@mhg/blog
Version:
1 lines • 170 kB
HTML
<!DOCTYPE html><html lang="zh-Hans"><head hexo-theme="https://github.com/volantis-x/hexo-theme-volantis/#6.0.3"><meta name="generator" content="Hexo 8.1.2"><meta name="Volantis" content="6.0.3"><meta charset="utf-8"><meta name="robots" content="index,follow,max-image-preview:large"><link rel="canonical" href="https://blog.mhuig.top/notes/Zeta/10"><meta http-equiv="x-dns-prefetch-control" content="on"><link rel="dns-prefetch" href="https://static.mhuig.top"><link rel="preconnect" href="https://static.mhuig.top" crossorigin=""><meta name="renderer" content="webkit"><meta name="force-rendering" content="webkit"><meta http-equiv="X-UA-Compatible" content="IE=Edge,chrome=1"><meta name="HandheldFriendly" content="True"><meta name="mobile-web-app-capable" content="yes"><meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=5"><meta content="black-translucent" name="apple-mobile-web-app-status-bar-style"><meta content="telephone=no" name="format-detection"><script>function registerServiceWorker(e){"localhost"!=window.location.hostname&&"serviceWorker"in navigator&&navigator.serviceWorker.register(`${e}`).then((function(e){"localhost"==window.location.hostname&&(e.onupdatefound=function(){var r=e.installing;r.onstatechange=function(){switch(r.state){case"installed":navigator.serviceWorker.controller?console.log("Updated Service Worker."):console.log("Service Worker Sucess!");break;case"redundant":console.log("The installing service worker became redundant.")}}})})).catch((function(e){console.error("Error during service worker registration:",e),"undefined"==typeof swinstallretry&&(swinstallretry=1,registerServiceWorker("/jquery.js"))}))}registerServiceWorker("/jquery.js")</script><link rel="apple-touch-icon" sizes="180x180" href="/lib/favicon/apple-touch-icon.png"><link rel="icon" type="image/png" sizes="32x32" href="/lib/favicon/favicon-32x32.png"><link rel="icon" type="image/png" sizes="192x192" href="/lib/favicon/android-chrome-192x192.png"><link rel="icon" type="image/png" sizes="144x144" href="/lib/favicon/android-chrome-144x144.png"><link rel="icon" type="image/png" sizes="16x16" href="/lib/favicon/favicon-16x16.png"><link rel="manifest" href="/lib/favicon/site.webmanifest"><link rel="mask-icon" href="/lib/favicon/safari-pinned-tab.svg" color="#5bbad5"><meta name="apple-mobile-web-app-title" content="MHuiG Magicland"><meta name="apple-mobile-web-app-status-bar-style" content="black"><meta name="application-name" content="MHuiG Magicland"><meta name="msapplication-TileColor" content="#87ceeb"><meta name="msapplication-TileImage" content="/lib/favicon/mstile-144x144.png"><meta name="theme-color" content="#87ceeb" media="(prefers-color-scheme: light)"><meta name="theme-color" content="#21232f" media="(prefers-color-scheme: dark)"><link href="/opensearch.xml" rel="search" title="MHuiG Magicland" type="application/opensearchdescription+xml"><link rel="sitemap" type="application/xml" title="MHuiG Blog Site Map" href="https://blog.mhuig.top/sitemap.xml"><link rel="author" href="https://mhuig.top"><meta name="author" content="MHuiG"><meta name="creator" content="MHuiG"><link rel="archives" href="https://blog.mhuig.top/archives/"><link rel="preload" href="/css/style.css" as="style"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="alternate" href="/atom.xml" title="Magicland" type="application/atom+xml"><link rel="alternate" href="/rss2.xml" title="Magicland" type="application/rss+xml"><title>Zeta Archive: 埃拉托斯特尼筛法 - Magicland</title><meta name="keywords" content="数学,Zeta, Math,埃拉托斯特尼筛法,素数识别,算法原理,MHuiG, @MHuiG, Blog, 博客, Magicland, 魔法世界"><meta desc="" name="description" content="该文档详解古希腊数学家埃拉托斯特尼提出的素数识别算法，核心步骤为剔除不大于根号n的素数倍数，以100以内整数为例演示操作过程，通过保留2、3、5、7并删除其倍数得到素数，清晰呈现该经典算法的基本原理。 - MHuiG - Magicland"><meta property="og:type" content="website"><meta property="og:title" content="Magicland"><meta property="og:url" content="https://blog.mhuig.top/notes/Zeta/10"><meta property="og:site_name" content="Magicland"><meta property="og:description" content="该文档详解古希腊数学家埃拉托斯特尼提出的素数识别算法，核心步骤为剔除不大于根号n的素数倍数，以100以内整数为例演示操作过程，通过保留2、3、5、7并删除其倍数得到素数，清晰呈现该经典算法的基本原理。"><meta property="og:locale"><meta property="og:image" content="https://blog.mhuig.top/lib/favicon/android-chrome-192x192.png"><meta property="article:published_time" content="2025-09-15T02:28:00.000Z"><meta property="article:modified_time" content="2025-11-20T10:18:00.000Z"><meta property="article:author" content="MHuiG"><meta property="article:tag" content="Math"><meta property="article:tag" content="埃拉托斯特尼筛法"><meta property="article:tag" content="算法原理"><meta property="article:tag" content="素数识别"><meta name="twitter:card" content="summary"><meta name="twitter:image" content="https://blog.mhuig.top/lib/favicon/android-chrome-192x192.png"><meta name="twitter:creator" content="@iMHuiG"><meta name="twitter:site" content="@iMHuiG"><style>#safearea{display:none}.post-story+.post-story{content-visibility:auto;contain-intrinsic-size:10px 500px}:root{--color-site-body:#87ceeb;--color-site-bg:#87ceeb;--color-site-inner:#555;--color-site-footer:#666;--color-card:#fff;--color-text:#444;--color-block:#f6f6f6;--color-inlinecode:#d56d28;--color-codeblock:#fff7ea;--color-h1:#3a3a3a;--color-h2:#3a3a3a;--color-h3:#333;--color-h4:#444;--color-h5:#555;--color-h6:#666;--color-p:#444;--color-list:#666;--color-list-hl:#1a78c2;--color-meta:#888;--color-read-bkg:#e0d8c8;--color-read-post:#f8f1e2;--color-copyright-bkg:#f5f5f5}*{box-sizing:border-box;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;outline:0;margin:0;padding:0}::-webkit-scrollbar{height:4px;width:4px}::-webkit-scrollbar-track-piece{background:0 0}::-webkit-scrollbar-thumb{background:#2196f3;cursor:pointer;border-radius:2px;-webkit-border-radius:2px}::-webkit-scrollbar-thumb:hover{background:#ff5722}html{color:var(--color-text);width:100%;height:100%;font-family:"Varela