารถเขียนได้ในรูปผลคูณของจำนวนเฉพาะ และเขียนได้แบบเดียวเท่านั้น จำนวนเฉพาะเป็นเหมือน "บล็อกก่อสร้าง" ของจำนวนธรรมชาติ ตัวอย่างเช่น </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 23244=2^{2}\times 3\times 13\times 149}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>23244</mn> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>×</mo> <mn>3</mn> <mo>×</mo> <mn>13</mn> <mo>×</mo> <mn>149</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 23244=2^{2}\times 3\times 13\times 149}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33fbb9a7115201dfdcfa0216c868b3985e40cda0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:26.623ex; height:2.676ex;" alt="{\displaystyle 23244=2^{2}\times 3\times 13\times 149}"></span></dd></dl> <p>ไม่ว่าเราจะแยกตัวประกอบของ 23244 แบบใดโดยไม่คำนึงถึงลำดับของตัวประกอบแล้ว มันก็จะไม่ต่างไปจากนี้ </p> <div class="mw-heading mw-heading2"><h2 id="สมบัติมูลฐาน"><span id=".E0.B8.AA.E0.B8.A1.E0.B8.9A.E0.B8.B1.E0.B8.95.E0.B8.B4.E0.B8.A1.E0.B8.B9.E0.B8.A5.E0.B8.90.E0.B8.B2.E0.B8.99"></span>สมบัติมูลฐาน</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=2" title="แก้ไขส่วน: สมบัติมูลฐาน"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="การแยกตัวประกอบได้อย่างเดียว"><span id=".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.B9.84.E0.B8.94.E0.B9.89.E0.B8.AD.E0.B8.A2.E0.B9.88.E0.B8.B2.E0.B8.87.E0.B9.80.E0.B8.94.E0.B8.B5.E0.B8.A2.E0.B8.A7"></span>การแยกตัวประกอบได้อย่างเดียว</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=3" title="แก้ไขส่วน: การแยกตัวประกอบได้อย่างเดียว"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>ถ้า <i>p</i> เป็นจำนวนเฉพาะ และ <i>p</i> หาร <i>ab</i> ลงตัวแล้ว <i>p</i> หาร <i>a</i> ลงตัว หรือ <i>p</i> หาร <i>b</i> ลงตัว ประพจน์นี้พิสูจน์โดยยุคลิด และมีชื่อเรียกว่า <i>บทตั้งของยุคลิด</i> ใช้ในการพิสูจน์เรื่องการแยกตัวประกอบได้อย่างเดียว</li></ul> <style data-mw-deduplicate="TemplateStyles:r10224066">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style><table class="box-โครงส่วน plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span"><b>ส่วนนี้รอเพิ่มเติมข้อมูล</b> <small>คุณสามารถช่วย<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=">เพิ่มข้อมูลส่วนนี้</a>ได้</small></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="การมีอยู่นับไม่ถ้วน"><span id=".E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B8.A1.E0.B8.B5.E0.B8.AD.E0.B8.A2.E0.B8.B9.E0.B9.88.E0.B8.99.E0.B8.B1.E0.B8.9A.E0.B9.84.E0.B8.A1.E0.B9.88.E0.B8.96.E0.B9.89.E0.B8.A7.E0.B8.99"></span>การมีอยู่นับไม่ถ้วน</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=4" title="แก้ไขส่วน: การมีอยู่นับไม่ถ้วน"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9751016"><div role="note" class="hatnote navigation-not-searchable">บทความหลัก: <a href="/w/index.php?title=%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%A5%E0%B8%B4%E0%B8%94&action=edit&redlink=1" class="new" title="ทฤษฎีบทของยุคลิด (ไม่มีหน้านี้)">ทฤษฎีบทของยุคลิด</a></div> <p>มีจำนวนเฉพาะอยู่มากมายนับไม่ถ้วน ข้อเท็จจริงนี้พร้อมบทพิสูจน์ปรากฏเป็นครั้งแรกในหนังสือ <i>Elements</i> โดย<a href="/wiki/%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%A5%E0%B8%B4%E0%B8%94" title="ยุคลิด">ยุคลิด</a> จึงได้ชื่อว่า<a href="/w/index.php?title=%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%A5%E0%B8%B4%E0%B8%94&action=edit&redlink=1" class="new" title="ทฤษฎีบทของยุคลิด (ไม่มีหน้านี้)">ทฤษฎีบทของยุคลิด</a> </p><p>บทพิสูจน์ของยุคลิดนั้นเริ่มต้นโดยพิสูจน์ว่า<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> รายการจำกัด <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_{1},p_{2},\dotsc ,p_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1814990dc41b9a4f88835d4ccd79a152469f4324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:13.137ex; height:2.009ex;" alt="{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}"></span> ของจำนวนเฉพาะใด ๆ จะมีจำนวนเฉพาะอื่นที่ไม่อยู่ในลำดับนี้ แนวคิดหลักของบทพิสูจน์นี้คือ คูณจำนวนเฉพาะ <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_{1},p_{2},\dotsc ,p_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1814990dc41b9a4f88835d4ccd79a152469f4324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:13.137ex; height:2.009ex;" alt="{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}"></span> ในรายการทุกตัวเข้าด้วยกัน แล้วบวกหนึ่งให้กับผลคูณที่ได้ ซึ่งจะได้เป็นจำนวนใหม่ </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 N=p_{1}\cdot p_{2}\dotsb p_{n}+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=p_{1}\cdot p_{2}\dotsb p_{n}+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de737aae89369a6b2de9873b610861b770d3fdd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:21.177ex; height:2.509ex;" alt="{\displaystyle N=p_{1}\cdot p_{2}\dotsb p_{n}+1}"></span></dd></dl> <p>โดย<a href="/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%AB%E0%B8%A5%E0%B8%B1%E0%B8%81%E0%B8%A1%E0%B8%B9%E0%B8%A5%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" class="mw-redirect" title="ทฤษฎีบทหลักมูลของเลขคณิต">ทฤษฎีบทหลักมูลของเลขคณิต</a> จะได้ว่าจำนวนนี้ต้องแยกตัวประกอบเป็นผลคูณของจำนวนเฉพาะได้ </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 N=q_{1}\cdot q_{2}\dotsb q_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⋯</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=q_{1}\cdot q_{2}\dotsb q_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/827802acd97b67eecddb749a11ec7a5d57535c83" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.233ex; height:2.509ex;" alt="{\displaystyle N=q_{1}\cdot q_{2}\dotsb q_{m}}"></span></dd></dl> <p>(<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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> อาจะมีตัวประกอบเป็นจำนวนเฉพาะตัวเดียวหรือหลายตัวก็ได้ และตัวประกอบเฉพาะเหล่านั้นอาจซ้ำกันก็ได้) แต่เนื่องจากจำนวนเฉพาะใด ๆ ในรายการ <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_{1},p_{2},\dotsc ,p_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1814990dc41b9a4f88835d4ccd79a152469f4324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:13.137ex; height:2.009ex;" alt="{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}"></span> เมื่อนำไปหาร <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> แล้วจะหารไม่ลงตัวเสมอ ดังนั้น ตัวประกอบเฉพาะ <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 q_{1},q_{2}\dotsc ,q_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>…</mo> <mo>,</mo> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{1},q_{2}\dotsc ,q_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16272c8e3873916e3527d425a2b6af2932cffa45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.46ex; height:2.009ex;" alt="{\displaystyle q_{1},q_{2}\dotsc ,q_{m}}"></span> ของ <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> ต้องเป็นจำนวนเฉพาะอื่นนอกเหนือจากในรายการ <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_{1},p_{2},\dotsc ,p_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1814990dc41b9a4f88835d4ccd79a152469f4324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:13.137ex; height:2.009ex;" alt="{\displaystyle p_{1},p_{2},\dotsc ,p_{n}}"></span> จึงทำให้ได้ทันทีว่า มีจำนวนเฉพาะอยู่เป็นอนันต์ </p><p>นอกจากบทพิสูจน์ของยูคลิดแล้ว ยังมีบทพิสูจน์ว่าจำนวนเฉพาะมีเป็นอนันต์ในแบบอื่น ๆ อีก เช่น บทพิสูจน์ของ<a href="/wiki/%E0%B9%80%E0%B8%A5%E0%B8%AD%E0%B8%AD%E0%B8%99%E0%B8%AE%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%94_%E0%B8%AD%E0%B8%AD%E0%B8%A2%E0%B9%80%E0%B8%A5%E0%B8%AD%E0%B8%A3%E0%B9%8C" class="mw-redirect" title="เลออนฮาร์ด ออยเลอร์">ออยเลอร์</a>โดยใช้วิธีการทาง<a href="/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A7%E0%B8%B4%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B2%E0%B8%B0%E0%B8%AB%E0%B9%8C" title="คณิตวิเคราะห์">คณิตวิเคราะห์</a> บทพิสูจน์ของ<a href="/w/index.php?title=%E0%B8%84%E0%B8%A3%E0%B8%B4%E0%B8%AA%E0%B9%80%E0%B8%95%E0%B8%B5%E0%B8%A2%E0%B8%99_%E0%B8%81%E0%B9%87%E0%B8%AD%E0%B8%A5%E0%B8%97%E0%B9%8C%E0%B8%9A%E0%B8%B1%E0%B8%84&action=edit&redlink=1" class="new" title="คริสเตียน ก็อลท์บัค (ไม่มีหน้านี้)">คริสเตียน ก็อลท์บัค</a>โดยอาศัย<a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%81%E0%B8%9F%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%B2" title="จำนวนแฟร์มา">จำนวนแฟร์มา</a><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> บทพิสูจน์เชิง<a