Round","PingFang SC","Microsoft YaHei",Helvetica,Arial,Menlo,Monaco,monospace,sans-serif;font-size:16px}html>::-webkit-scrollbar{height:4px;width:4px}html>::-webkit-scrollbar-track-piece{background:0 0}html>::-webkit-scrollbar-thumb{background:#2196f3;cursor:pointer;border-radius:2px;-webkit-border-radius:2px}html>::-webkit-scrollbar-thumb:hover{background:#ff5722}body{background-color:var(--color-site-body);text-rendering:optimizelegibility;-webkit-tap-highlight-color:transparent;line-height:1.6;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}body.modal-active{overflow:hidden}@media screen and (max-width:680px){body.modal-active{position:fixed;top:0;right:0;bottom:0;left:0}}a{color:#2196f3;cursor:pointer;text-decoration:none;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}a:hover{color:#ff5722}a:active,a:hover{outline:0}ol,ul{padding-left:0}ol li,ul li{list-style:none}header{display:-webkit-box;display:-moz-box;display:block}img{border:0;background:0 0;max-width:100%}svg:not(:root){overflow:hidden}hr{-moz-box-sizing:content-box;box-sizing:content-box;-webkit-box-sizing:content-box;-moz-box-sizing:content-box;height:0;border:0;border-radius:1px;-webkit-border-radius:1px;border-bottom:1px solid rgba(68,68,68,.1)}button,input{color:inherit;font:inherit;margin:0}button{overflow:visible;text-transform:none;-webkit-appearance:button;cursor:pointer}@supports (backdrop-filter:blur(20px)){.blur{background:rgba(255,255,255,.9)!important;backdrop-filter:saturate(200%) blur(20px)}}.shadow{box-shadow:0 1px 2px 0 rgba(0,0,0,.1);-webkit-box-shadow:0 1px 2px 0 rgba(0,0,0,.1)}.shadow.floatable{transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}.shadow.floatable:hover{box-shadow:0 2px 4px 0 rgba(0,0,0,.1),0 4px 8px 0 rgba(0,0,0,.1),0 8px 16px 0 rgba(0,0,0,.1);-webkit-box-shadow:0 2px 4px 0 rgba(0,0,0,.1),0 4px 8px 0 rgba(0,0,0,.1),0 8px 16px 0 rgba(0,0,0,.1)}#l_cover{min-height:64px}.cover-wrapper{top:0;left:0;max-width:100%;height:100vh;display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;flex-wrap:nowrap;-webkit-flex-wrap:nowrap;-khtml-flex-wrap:nowrap;-moz-flex-wrap:nowrap;-o-flex-wrap:nowrap;-ms-flex-wrap:nowrap;-webkit-box-direction:normal;-moz-box-direction:normal;-webkit-box-orient:vertical;-moz-box-orient:vertical;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;align-items:center;align-self:center;align-content:center;color:var(--color-site-inner);padding:0 16px;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;position:relative;overflow:hidden;margin-bottom:-100px}.cover-wrapper .cover-bg{position:absolute;width:100%;height:100%;background-position:center;background-size:cover;-webkit-background-size:cover;-moz-background-size:cover}.cover-wrapper .cover-bg.lazyload:not(.loaded){opacity:0;-webkit-opacity:0;-moz-opacity:0}.cover-wrapper .cover-bg.lazyload.loaded{animation-delay:0s;animation-duration:.5s;animation-fill-mode:forwards;animation-timing-function:ease-out;animation-name:fadeIn}@-moz-keyframes fadeIn{0%{opacity:0;-webkit-opacity:0;-moz-opacity:0;filter:blur(12px);transform:scale(1.02);-webkit-transform:scale(1.02);-khtml-transform:scale(1.02);-moz-transform:scale(1.02);-o-transform:scale(1.02);-ms-transform:scale(1.02)}100%{opacity:1;-webkit-opacity:1;-moz-opacity:1}}@-webkit-keyframes fadeIn{0%{opacity:0;-webkit-opacity:0;-moz-opacity:0;filter:blur(12px);transform:scale(1.02);-webkit-transform:scale(1.02);-khtml-transform:scale(1.02);-moz-transform:scale(1.02);-o-transform:scale(1.02);-ms-transform:scale(1.02)}100%{opacity:1;-webkit-opacity:1;-moz-opacity:1}}@-o-keyframes fadeIn{0%{opacity:0;-webkit-opacity:0;-moz-opacity:0;filter:blur(12px);transform:scale(1.02);-webkit-transform:scale(1.02);-khtml-transform:scale(1.02);-moz-transform:scale(1.02);-o-transform:scale(1.02);-ms-transform:scale(1.02)}100%{opacity:1;-webkit-opacity:1;-moz-opacity:1}}@keyframes fadeIn{0%{opacity:0;-webkit-opacity:0;-moz-opacity:0;filter:blur(12px);transform:scale(1.02);-webkit-transform:scale(1.02);-khtml-transform:scale(1.02);-moz-transform:scale(1.02);-o-transform:scale(1.02);-ms-transform:scale(1.02)}100%{opacity:1;-webkit-opacity:1;-moz-opacity:1}}.cover-wrapper .cover-body{z-index:1;position:relative;width:100%;height:100%}.cover-wrapper#full{height:calc(100vh + 100px);padding-bottom:100px}.cover-wrapper#half{max-height:640px;min-height:400px;height:calc(36vh - 64px + 200px)}.cover-wrapper #scroll-down{width:100%;height:64px;position:absolute;bottom:100px;text-align:center;cursor:pointer}.cover-wrapper #scroll-down .scroll-down-effects{color:#fff;font-size:24px;line-height:64px;position:absolute;width:24px;left:calc(50% - 12px);text-shadow:0 1px 2px rgba(0,0,0,.1);animation:scroll-down-effect 1.5s infinite;-webkit-animation:scroll-down-effect 1.5s infinite;-khtml-animation:scroll-down-effect 1.5s infinite;-moz-animation:scroll-down-effect 1.5s infinite;-o-animation:scroll-down-effect 1.5s infinite;-ms-animation:scroll-down-effect 1.5s infinite}@-moz-keyframes scroll-down-effect{0%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}50%{top:-16px;opacity:.4;-webkit-opacity:0.4;-moz-opacity:0.4}100%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}}@-webkit-keyframes scroll-down-effect{0%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}50%{top:-16px;opacity:.4;-webkit-opacity:0.4;-moz-opacity:0.4}100%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}}@-o-keyframes scroll-down-effect{0%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}50%{top:-16px;opacity:.4;-webkit-opacity:0.4;-moz-opacity:0.4}100%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}}@keyframes scroll-down-effect{0%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}50%{top:-16px;opacity:.4;-webkit-opacity:0.4;-moz-opacity:0.4}100%{top:0;opacity:1;-webkit-opacity:1;-moz-opacity:1}}.cover-wrapper .cover-body{margin-top:64px;margin-bottom:100px}.cover-wrapper .cover-body,.cover-wrapper .cover-body .bottom,.cover-wrapper .cover-body .top{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;-webkit-box-direction:normal;-moz-box-direction:normal;-webkit-box-orient:vertical;-moz-box-orient:vertical;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;align-items:center;justify-content:center;-webkit-justify-content:center;-khtml-justify-content:center;-moz-justify-content:center;-o-justify-content:center;-ms-justify-content:center;max-width:100%}.cover-wrapper .cover-body .bottom{margin-top:32px}.cover-wrapper .cover-body .title{font-family:"Varela Round","PingFang SC","Microsoft YaHei",Helvetica,Arial,Helvetica,monospace;font-size:3.125rem;line-height:1.2;text-shadow:0 1px 2px rgba(0,0,0,.1)}.cover-wrapper .cover-body .subtitle{font-size:20px}.cover-wrapper .cover-body .logo{max-height:120px;max-width:calc(100% - 4 * 16px)}@media screen and (min-height:1024px){.cover-wrapper .cover-body .title{font-size:3rem}.cover-wrapper .cover-body .subtitle{font-size:1.05rem}.cover-wrapper .cover-body .logo{max-height:150px}}.cover-wrapper .cover-body .m_search{position:relative;max-width:calc(100% - 16px);width:320px;vertical-align:middle}.cover-wrapper .cover-body .m_search .form{position:relative;display:-webkit-box;display:-moz-box;display:block;width:100%}.cover-wrapper .cover-body .m_search .icon,.cover-wrapper .cover-body .m_search .input{transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}.cover-wrapper .cover-body .m_search .icon{position:absolute;display:-webkit-box;display:-moz-box;display:block;line-height:2.5rem;width:32px;top:0;left:5px;color:rgba(68,68,68,.75)}.cover-wrapper .cover-body .m_search .input{display:-webkit-box;display:-moz-box;display:block;height:2.5rem;width:100%;box-shadow:none;-webkit-box-shadow:none;box-sizing:border-box;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;font-size:.875rem;-webkit-appearance:none;padding-left:36px;border-radius:1.4rem;-webkit-border-radius:1.4rem;background:rgba(255,255,255,.6);backdrop-filter:blur(10px);border:none;color:var(--color-text)}@media screen and (max-width:500px){.cover-wrapper .cover-body .m_search .input{padding-left:36px}}.cover-wrapper .cover-body .m_search .input:hover{background:rgba(255,255,255,.8)}.cover-wrapper .cover-body .m_search .input:focus{background:#fff}.cover-wrapper .list-h{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;-webkit-box-direction:normal;-moz-box-direction:normal;-webkit-box-orient:horizontal;-moz-box-orient:horizontal;-webkit-flex-direction:row;-ms-flex-direction:row;flex-direction:row;flex-wrap:wrap;-webkit-flex-wrap:wrap;-khtml-flex-wrap:wrap;-moz-flex-wrap:wrap;-o-flex-wrap:wrap;-ms-flex-wrap:wrap;align-items:stretch;border-radius:4px;-webkit-border-radius:4px;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none}.cover-wrapper .list-h a{-webkit-box-flex:1;-moz-box-flex:1;-webkit-flex:1 0;-ms-flex:1 0;flex:1 0;display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;font-weight:600}.cover-wrapper .list-h a img{display:-webkit-box;display:-moz-box;display:block;border-radius:2px;-webkit-border-radius:2px;margin:4px;min-width:40px;max-width:44px}@media screen and (max-width:768px){.cover-wrapper .list-h a img{min-width:36px;max-width:40px}}@media screen and (max-width:500px){.cover-wrapper .list-h a img{margin:2px 4px;min-width:32px;max-width:36px}}@media screen and (max-width:375px){.cover-wrapper .list-h a img{min-width:28px;max-width:32px}}.cover-wrapper{max-width:100%}.cover-wrapper.search .bottom .menu{margin-top:16px}.cover-wrapper.search .bottom .menu .list-h a{white-space:nowrap;-webkit-box-direction:normal;-moz-box-direction:normal;-webkit-box-orient:horizontal;-moz-box-orient:horizontal;-webkit-flex-direction:row;-ms-flex-direction:row;flex-direction:row;align-items:baseline;padding:2px;margin:4px;color:var(--color-site-inner);opacity:.75;-webkit-opacity:0.75;-moz-opacity:0.75;text-shadow:0 1px 2px rgba(0,0,0,.05);border-bottom:2px solid transparent}.cover-wrapper.search .bottom .menu .list-h a i{margin-right:4px}.cover-wrapper.search .bottom .menu .list-h a p{font-size:.9375rem}.cover-wrapper.search .bottom .menu .list-h a.active,.cover-wrapper.search .bottom .menu .list-h a:active,.cover-wrapper.search .bottom .menu .list-h a:hover{opacity:1;-webkit-opacity:1;-moz-opacity:1;border-bottom:2px solid var(--color-site-inner)}.cover-wrapper.dock .menu,.cover-wrapper.featured .menu,.cover-wrapper.focus .menu{border-radius:6px;-webkit-border-radius:6px}.cover-wrapper.dock .menu .list-h a,.cover-wrapper.featured .menu .list-h a,.cover-wrapper.focus .menu .list-h a{-webkit-box-direction:normal;-moz-box-direction:normal;-webkit-box-orient:vertical;-moz-box-orient:vertical;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;align-items:center;padding:12px;line-height:24px;border-radius:4px;-webkit-border-radius:4px;border-bottom:none;text-align:center;align-content:flex-end;color:rgba(68,68,68,.7);font-size:1.5rem}@media screen and (max-width:500px){.cover-wrapper.dock .menu .list-h a,.cover-wrapper.featured .menu .list-h a,.cover-wrapper.focus .menu .list-h a{padding:12px 8px}}.cover-wrapper.dock .menu .list-h a i,.cover-wrapper.featured .menu .list-h a i,.cover-wrapper.focus .menu .list-h a i{margin:8px}.cover-wrapper.dock .menu .list-h a p,.cover-wrapper.featured .menu .list-h a p,.cover-wrapper.focus .menu .list-h a p{font-size:.875rem}.cover-wrapper.dock .menu .list-h a.active,.cover-wrapper.featured .menu .list-h a.active,.cover-wrapper.focus .menu .list-h a.active{background:var(--color-card);backdrop-filter:none}.cover-wrapper.dock .menu .list-h a.active i,.cover-wrapper.dock .menu .list-h a.active i+p,.cover-wrapper.featured .menu .list-h a.active i,.cover-wrapper.featured .menu .list-h a.active i+p,.cover-wrapper.focus .menu .list-h a.active i,.cover-wrapper.focus .menu .list-h a.active i+p{color:#2196f3}.cover-wrapper.dock .menu .list-h a.active img+p,.cover-wrapper.featured .menu .list-h a.active img+p,.cover-wrapper.focus .menu .list-h a.active img+p{color:var(--color-text)}.cover-wrapper.dock .menu .list-h a:hover,.cover-wrapper.featured .menu .list-h a:hover,.cover-wrapper.focus .menu .list-h a:hover{background:var(--color-card)}.cover-wrapper.featured .menu .list-h{margin:-2px}.cover-wrapper.featured .menu .list-h a{margin:2px;background:rgba(255,255,255,.5)}@supports (backdrop-filter:blur(20px)){.cover-wrapper.featured .menu .list-h a{background:rgba(255,255,255,.5);backdrop-filter:saturate(200%) blur(20px)}}@media (prefers-color-scheme:dark){:root{--color-mode:'dark'}:root:not([color-scheme]){--color-site-body:#121212;--color-read-bkg:#21232f;--color-read-post:#252d38;--color-site-bg:#21232f;--color-site-inner:#efefef;--color-site-footer:#666;--color-card:#252d38;--color-text:rgba(238,238,238,0.871);--color-block:rgba(68,68,68,0.65);--color-codeblock:#444;--color-inlinecode:#d56d28;--color-h1:rgba(255,255,255,0.871);--color-h2:rgba(255,255,255,0.871);--color-h3:rgba(255,255,255,0.6);--color-h4:rgba(255,255,255,0.6);--color-h5:rgba(255,255,255,0.6);--color-h6:rgba(255,255,255,0.6);--color-p:rgba(217,217,217,0.871);--color-list:rgba(217,217,217,0.871);--color-list-hl:#4dabf5;--color-meta:rgba(191,191,191,0.871);--color-link:rgba(191,191,191,0.871);--color-copyright-bkg:#21252b}:root:not([color-scheme]) img{filter:brightness(70%)!important}:root:not([color-scheme]) .blur{background:rgba(33,35,47,.9)!important}:root:not([color-scheme]) .white-box.blur{background:rgba(37,45,56,.9)!important}:root:not([color-scheme]) .nav-main .u-search-input{background:var(--color-card)!important}:root:not([color-scheme]) #l_main .article .prev-next>a{background:var(--color-block)!important}:root:not([color-scheme]) #l_main .article .prev-next>a:hover{background:var(--color-site-bg)!important}:root:not([color-scheme]) .article blockquote{background:var(--color-block)!important}:root:not([color-scheme]) .article-title a{color:var(--color-h1)!important}:root:not([color-scheme]) details>summary{color:var(--color-p)!important;background:var(--color-site-bg)!important}:root:not([color-scheme]) details{border:1px solid var(--color-site-bg)!important;background:var(--color-site-bg)!important}:root:not([color-scheme]) #u-search .modal,:root:not([color-scheme]) #u-search .modal-body,:root:not([color-scheme]) #u-search .modal-header{background:var(--color-card)!important}:root:not([color-scheme]) #u-search .modal-body .modal-results .result:hover{background:var(--color-block)!important}:root:not([color-scheme]) .u-search-input:hover{background:var(--color-block)!important}:root:not([color-scheme]) .u-search-input:focus{background:var(--color-site-body)!important}}[color-scheme=dark]{--color-site-body:#121212;--color-read-bkg:#21232f;--color-read-post:#252d38;--color-site-bg:#21232f;--color-site-inner:#efefef;--color-site-footer:#666;--color-card:#252d38;--color-text:rgba(238,238,238,0.871);--color-block:rgba(68,68,68,0.65);--color-codeblock:#444;--color-inlinecode:#d56d28;--color-h1:rgba(255,255,255,0.871);--color-h2:rgba(255,255,255,0.871);--color-h3:rgba(255,255,255,0.6);--color-h4:rgba(255,255,255,0.6);--color-h5:rgba(255,255,255,0.6);--color-h6:rgba(255,255,255,0.6);--color-p:rgba(217,217,217,0.871);--color-list:rgba(217,217,217,0.871);--color-list-hl:#4dabf5;--color-meta:rgba(191,191,191,0.871);--color-link:rgba(191,191,191,0.871);--color-copyright-bkg:#21252b}[color-scheme=dark] img{filter:brightness(70%)!important}[color-scheme=dark] .blur{background:rgba(33,35,47,.9)!important}[color-scheme=dark] .white-box.blur{background:rgba(37,45,56,.9)!important}[color-scheme=dark] .nav-main .u-search-input{background:var(--color-card)!important}[color-scheme=dark] #l_main .article .prev-next>a{background:var(--color-block)!important}[color-scheme=dark] #l_main .article .prev-next>a:hover{background:var(--color-site-bg)!important}[color-scheme=dark] .article blockquote{background:var(--color-block)!important}[color-scheme=dark] .article-title a{color:var(--color-h1)!important}[color-scheme=dark] details>summary{color:var(--color-p)!important;background:var(--color-site-bg)!important}[color-scheme=dark] details{border:1px solid var(--color-site-bg)!important;background:var(--color-site-bg)!important}[color-scheme=dark] #u-search .modal,[color-scheme=dark] #u-search .modal-body,[color-scheme=dark] #u-search .modal-header{background:var(--color-card)!important}[color-scheme=dark] #u-search .modal-body .modal-results .result:hover{background:var(--color-block)!important}[color-scheme=dark] .u-search-input:hover{background:var(--color-block)!important}[color-scheme=dark] .u-search-input:focus{background:var(--color-site-body)!important}@media screen and (max-width:500px){[color-scheme=dark] .l_header .m_search{background:var(--color-site-bg)!important}}@font-face{font-family:'Varela Round';src:url("https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf");font-weight:'normal';font-style:'normal';font-display:swap}@font-face{font-family:'Varela Round';src:url("https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf");font-weight:'normal';font-style:'normal';font-display:swap}.l_header{position:fixed;z-index:1000;top:0;width:100%;height:64px;background:var(--color-card);box-shadow:0 1px 2px 0 rgba(0,0,0,.1);-webkit-box-shadow:0 1px 2px 0 rgba(0,0,0,.1)}.l_header.auto{transition:opacity .4s ease;-webkit-transition:opacity .4s ease;-khtml-transition:opacity 0.4s ease;-moz-transition:opacity .4s ease;-o-transition:opacity .4s ease;-ms-transition:opacity .4s ease;visibility:hidden}.l_header.auto.show{opacity:1!important;-webkit-opacity:1!important;-moz-opacity:1!important;visibility:visible}.l_header .container{margin-left:16px;margin-right:16px}.l_header #wrapper{height:100%;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none}.l_header #wrapper .nav-main,.l_header #wrapper .nav-sub{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;flex-wrap:nowrap;-webkit-flex-wrap:nowrap;-khtml-flex-wrap:nowrap;-moz-flex-wrap:nowrap;-o-flex-wrap:nowrap;-ms-flex-wrap:nowrap;justify-content:space-between;-webkit-justify-content:space-between;-khtml-justify-content:space-between;-moz-justify-content:space-between;-o-justify-content:space-between;-ms-justify-content:space-between;align-items:center}.l_header #wrapper .nav-main{transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}.l_header #wrapper.sub .nav-main{transform:translateY(-64px);-webkit-transform:translateY(-64px);-khtml-transform:translateY(-64px);-moz-transform:translateY(-64px);-o-transform:translateY(-64px);-ms-transform:translateY(-64px)}.l_header #wrapper .nav-sub{transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease;opacity:0;-webkit-opacity:0;-moz-opacity:0;height:64px;width:calc(100% - 2 * 16px);position:absolute}.l_header #wrapper .nav-sub ::-webkit-scrollbar{display:-webkit-box;display:-moz-box;display:none}@media screen and (min-width:2048px){.l_header #wrapper .nav-sub{max-width:55vw;margin:auto}}.l_header #wrapper.sub .nav-sub{opacity:1;-webkit-opacity:1;-moz-opacity:1}.l_header #wrapper .title{position:relative;color:var(--color-text);padding-left:24px;max-height:64px}.l_header #wrapper .nav-main .title{white-space:nowrap;overflow:hidden;text-overflow:ellipsis;flex-shrink:0;line-height:64px;padding:0 24px;font-size:1.25rem;font-family:"Varela Round","PingFang SC","Microsoft YaHei",Helvetica,Arial,Helvetica,monospace}.l_header #wrapper .nav-main .title img{height:64px}.l_header .nav-sub{max-width:1080px;margin:auto}.l_header .nav-sub .title{font-weight:700;font-family:"Varela Round","PingFang SC","Microsoft YaHei",Helvetica,Arial,Menlo,Monaco,monospace,sans-serif;line-height:1.2;max-height:64px;white-space:normal;flex-shrink:1}.l_header .switcher{display:-webkit-box;display:-moz-box;display:none;line-height:64px;align-items:center}.l_header .switcher .s-toc{display:-webkit-box;display:-moz-box;display:none}@media screen and (max-width:768px){.l_header .switcher .s-toc{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex}}.l_header .switcher>li{height:48px;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease;margin:2px}@media screen and (max-width:500px){.l_header .switcher>li{margin:0 1px;height:48px}}.l_header .switcher>li>a{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;justify-content:center;-webkit-justify-content:center;-khtml-justify-content:center;-moz-justify-content:center;-o-justify-content:center;-ms-justify-content:center;align-items:center;width:48px;height:48px;padding:.85em 1.1em;border-radius:100px;-webkit-border-radius:100px;border:none;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease;color:#2196f3}.l_header .switcher>li>a:hover{border:none}.l_header .switcher>li>a.active,.l_header .switcher>li>a:active{border:none;background:var(--color-site-bg)}@media screen and (max-width:500px){.l_header .switcher>li>a{width:36px;height:48px}}.l_header .nav-sub .switcher{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex}.l_header .m_search{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;height:64px;width:240px;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}@media screen and (max-width:1024px){.l_header .m_search{width:44px;min-width:44px}.l_header .m_search input::placeholder{opacity:0;-webkit-opacity:0;-moz-opacity:0}.l_header .m_search:hover{width:240px}.l_header .m_search:hover input::placeholder{opacity:1;-webkit-opacity:1;-moz-opacity:1}}@media screen and (min-width:500px){.l_header .m_search:hover .input{width:100%}.l_header .m_search:hover .input::placeholder{opacity:1;-webkit-opacity:1;-moz-opacity:1}}@media screen and (max-width:500px){.l_header .m_search{min-width:0}.l_header .m_search input::placeholder{opacity:1;-webkit-opacity:1;-moz-opacity:1}}.l_header .m_search .form{position:relative;display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;width:100%;align-items:center}.l_header .m_search .icon{position:absolute;width:36px;left:5px;color:var(--color-meta)}@media screen and (max-width:500px){.l_header .m_search .icon{display:-webkit-box;display:-moz-box;display:none}}.l_header .m_search .input{display:-webkit-box;display:-moz-box;display:block;padding-top:8px;padding-bottom:8px;line-height:1.3;width:100%;color:var(--color-text);background:#fafafa;box-shadow:none;-webkit-box-shadow:none;box-sizing:border-box;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;padding-left:40px;font-size:.875rem;border-radius:8px;-webkit-border-radius:8px;border:none;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}@media screen and (min-width:500px){.l_header .m_search .input:focus{box-shadow:0 4px 8px 0 rgba(0,0,0,.1);-webkit-box-shadow:0 4px 8px 0 rgba(0,0,0,.1)}}@media screen and (max-width:500px){.l_header .m_search .input{background:var(--color-block);padding-left:8px;border:none}.l_header .m_search .input:focus,.l_header .m_search .input:hover{border:none}}@media (max-width:500px){.l_header .m_search{left:0;width:0;overflow:hidden;position:absolute;background:#fff;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}.l_header .m_search .input{border-radius:32px;-webkit-border-radius:32px;margin-left:16px;padding-left:16px}.l_header.z_search-open .m_search{width:100%}.l_header.z_search-open .m_search .input{width:calc(100% - 120px)}}ul.m-pc>li>a{color:inherit;border-bottom:2px solid