href="/wiki/%E0%B8%97%E0%B8%AD%E0%B8%9E%E0%B8%AD%E0%B9%82%E0%B8%A5%E0%B8%A2%E0%B8%B5" title="ทอพอโลยี">ทอพอโลยี</a>ของ<a href="/w/index.php?title=%E0%B8%AE%E0%B8%B4%E0%B8%A5%E0%B9%81%E0%B8%A5%E0%B8%A5_%E0%B8%9F%E0%B8%B1%E0%B8%A7%E0%B8%A3%E0%B9%8C%E0%B8%97%E0%B8%AA%E0%B9%80%E0%B8%95%E0%B8%99%E0%B9%81%E0%B8%9A%E0%B8%A3%E0%B9%8C%E0%B8%81&action=edit&redlink=1" class="new" title="ฮิลแลล ฟัวร์ทสเตนแบร์ก (ไม่มีหน้านี้)">ฮิลแลล ฟัวร์ทสเตนแบร์ก</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> และบทพิสูจน์ของ<a href="/w/index.php?title=%E0%B9%80%E0%B8%AD%E0%B8%B4%E0%B8%A3%E0%B9%8C%E0%B8%99%E0%B8%AA%E0%B9%8C_%E0%B8%84%E0%B8%B8%E0%B8%A1%E0%B9%80%E0%B8%A1%E0%B8%AD%E0%B8%A3%E0%B9%8C&action=edit&redlink=1" class="new" title="เอิร์นส์ คุมเมอร์ (ไม่มีหน้านี้)">เอิร์นส์ คุมเมอร์</a><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> <div class="mw-heading mw-heading3"><h3 id="การหาจำนวนเฉพาะ"><span id=".E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B8.AB.E0.B8.B2.E0.B8.88.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.99.E0.B9.80.E0.B8.89.E0.B8.9E.E0.B8.B2.E0.B8.B0"></span>การหาจำนวนเฉพาะ</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=5" title="แก้ไขส่วน: การหาจำนวนเฉพาะ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9751016"><div role="note" class="hatnote navigation-not-searchable">บทความหลัก: <a href="/wiki/%E0%B8%8A%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%A7%E0%B9%88%E0%B8%B2%E0%B8%87%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" title="ช่องว่างจำนวนเฉพาะ">ช่องว่างจำนวนเฉพาะ</a></div> <p><a href="/wiki/%E0%B8%95%E0%B8%B0%E0%B9%81%E0%B8%81%E0%B8%A3%E0%B8%87%E0%B9%80%E0%B8%AD%E0%B8%A3%E0%B8%B2%E0%B8%97%E0%B8%AD%E0%B8%AA%E0%B9%80%E0%B8%97%E0%B8%99%E0%B8%B5%E0%B8%AA" class="mw-redirect" title="ตะแกรงเอราทอสเทนีส">ตะแกรงเอราทอสเทนีส</a> และ <a href="/w/index.php?title=%E0%B8%95%E0%B8%B0%E0%B9%81%E0%B8%81%E0%B8%A3%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87_Atkin&action=edit&redlink=1" class="new" title="ตะแกรงของ Atkin (ไม่มีหน้านี้)">ตะแกรงของ Atkin</a> เป็นวิธีที่ใช้สร้างรายการจำนวนเฉพาะทั้งหมดตามจำนวนที่กำหนดอย่างรวดเร็ว </p><p>ในทางปฏิบัติ เราต้องการตรวจสอบว่าเลขที่กำหนดให้ว่าเป็นจำนวนเฉพาะหรือไม่ มากกว่าจะสร้างรายการจำนวนเฉพาะทั้งหมดขึ้นมา ซึ่งวิธีที่ทดสอบ จะให้คำตอบด้วย<a href="/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%99%E0%B9%88%E0%B8%B2%E0%B8%88%E0%B8%B0%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99" title="ความน่าจะเป็น">ความน่าจะเป็น</a> เราสามารถตรวจสอบเลขที่มีขนาดใหญ่ (มี 1 พันหลักขึ้นไป) ว่าเป็นจำนวนเฉพาะหรือไม่ได้อย่างรวดเร็ว โดยใช้<a href="/w/index.php?title=%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%97%E0%B8%94%E0%B8%AA%E0%B8%AD%E0%B8%9A%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%9B%E0%B9%87%E0%B8%99%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&redlink=1" class="new" title="การทดสอบความเป็นจำนวนเฉพาะ (ไม่มีหน้านี้)">การทดสอบความเป็นจำนวนเฉพาะ</a>ด้วยความน่าจะเป็น (probabilistic primality tests) ซึ่งวิธีนี้ จะต้องทำการสุ่มตัวเลขขึ้นมาตัวหนึ่ง เรียกว่า "พยาน" (witness) และใช้สูตรที่เกี่ยวข้องกับพยาน และจำนวนเฉพาะ <i>N</i> ทำการทดสอบ หลังจากที่ทดสอบไปหลายรอบ เราจะตอบได้ว่า <i>N</i> เป็น "จำนวนประกอบอย่างแน่นอน" หรือ <i>N</i> "อาจเป็นจำนวนเฉพาะ" วิธีทดสอบไม่สามารถให้คำตอบได้ว่าเป็นจำนวนเฉพาะอย่างแน่นอนหรือไม่ การทดสอบบางครั้ง เมื่อใส่จำนวนประกอบลงไป ก็ให้คำตอบว่า "อาจเป็นจำนวนเฉพาะ" เสมอ ไม่ว่าจะเลือกพยานตัวใดก็ตาม จำนวนเหล่านี้เรียกว่า <a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0%E0%B9%80%E0%B8%97%E0%B8%B5%E0%B8%A2%E0%B8%A1&action=edit&redlink=1" class="new" title="จำนวนเฉพาะเทียม (ไม่มีหน้านี้)">จำนวนเฉพาะเทียม</a> (pseudoprimes) สำหรับการทดสอบ </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10224066"><table class="box-โครงส่วน plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span"><b>ส่วนนี้รอเพิ่มเติมข้อมูล</b> <small>คุณสามารถช่วย<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=">เพิ่มข้อมูลส่วนนี้</a>ได้</small></div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="สมบัติเชิงวิเคราะห์"><span