transparent}ul.m-pc>li>a.active,ul.m-pc>li>a:active{border-bottom:2px solid #2196f3}ul.list-v li:hover>ul.list-v,ul.m-pc li:hover>ul.list-v{display:-webkit-box;display:-moz-box;display:block}ul.nav-list-h{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;align-items:stretch}ul.nav-list-h>li{position:relative;justify-content:center;-webkit-justify-content:center;-khtml-justify-content:center;-moz-justify-content:center;-o-justify-content:center;-ms-justify-content:center;height:100%;line-height:2.4;border-radius:4px;-webkit-border-radius:4px}ul.nav-list-h>li>a{-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;font-weight:600}ul.list-v{z-index:1;display:-webkit-box;display:-moz-box;display:none;position:absolute;background:var(--color-card);box-shadow:0 2px 4px 0 rgba(0,0,0,.08),0 4px 8px 0 rgba(0,0,0,.08),0 8px 16px 0 rgba(0,0,0,.08);-webkit-box-shadow:0 2px 4px 0 rgba(0,0,0,.08),0 4px 8px 0 rgba(0,0,0,.08),0 8px 16px 0 rgba(0,0,0,.08);margin-top:-6px;border-radius:4px;-webkit-border-radius:4px;padding:8px 0}ul.list-v.show{display:-webkit-box;display:-moz-box;display:block}ul.list-v hr{margin-top:8px;margin-bottom:8px}ul.list-v>li{white-space:nowrap;word-break:keep-all}ul.list-v>li.header{font-size:.78125rem;font-weight:700;line-height:2em;color:var(--color-meta);margin:8px 16px 4px}ul.list-v>li.header i{margin-right:8px}ul.list-v>li ul{margin-left:0;display:-webkit-box;display:-moz-box;display:none;margin-top:-40px}ul.list-v .aplayer-container{min-height:64px;padding:6px 16px}ul.list-v>li>a{transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease;display:-webkit-box;display:-moz-box;display:block;color:var(--color-list);font-size:.875rem;font-weight:700;line-height:36px;padding:0 20px 0 16px;text-overflow:ellipsis;margin:0 4px;border-radius:4px;-webkit-border-radius:4px}@media screen and (max-width:1024px){ul.list-v>li>a{line-height:40px}}ul.list-v>li>a>i{margin-right:8px}ul.list-v>li>a.active,ul.list-v>li>a:active{color:var(--color-list-hl)}ul.list-v>li>a:hover{color:var(--color-list-hl);background:var(--color-site-bg)}.l_header .menu>ul>li>a{display:-webkit-box;display:-moz-box;display:block;padding:0 8px}.l_header .menu>ul>li>a>i{margin-right:4px}.l_header ul.nav-list-h>li{color:var(--color-list);line-height:64px}.l_header ul.nav-list-h>li>a{max-height:64px;overflow:hidden;color:inherit}.l_header ul.nav-list-h>li>a.active,.l_header ul.nav-list-h>li>a:active{color:#2196f3}.l_header ul.nav-list-h>li:hover>a{color:var(--color-list-hl)}.l_header ul.nav-list-h>li i.music{animation:rotate-effect 1.5s linear infinite;-webkit-animation:rotate-effect 1.5s linear infinite;-khtml-animation:rotate-effect 1.5s linear infinite;-moz-animation:rotate-effect 1.5s linear infinite;-o-animation:rotate-effect 1.5s linear infinite;-ms-animation:rotate-effect 1.5s linear infinite}@-moz-keyframes rotate-effect{0%{transform:rotate(0);-webkit-transform:rotate(0);-khtml-transform:rotate(0);-moz-transform:rotate(0);-o-transform:rotate(0);-ms-transform:rotate(0)}25%{transform:rotate(90deg);-webkit-transform:rotate(90deg);-khtml-transform:rotate(90deg);-moz-transform:rotate(90deg);-o-transform:rotate(90deg);-ms-transform:rotate(90deg)}50%{transform:rotate(180deg);-webkit-transform:rotate(180deg);-khtml-transform:rotate(180deg);-moz-transform:rotate(180deg);-o-transform:rotate(180deg);-ms-transform:rotate(180deg)}75%{transform:rotate(270deg);-webkit-transform:rotate(270deg);-khtml-transform:rotate(270deg);-moz-transform:rotate(270deg);-o-transform:rotate(270deg);-ms-transform:rotate(270deg)}100%{transform:rotate(360deg);-webkit-transform:rotate(360deg);-khtml-transform:rotate(360deg);-moz-transform:rotate(360deg);-o-transform:rotate(360deg);-ms-transform:rotate(360deg)}}@-webkit-keyframes rotate-effect{0%{transform:rotate(0);-webkit-transform:rotate(0);-khtml-transform:rotate(0);-moz-transform:rotate(0);-o-transform:rotate(0);-ms-transform:rotate(0)}25%{transform:rotate(90deg);-webkit-transform:rotate(90deg);-khtml-transform:rotate(90deg);-moz-transform:rotate(90deg);-o-transform:rotate(90deg);-ms-transform:rotate(90deg)}50%{transform:rotate(180deg);-webkit-transform:rotate(180deg);-khtml-transform:rotate(180deg);-moz-transform:rotate(180deg);-o-transform:rotate(180deg);-ms-transform:rotate(180deg)}75%{transform:rotate(270deg);-webkit-transform:rotate(270deg);-khtml-transform:rotate(270deg);-moz-transform:rotate(270deg);-o-transform:rotate(270deg);-ms-transform:rotate(270deg)}100%{transform:rotate(360deg);-webkit-transform:rotate(360deg);-khtml-transform:rotate(360deg);-moz-transform:rotate(360deg);-o-transform:rotate(360deg);-ms-transform:rotate(360deg)}}@-o-keyframes rotate-effect{0%{transform:rotate(0);-webkit-transform:rotate(0);-khtml-transform:rotate(0);-moz-transform:rotate(0);-o-transform:rotate(0);-ms-transform:rotate(0)}25%{transform:rotate(90deg);-webkit-transform:rotate(90deg);-khtml-transform:rotate(90deg);-moz-transform:rotate(90deg);-o-transform:rotate(90deg);-ms-transform:rotate(90deg)}50%{transform:rotate(180deg);-webkit-transform:rotate(180deg);-khtml-transform:rotate(180deg);-moz-transform:rotate(180deg);-o-transform:rotate(180deg);-ms-transform:rotate(180deg)}75%{transform:rotate(270deg);-webkit-transform:rotate(270deg);-khtml-transform:rotate(270deg);-moz-transform:rotate(270deg);-o-transform:rotate(270deg);-ms-transform:rotate(270deg)}100%{transform:rotate(360deg);-webkit-transform:rotate(360deg);-khtml-transform:rotate(360deg);-moz-transform:rotate(360deg);-o-transform:rotate(360deg);-ms-transform:rotate(360deg)}}@keyframes