id=".E0.B8.AA.E0.B8.A1.E0.B8.9A.E0.B8.B1.E0.B8.95.E0.B8.B4.E0.B9.80.E0.B8.8A.E0.B8.B4.E0.B8.87.E0.B8.A7.E0.B8.B4.E0.B9.80.E0.B8.84.E0.B8.A3.E0.B8.B2.E0.B8.B0.E0.B8.AB.E0.B9.8C"></span>สมบัติเชิงวิเคราะห์</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=6" title="แก้ไขส่วน: สมบัติเชิงวิเคราะห์"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="พีชคณิตนามธรรม"><span id=".E0.B8.9E.E0.B8.B5.E0.B8.8A.E0.B8.84.E0.B8.93.E0.B8.B4.E0.B8.95.E0.B8.99.E0.B8.B2.E0.B8.A1.E0.B8.98.E0.B8.A3.E0.B8.A3.E0.B8.A1"></span>พีชคณิตนามธรรม</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=7" title="แก้ไขส่วน: พีชคณิตนามธรรม"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด"><span id=".E0.B8.AA.E0.B8.B2.E0.B8.82.E0.B8.B2.E0.B9.80.E0.B8.A5.E0.B8.82.E0.B8.84.E0.B8.93.E0.B8.B4.E0.B8.95.E0.B8.A1.E0.B8.AD.E0.B8.94.E0.B8.B8.E0.B8.A5.E0.B8.B2.E0.B8.A3.E0.B9.8C.E0.B9.81.E0.B8.A5.E0.B8.B0.E0.B8.9F.E0.B8.B5.E0.B8.A5.E0.B8.94.E0.B9.8C.E0.B8.88.E0.B8.B3.E0.B8.81.E0.B8.B1.E0.B8.94"></span>สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=8" title="แก้ไขส่วน: สาขาเลขคณิตมอดุลาร์และฟีลด์จำกัด"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>ถ้า <i>p</i> เป็นจำนวนเฉพาะ และ <i>a</i> เป็นจำนวนเต็มใดๆแล้ว <i>a</i><sup><i>p</i></sup> − <i>a</i> หารด้วย <i>p</i> ลงตัว (<a href="/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%99%E0%B9%89%E0%B8%AD%E0%B8%A2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%81%E0%B8%9F%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%B2%E0%B8%95%E0%B9%8C" class="mw-redirect" title="ทฤษฎีบทน้อยของแฟร์มาต์">ทฤษฎีบทน้อยของแฟร์มาต์</a>)</li> <li>จำนวนเต็ม <i>p</i> > 1 เป็นจำนวนเฉพาะ ก็ต่อเมื่อ (<i>p</i> − 1) ! + 1 หารด้วย <i>p</i> ลงตัว (<a href="/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A7%E0%B8%B4%E0%B8%A5%E0%B8%AA%E0%B8%B1%E0%B8%99" title="ทฤษฎีบทของวิลสัน">ทฤษฎีบทของวิลสัน</a>) ยิ่งไปกว่านั้น จำนวนเต็ม <i>n</i> > 4 เป็นจำนวนประกอบ ก็ต่อเมื่อ (<i>n</i>− 1) ! หารด้วย <i>n</i> ลงตัว</li></ul> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10224066"><table class="box-โครงส่วน plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span"><b>ส่วนนี้รอเพิ่มเติมข้อมูล</b> <small>คุณสามารถช่วย<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=">เพิ่มข้อมูลส่วนนี้</a>ได้</small></div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="การประยุกต์"><span id=".E0.B8.81.E0.B8.B2.E0.B8.A3.E0.B8.9B.E0.B8.A3.E0.B8.B0.E0.B8.A2.E0.B8.B8.E0.B8.81.E0.B8.95.E0.B9.8C"></span>การประยุกต์</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=9" title="แก้ไขส่วน: การประยุกต์"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>จำนวนเฉพาะที่มีขนาดใหญ่มาก (ใหญ่กว่า 10<sup>100</sup>) นำไปใช้ประโยชน์ในขั้นตอนวิธี<a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%97%E0%B8%A2%E0%B8%B2%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%82%E0%B9%89%E0%B8%B2%E0%B8%A3%E0%B8%AB%E0%B8%B1%E0%B8%AA%E0%B8%A5%E0%B8%B1%E0%B8%9A" class="mw-redirect" title="วิทยาการเข้ารหัสลับ">เข้ารหัสลับแบบกุญแจสาธารณะ</a> นอกจากนี้ยังใช้ใน<a href="/wiki/%E0%B8%95%E0%B8%B2%E0%B8%A3%E0%B8%B2%E0%B8%87%E0%B9%81%E0%B8%AE%E0%B8%8A" title="ตารางแฮช">ตารางแฮช</a> (hash tables) และ<a href="/w/index.php?title=%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%AA%E0%B8%B8%E0%B9%88%E0%B8%A1%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B9%80%E0%B8%97%E0%B8%B5%E0%B8%A2%E0%B8%A1&action=edit&redlink=1" class="new" title="เครื่องสุ่มเลขเทียม (ไม่มีหน้านี้)">เครื่องสุ่มเลขเทียม</a> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10224066"><table class="box-โครงส่วน plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span"><b>ส่วนนี้รอเพิ่มเติมข้อมูล</b> <small>คุณสามารถช่วย<a class="external text" href="https://th.wikipedia.org/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=">เพิ่มข้อมูลส่วนนี้</a>ได้</small></div></td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="ดูเพิ่ม"><span id=".E0.B8.94.E0.B8.B9.E0.B9.80.E0.B8.9E.E0.B8.B4.E0.B9.88.E0.B8.A1"></span>ดูเพิ่ม</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=10" title="แก้ไขส่วน: ดูเพิ่ม"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9E%E0%B8%B4%E0%B8%AA%E0%B8%B9%E0%B8%88%E0%B8%99%E0%B9%8C%E0%B8%A7%E0%B9%88%E0%B8%B2%E0%B8%9C%E0%B8%A5%E0%B8%A3%E0%B8%A7%E0%B8%A1%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B8%81%E0%B8%A5%E0%B8%B1%E0%B8%9A%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0%E0%B8%97%E0%B8%B1%E0%B9%89%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%94%E0%B8%A5%E0%B8%B9%E0%B9%88%E0%B8%AD%E0%B8%AD%E0%B8%81&action=edit&redlink=1" class="new" title="การพิสูจน์ว่าผลรวมของส่วนกลับของจำนวนเฉพาะทั้งหมดลู่ออก (ไม่มีหน้านี้)">การพิสูจน์ว่าผลรวมของส่วนกลับของจำนวนเฉพาะทั้งหมดลู่ออก</a></li> <li><a href="/w/index.php?title=%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9E%E0%B8%B4%E0%B8%AA%E0%B8%B9%E0%B8%88%E0%B8%99%E0%B9%8C%E0%B8%AA%E0%B8%B9%E0%B8%95%E0%B8%A3%E0%B8%9C%E0%B8%A5%E0%B8%84%E0%B8%B9%E0%B8%93%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%AD%E0%B8%AD%E0%B8%A2%E0%B9%80%E0%B8%A5%E0%B8%AD%E0%B8%A3%E0%B9%8C%E0%B8%AA%E0%B8%B3%E0%B8%AB%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99%E0%B8%8B%E0%B8%B5%E0%B8%95%E0%B8%B2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A3%E0%B8%B5%E0%B8%A1%E0%B8%B1%E0%B8%99%E0%B8%99%E0%B9%8C&action=edit&redlink=1" class="new" title="การพิสูจน์สูตรผลคูณของออยเลอร์สำหรับฟังก์ชันซีตาของรีมันน์ (ไม่มีหน้านี้)">การพิสูจน์สูตรผลคูณของออยเลอร์สำหรับฟังก์ชันซีตาของรีมันน์</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="อ้างอิง"><span id=".E0.B8.AD.E0.B9.89.E0.B8.B2.E0.B8.87.E0.B8.AD.E0.B8.B4.E0.B8.87"></span>อ้างอิง</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=11" title="แก้ไขส่วน: อ้างอิง"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-GIMPS-2018-1"><span class="mw-cite-backlink"><a href="#cite_ref-GIMPS-2018_1-0">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r10205087">.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 a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),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 a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),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:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.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}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/press/M82589933.html">"GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1"</a>. <i>Mersenne Research, Inc</i>. 21 December 2018<span class="reference-accessdate">. สืบค้นเมื่อ <span class="nowrap">21 December</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=Mersenne+Research%2C+Inc.&rft.atitle=GIMPS+Project+Discovers+Largest+Known+Prime+Number%3A+2%3Csup%3E82%2C589%2C933%3C%2Fsup%3E-1&rft.date=2018-12-21&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM82589933.html&rfr_id=info%3Asid%2Fth.wikipedia.org%3A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10205087"><cite class="citation book cs1"><i>Euclid's Elements : all thirteen books complete in one volume : the Thomas L. Heath translation</i>. Santa Fe, N.M.: Green Lion Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B9%81%E0%B8%AB%E0%B8%A5%E0%B9%88%E0%B8%87%E0%B8%AB%E0%B8%99%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B7%E0%B8%AD/9781888009194" title="พิเศษ:แหล่งหนังสือ/9781888009194"><bdi>9781888009194</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Euclid%27s+Elements+%3A+all+thirteen+books+complete+in+one+volume+%3A+the+Thomas+L.+Heath+translation&rft.place=Santa+Fe%2C+N.M.&rft.pub=Green+Lion+Press&rft.isbn=9781888009194&rfr_id=info%3Asid%2Fth.wikipedia.org%3A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.math.dartmouth.edu/~euler/correspondence/letters/OO0722.pdf">จดหมาย</a> จากก็อลท์บัคถึงออยเลอร์, กรกฎาคม ค.ศ. 1730.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10205087"><cite id="CITEREFFurstenberg1955" class="citation journal cs1">Furstenberg, Harry (May 1955). "On the Infinitude of Primes". <i>The American Mathematical Monthly</i>. <b>62</b> (5): 353. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2307043">10.2307/2307043</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0002-9890">0002-9890</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=On+the+Infinitude+of+Primes&rft.volume=62&rft.issue=5&rft.pages=353&rft.date=1955-05&rft_id=info%3Adoi%2F10.2307%2F2307043&rft.issn=0002-9890&rft.aulast=Furstenberg&rft.aufirst=Harry&rfr_id=info%3Asid%2Fth.wikipedia.org%3A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r10205087"><cite id="CITEREFRibenboim" class="citation book cs1">Ribenboim, Paulo. <i>The little book of bigger primes</i> (2nd ed.). New York: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B9%81%E0%B8%AB%E0%B8%A5%E0%B9%88%E0%B8%87%E0%B8%AB%E0%B8%99%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B7%E0%B8%AD/978-0-387-20169-6" title="พิเศษ:แหล่งหนังสือ/978-0-387-20169-6"><bdi>978-0-387-20169-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+little+book+of+bigger+primes&rft.place=New+York&rft.edition=2nd&rft.pub=Springer&rft.isbn=978-0-387-20169-6&rft.aulast=Ribenboim&rft.aufirst=Paulo&rfr_id=info%3Asid%2Fth.wikipedia.org%3A%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="แหล่งข้อมูลอื่น"><span id=".E0.B9.81.E0.B8.AB.E0.B8.A5.E0.B9.88.E0.B8.87.E0.B8.82.E0.B9.89.E0.B8.AD.E0.B8.A1.E0.B8.B9.E0.B8.A5.E0.B8.AD.E0.B8.B7.E0.B9.88.E0.B8.99"></span>แหล่งข้อมูลอื่น</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=12" title="แก้ไขส่วน: แหล่งข้อมูลอื่น"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r10827797">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r9259874">.mw-parser-output .plainlist ul{line-height:inherit;list-style:none none;margin:0}.mw-parser-output .plainlist ul li{margin-bottom:0}body.skin-minerva .mw-parser-output .plainlist ul{list-style:none;padding-left:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">วิกิคำคมมีคำคมเกี่ยวกับ <i><b><a href="https://th.wikiquote.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0" class="extiw" title="q:จำนวนเฉพาะ">จำนวนเฉพาะ</a></b></i></div></div> </div> <ul><li>Caldwell, Chris, The <a href="/w/index.php?title=Prime_Pages&action=edit&redlink=1" class="new" title="Prime Pages (ไม่มีหน้านี้)">Prime Pages</a> at <a rel="nofollow" class="external text" href="http://primes.utm.edu/">primes.utm.edu</a>.</li> <li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/topics/PrimeNumbers.html">Prime Numbers at MathWorld</a></li> <li><a rel="nofollow" class="external text" href="http://www.quikstream.com.au/primenumbers.html">Prime sequencing technologies</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080413141436/http://www.quikstream.com.au/primenumbers.html">เก็บถาวร</a> 2008-04-13 ที่ <a href="/wiki/%E0%B9%80%E0%B8%A7%E0%B8%A2%E0%B9%8C%E0%B9%81%E0%B8%9A%E0%B9%87%E0%B8%81%E0%B9%81%E0%B8%A1%E0%B8%8A%E0%B8%8A%E0%B8%B5%E0%B8%99" title="เวย์แบ็กแมชชีน">เวย์แบ็กแมชชีน</a></li> <li><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/Prime_numbers.html">MacTutor history of prime numbers</a></li> <li><a rel="nofollow" class="external text" href="http://www.primepuzzles.net/">The prime puzzles</a></li> <li><a rel="nofollow" class="external text" href="http://aleph0.clarku.edu/~djoyce/java/elements/bookIX/propIX20.html">An English translation of Euclid's proof that there are infinitely many primes</a></li> <li><a rel="nofollow" class="external text" href="http://www.numberspiral.com/index.html">Number Spiral with prime patterns</a></li> <li><a rel="nofollow" class="external text" href="http://www.maths.ex.ac.uk/~mwatkins/zeta/vardi.html">An Introduction to Analytic Number Theory, by Ilan Vardi and Cyril Banderier</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060925090553/http://www.maths.ex.ac.uk/~mwatkins/zeta/vardi.html">เก็บถาวร</a> 2006-09-25 ที่ <a href="/wiki/%E0%B9%80%E0%B8%A7%E0%B8%A2%E0%B9%8C%E0%B9%81%E0%B8%9A%E0%B9%87%E0%B8%81%E0%B9%81%E0%B8%A1%E0%B8%8A%E0%B8%8A%E0%B8%B5%E0%B8%99" title="เวย์แบ็กแมชชีน">เวย์แบ็กแมชชีน</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040604053354/http://www.eff.org/awards/coop.php">EFF Cooperative Computing Awards</a></li> <li><i><a rel="nofollow" class="external text" href="http://demonstrations.wolfram.com/WhyANumberIsPrime/">Why a Number Is Prime</a></i> by Enrique Zeleny, <a href="/w/index.php?title=The_Wolfram_Demonstrations_Project&action=edit&redlink=1" class="new" title="The Wolfram Demonstrations Project (ไม่มีหน้านี้)">The Wolfram Demonstrations Project</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="คำนวณและสร้างจำนวนเฉพาะ"><span id=".E0.B8.84.