rotate-effect{0%{transform:rotate(0);-webkit-transform:rotate(0);-khtml-transform:rotate(0);-moz-transform:rotate(0);-o-transform:rotate(0);-ms-transform:rotate(0)}25%{transform:rotate(90deg);-webkit-transform:rotate(90deg);-khtml-transform:rotate(90deg);-moz-transform:rotate(90deg);-o-transform:rotate(90deg);-ms-transform:rotate(90deg)}50%{transform:rotate(180deg);-webkit-transform:rotate(180deg);-khtml-transform:rotate(180deg);-moz-transform:rotate(180deg);-o-transform:rotate(180deg);-ms-transform:rotate(180deg)}75%{transform:rotate(270deg);-webkit-transform:rotate(270deg);-khtml-transform:rotate(270deg);-moz-transform:rotate(270deg);-o-transform:rotate(270deg);-ms-transform:rotate(270deg)}100%{transform:rotate(360deg);-webkit-transform:rotate(360deg);-khtml-transform:rotate(360deg);-moz-transform:rotate(360deg);-o-transform:rotate(360deg);-ms-transform:rotate(360deg)}}.menu-phone li ul.list-v{right:calc(100% - .5 * 16px)}.menu-phone li ul.list-v ul{right:calc(100% - .5 * 16px)}#wrapper{max-width:1080px;margin:auto}@media screen and (min-width:2048px){#wrapper{max-width:55vw}}#wrapper .menu{-webkit-box-flex:1;-moz-box-flex:1;-webkit-flex:1 1;-ms-flex:1 1;flex:1 1;margin:0 16px 0 0}#wrapper .menu .list-v ul{left:calc(100% - .5 * 16px)}.menu-phone{display:-webkit-box;display:-moz-box;display:none;margin-top:16px;right:8px;transition:all .28s ease;-webkit-transition:all .28s ease;-khtml-transition:all 0.28s ease;-moz-transition:all .28s ease;-o-transition:all .28s ease;-ms-transition:all .28s ease}.menu-phone ul{right:calc(100% - .5 * 16px)}@media screen and (max-width:500px){.menu-phone{display:-webkit-box;display:-moz-box;display:block}}.l_header{max-width:65vw;left:calc((100% - 65vw) * .5);border-bottom-left-radius:8px;border-bottom-right-radius:8px}@media screen and (max-width:2048px){.l_header{max-width:1112px;left:calc((100% - 1112px) * .5)}}@media screen and (max-width:1112px){.l_header{left:0;border-radius:0;-webkit-border-radius:0;max-width:100%}}@media screen and (max-width:500px){.l_header .container{margin-left:0;margin-right:0}.l_header #wrapper .nav-main .title{padding-left:16px;padding-right:16px}.l_header #wrapper .nav-sub{width:100%}.l_header #wrapper .nav-sub .title{overflow-y:scroll;margin-top:2px;padding:8px 16px}.l_header #wrapper .switcher{display:-webkit-box;display:-moz-box;display:-ms-flexbox;display:-webkit-flex;display:flex;display:flex;margin-right:8px}.l_header .menu{display:-webkit-box;display:-moz-box;display:none}}@media screen and (max-width:500px){.list-v li{max-width:270px}}#u-search{display:-webkit-box;display:-moz-box;display:none;position:fixed;top:0;left:0;width:100%;height:100%;padding:60px 20px;z-index:1001}@media screen and (max-width:680px){#u-search{padding:0}}@media screen and (prefers-color-scheme:dark) and (max-width:500px){.l_header .m_search{background:var(--color-site-bg)!important}}.cover-wrapper .cover-body .subtitle{font-size:.875rem}.fa-brands.color-github,.fa-duotone.color-github,.fa-light.color-github,.fa-regular.color-github,.fa-solid.color-github,.fa-thin.color-github,.fa.color-github,.fad.color-github,.fal.color-github,.far.color-github,.fas.color-github,.iziToast>.iziToast-body .iziToast-icon.color-github{color:#000}.fa-brands.color-friends,.fa-duotone.color-friends,.fa-light.color-friends,.fa-regular.color-friends,.fa-solid.color-friends,.fa-thin.color-friends,.fa.color-friends,.fad.color-friends,.fal.color-friends,.far.color-friends,.fas.color-friends,.iziToast>.iziToast-body .iziToast-icon.color-friends{color:#d31ee9}.fa-brands.color-about,.fa-duotone.color-about,.fa-light.color-about,.fa-regular.color-about,.fa-solid.color-about,.fa-thin.color-about,.fa.color-about,.fad.color-about,.fal.color-about,.far.color-about,.fas.color-about,.iziToast>.iziToast-body .iziToast-icon.color-about{color:#0095ff}.fa-brands.color-travellings,.fa-duotone.color-travellings,.fa-light.color-travellings,.fa-regular.color-travellings,.fa-solid.color-travellings,.fa-thin.color-travellings,.fa.color-travellings,.fad.color-travellings,.fal.color-travellings,.far.color-travellings,.fas.color-travellings,.iziToast>.iziToast-body .iziToast-icon.color-travellings{color:#734ae6}mjx-container{padding:0 0!important}mjx-container:not([display=true]){padding:4px 2px 4px 6px!important}mjx-container[jax=SVG]{direction:ltr}mjx-container[jax=SVG]>svg{overflow:visible}mjx-container[jax=SVG][display=true]{display:-webkit-box;display:-moz-box;display:block;text-align:center;margin:1em 0}mjx-container[jax=SVG][justify=left]{text-align:left}mjx-container[jax=SVG][justify=right]{text-align:right}g[data-mml-node=merror]>g{fill:#f00;stroke:#f00}g[data-mml-node=merror]>rect[data-background]{fill:#ff0;stroke:none}g[data-mml-node=mtable]>line[data-line]{stroke-width:70px;fill:none}g[data-mml-node=mtable]>rect[data-frame]{stroke-width:70px;fill:none}g[data-mml-node=mtable]>.mjx-dashed{stroke-dasharray:140}g[data-mml-node=mtable]>.mjx-dotted{stroke-linecap:round;stroke-dasharray:0,140}g[data-mml-node=mtable]>svg{overflow:visible}[jax=SVG] mjx-tool{display:-webkit-box;display:-moz-box;display:inline-block;position:relative;width:0;height:0}[jax=SVG] mjx-tool>mjx-tip{position:absolute;top:0;left:0}mjx-tool>mjx-tip{display:-webkit-box;display:-moz-box;display:inline-block;padding:.2em;border:1px solid #888;font-size:70%;background-color:#f8f8f8;color:#000;box-shadow:2px 2px 5px #aaa;-webkit-box-shadow:2px 2px 5px #aaa}g[data-mml-node=maction][data-toggle]{cursor:pointer}mjx-status{display:-webkit-box;display:-moz-box;display:block;position:fixed;left:1em;bottom:1em;min-width:25%;padding:.2em .4em;border:1px solid #888;font-size:90%;background-color:#f8f8f8;color:#000}foreignObject[data-mjx-xml]{font-family:initial;line-height:normal;overflow:visible}.MathJax path{stroke-width:3}mjx-container[display=true]{overflow:auto hidden}mjx-container[display=true]+br{display:-webkit-box;display:-moz-box;display:none}</style><link rel="stylesheet" href="/css/style.css" media="print" onload='this.media="all",this.onload=null'><noscript><link rel="stylesheet" href="/css/style.css"></noscript><script>let userColorScheme=localStorage.getItem("color-scheme");userColorScheme&&document.documentElement.setAttribute("color-scheme",userColorScheme)</script><script>window.MSInputMethodContext&&document.documentMode&&document.write('<style>html{overflow-x: hidden !important;overflow-y: hidden !important;}.kill-ie{text-align:center;height: 100%;margin-top: 15%;margin-bottom: 5500%;}.kill-t{font-size: 2rem;}.kill-c{font-size: 1.2rem;}#l_header,#l_body{display: none;}</style><div class="kill-ie"><span class="kill-t"><b>抱歉，您的浏览器无法访问本站</b></span><br/><span class="kill-c">微软已经于2016年终止了对 Internet Explorer (IE) 10 及更早版本的支持，<br/>继续使用存在极大的安全隐患，请使用当代主流的浏览器进行访问。