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.93.E0.B9.81.E0.B8.A5.E0.B8.B0.E0.B8.AA.E0.B8.A3.E0.B9.89.E0.B8.B2.E0.B8.87.E0.B8.88.E0.B8.B3.E0.B8.99.E0.B8.A7.E0.B8.99.E0.B9.80.E0.B8.89.E0.B8.9E.E0.B8.B2.E0.B8.B0"></span>คำนวณและสร้างจำนวนเฉพาะ</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%89%E0%B8%9E%E0%B8%B2%E0%B8%B0&action=edit&section=13" title="แก้ไขส่วน: คำนวณและสร้างจำนวนเฉพาะ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.numberempire.com/primenumbers.php">Online Prime Number Generator and Checker</a> - instantly checks and finds prime numbers up to 128 digits long (does NOT require Java or Javascript)</li> <li><a rel="nofollow" class="external text" href="http://www.easycalculation.com/prime-number.php">Prime number calculator</a> — Check prime number, and find next largest and next smallest prime numbers (requires Javascript).</li> <li><a rel="nofollow" class="external text" href="https://www.alpertron.com.ar/ECM.HTM">Fast Online primality test — Dario Alpern's personal site</a> – Makes use of the Elliptic Curve Method (up to thousands digits numbers check!, requires Java)</li> <li><a rel="nofollow" class="external text" href="http://publicliterature.org/tools/prime_number_generator">Prime Number Generator</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090814005741/http://publicliterature.org/tools/prime_number_generator/">เก็บถาวร</a> 2009-08-14 ที่ <a href="/wiki/%E0%B9%80%E0%B8%A7%E0%B8%A2%E0%B9%8C%E0%B9%81%E0%B8%9A%E0%B9%87%E0%B8%81%E0%B9%81%E0%B8%A1%E0%B8%8A%E0%B8%8A%E0%B8%B5%E0%B8%99" title="เวย์แบ็กแมชชีน">เวย์แบ็กแมชชีน</a> — Generates a given number of primes above a given start number.</li> <li><a rel="nofollow" class="external text" href="http://wims.unice.fr/wims/wims.cgi?module=tool/number/primes.en">Primes</a> from WIMS is an online prime generator.</li> <li><a rel="nofollow" class="external text" href="http://www.bigprimes.net/archive/prime.php">Huge database of prime numbers</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r10552737">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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id="เซตจำนวนเต็มตามคุณสมบัติหารลงตัว" style="font-size:114%;margin:0 4em">เซตจำนวนเต็มตามคุณสมบัติหารลงตัว</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">รูปแบบ<a href="/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" title="การแยกตัวประกอบ">การแยกตัวประกอบ</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">จำนวนเฉพาะ</a></li> <li><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%81%E0%B8%AD%E0%B8%9A" title="จำนวนประกอบ">จำนวนประกอบ</a></li> <li><a href="/w/index.php?title=Powerful_number&action=edit&redlink=1" class="new" title="Powerful number (ไม่มีหน้านี้)">Powerful number</a></li> <li><a href="/w/index.php?title=Square-free_number&action=edit&redlink=1" class="new" title="Square-free number (ไม่มีหน้านี้)">Square-free number</a></li> <li><a href="/w/index.php?title=Achilles_number&action=edit&redlink=1" class="new" title="Achilles number (ไม่มีหน้านี้)">Achilles number</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Lattice_of_the_divisibility_of_60.svg" class="mw-file-description" title="Divisibility of 60"><img alt="Divisibility of 60" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/175px-Lattice_of_the_divisibility_of_60.svg.png" decoding="async" width="175" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/263px-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/350px-Lattice_of_the_divisibility_of_60.svg.png 2x" data-file-width="313" data-file-height="250" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E0%B8%9C%E0%B8%A5%E0%B8%9A%E0%B8%A7%E0%B8%81" class="mw-redirect" title="ผลบวก">ผลบวก</a>ตัวหารตามเงื่อนไข</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%AA%E0%B8%A1%E0%B8%9A%E0%B8%B9%E0%B8%A3%E0%B8%93%E0%B9%8C" title="จำนวนสมบูรณ์">จำนวนสมบูรณ์</a></li> <li><a href="/w/index.php?title=Almost_perfect_number&action=edit&redlink=1" class="new" title="Almost perfect number (ไม่มีหน้านี้)">Almost perfect number</a></li> <li><a href="/w/index.php?title=Quasiperfect_number&action=edit&redlink=1" class="new" title="Quasiperfect number (ไม่มีหน้านี้)">Quasiperfect number</a></li> <li><a href="/w/index.php?title=Multiply_perfect_number&action=edit&redlink=1" class="new" title="Multiply perfect number (ไม่มีหน้านี้)">Multiply perfect number</a></li> <li><a href="/w/index.php?title=Hyperperfect_number&action=edit&redlink=1" class="new" title="Hyperperfect number (ไม่มีหน้านี้)">Hyperperfect number</a></li> <li><a href="/w/index.php?title=Unitary_perfect_number&action=edit&redlink=1" class="new" title="Unitary perfect number (ไม่มีหน้านี้)">Unitary perfect number</a></li> <li><a href="/w/index.php?title=Semiperfect_number&action=edit&redlink=1" class="new" title="Semiperfect number (ไม่มีหน้านี้)">Semiperfect number</a></li> <li><a href="/w/index.php?title=Primitive_semiperfect_number&action=edit&redlink=1" class="new" title="Primitive semiperfect number (ไม่มีหน้านี้)">Primitive semiperfect number</a></li> <li><a href="/w/index.php?title=Practical_number&action=edit&redlink=1" class="new" title="Practical number (ไม่มีหน้านี้)">Practical number</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">เปรียบเทียบผลบวกตัวหาร</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%81%E0%B8%B4%E0%B8%99&action=edit&redlink=1" class="new" title="จำนวนเกิน (ไม่มีหน้านี้)">จำนวนเกิน</a></li> <li><a href="/w/index.php?title=Highly_abundant_number&action=edit&redlink=1" class="new" title="Highly abundant number (ไม่มีหน้านี้)">Highly abundant number</a></li> <li><a href="/w/index.php?title=Superabundant_number&action=edit&redlink=1" class="new" title="Superabundant number (ไม่มีหน้านี้)">Superabundant number</a></li> <li><a href="/w/index.php?title=Colossally_abundant_number&action=edit&redlink=1" class="new" title="Colossally abundant number (ไม่มีหน้านี้)">Colossally abundant number</a></li> <li><a href="/w/index.php?title=Highly_composite_number&action=edit&redlink=1" class="new" title="Highly composite number (ไม่มีหน้านี้)">Highly composite number</a></li> <li><a href="/w/index.php?title=Superior_highly_composite_number&action=edit&redlink=1" class="new" title="Superior highly composite number (ไม่มีหน้านี้)">Superior highly composite number</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">อื่น ๆ</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9E%E0%B8%A3%E0%B9%88%E0%B8%AD%E0%B8%87&action=edit&redlink=1" class="new" title="จำนวนพร่อง (ไม่มีหน้านี้)">จำนวนพร่อง</a></li> <li><a href="/w/index.php?title=Weird_number&action=edit&redlink=1" class="new" title="Weird number (ไม่มีหน้านี้)">Weird number</a></li> <li><a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%A1%E0%B8%B4%E0%B8%95%E0%B8%A3" title="จำนวนเชิงมิตร">จำนวนเชิงมิตร</a></li> <li><a href="/w/index.php?title=Friendly_number&action=edit&redlink=1" class="new" title="Friendly number (ไม่มีหน้านี้)">Friendly number</a></li> <li><a href="/w/index.php?title=Sociable_number&action=edit&redlink=1" class="new" title="Sociable number (ไม่มีหน้านี้)">Sociable number</a></li> <li><a href="/w/index.php?title=Solitary_number&action=edit&redlink=1" class="new" title="Solitary number (ไม่มีหน้านี้)">Solitary number</a></li> <li><a href="/w/index.php?title=Sublime_number&action=edit&redlink=1" class="new" title="Sublime number (ไม่มีหน้านี้)">Sublime number</a></li> <li><a href="/w/index.php?title=Harmonic_divisor_number&action=edit&redlink=1" class="new" title="Harmonic divisor number (ไม่มีหน้านี้)">Harmonic divisor number</a></li> <li><a href="/w/index.php?title=Frugal_number&action=edit&redlink=1" class="new" title="Frugal number (ไม่มีหน้านี้)">Frugal number</a></li> <li><a href="/w/index.php?title=Equidigital_number&action=edit&redlink=1" class="new" title="Equidigital 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