</span><br/><a target="_blank" rel="noopener" href="https://blogs.windows.com/windowsexperience/2021/05/19/the-future-of-internet-explorer-on-windows-10-is-in-microsoft-edge/"><strong>了解详情 ></strong></a></div>')</script><noscript><style>html{overflow-x:hidden!important;overflow-y:hidden!important}.kill-noscript{text-align:center;height:100%;margin-top:15%;margin-bottom:5500%}.kill-t{font-size:2rem}.kill-c{font-size:1.2rem}#l_body,#l_header{display:none}</style><div class="kill-noscript"> <span class="kill-t"><b>抱歉，您的浏览器无法访问本站</b></span><br> <span class="kill-c">本页面需要浏览器支持（启用）JavaScript</span><br> <a target="_blank" rel="external nofollow noopener noreferrer" href="https://www.baidu.com/s?wd=启用JavaScript"><strong>了解详情 ></strong></a></div></noscript><script>function volantisEventListener(e,t,n){this.type=e,this.f=t,this.ele=n}function volantisDom(e){return e||(e=document.createElement("div")),this.ele=e,this.ele.find=e=>{let t=this.ele.querySelector(e);if(t)return new volantisDom(t)},this.ele.hasClass=e=>this.ele.className.match(new RegExp("(\\s|^)"+e+"(\\s|$)")),this.ele.addClass=e=>(this.ele.classList.add(e),this.ele),this.ele.removeClass=e=>(this.ele.classList.remove(e),this.ele),this.ele.toggleClass=e=>(this.ele.hasClass(e)?this.ele.removeClass(e):this.ele.addClass(e),this.ele),this.ele.on=(e,t,n=1)=>(this.ele.addEventListener(e,t,!1),n&&volantis.EventListener.list.push(new volantisEventListener(e,t,this.ele)),this.ele),this.ele.click=(e,t)=>(this.ele.on("click",e,t),this.ele),this.ele.scroll=(e,t)=>(this.ele.on("scroll",e,t),this.ele),this.ele.html=e=>(this.ele.innerHTML=e,this.ele),this.ele.hide=e=>(this.ele.style.display="none",this.ele),this.ele.show=e=>(this.ele.style.display="block",this.ele),this.ele}function RunItem(){function e(e,t){this.name=t||volantis.getFunctionHash(e),this.run=()=>{try{e()}catch(e){console.log(e)}}}this.list=[],this.start=()=>{for(var e=0;e<this.list.length;e++)this.list[e].run()},this.push=(t,n,o=!0)=>{if("function"!=typeof t)return;let l=t;o&&(l=()=>{volantis.requestAnimationFrame(t)}),n=n||volantis.getFunctionHash(t);const i=this.list.findIndex((e=>e.name===n));-1===i?this.list.push(new e(l,n)):this.list[i]=new e(l,n)},this.remove=e=>{for(let t=0;t<this.list.length;t++){this.list[t].name==e&&this.list.splice(t,1)}}}function errorImgAvatar(e){e.src="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/avatar/round/3442075.svg",e.onerror=null}function errorImgCover(e){e.src="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/cover/76b86c0226ffd.svg",e.onerror=null}!function(){const e=new WeakMap,t=new Proxy({},{get(n,o){const l=e.get(t);return l?.[o]},set(n,o,l){e.has(t)||e.set(t,Object.create(null));return e.get(t)[o]=l,!0},deleteProperty(n,o){const l=e.get(t);return!(!l||!Object.prototype.hasOwnProperty.call(l,o))&&(delete l[o],0===Object.keys(l).length&&e.delete(t),!0)},ownKeys(n){const o=e.get(t);return o?Object.keys(o):[]},getOwnPropertyDescriptor(n,o){const l=e.get(t);if(l&&Object.prototype.hasOwnProperty.call(l,o))return{value:l[o],writable:!0,enumerable:!0,configurable:!0}}});Object.defineProperty(window,"volantis",{value:t,writable:!0,configurable:!0,enumerable:!0})}(),volantis.debug="false",volantis.dom={},volantis.simpleTextHash=e=>{let t=5381;for(let n=0;n<e.length;n++)t=(t<<5)+t+e.charCodeAt(n),t&=t;return t.toString(16).padStart(8,"0")},volantis.getFunctionHash=e=>{const t=e.toString();return volantis.simpleTextHash(t)},volantis.EventListener={},volantis.EventListener.list=[],volantis.EventListener.remove=()=>{volantis.EventListener.list.forEach((function(e){e.ele.removeEventListener(e.type,e.f,!1)})),volantis.EventListener.list=[]},volantis.dom.$=e=>e?new volantisDom(e):null,volantis.pjax={},volantis.pjax.method={complete:new RunItem,error:new RunItem,send:new RunItem},volantis.pjax=Object.assign(volantis.pjax,{push:volantis.pjax.method.complete.push,error:volantis.pjax.method.error.push,send:volantis.pjax.method.send.push}),volantis.rightmenu={},volantis.rightmenu.method={handle:new RunItem},volantis.rightmenu=Object.assign(volantis.rightmenu,{handle:volantis.rightmenu.method.handle.push}),volantis.dark={},volantis.dark.method={toggle:new RunItem},volantis.dark=Object.assign(volantis.dark,{push:volantis.dark.method.toggle.push}),volantis.js=(e,t)=>new Promise((n=>{setTimeout((function(){var o=document.getElementsByTagName("head")[0]||document.documentElement,l=document.createElement("script");if(l.setAttribute("type","text/javascript"),t)if(JSON.stringify(t))for(let e in t)"onload"==e?l[e]=()=>{t[e](),n()}:(l[e]=t[e],l.onload=n);else l.onload=()=>{t(),n()};else l.onload=n;l.setAttribute("src",e),o.appendChild(l)}))})),volantis.css=e=>new Promise((t=>{setTimeout((function(){var n=document.createElement("link");n.rel="stylesheet",n.href=e,n.onload=t,document.getElementsByTagName("head")[0].appendChild(n)}))})),volantis.import={jQuery:()=>"undefined"==typeof jQuery?volantis.js("https://cdn.bootcdn.net/ajax/libs/jquery/3.6.0/jquery.min.js"):new Promise((e=>{e()}))},volantis.throttle=(e,t=200)=>{let n=0;return function(...o){const l=Date.now();l-n>=t&&(e.apply(this,o),n=l)}},volantis.debounce=(e,t=200)=>{let n=null;return function(){n&&clearTimeout(n),n=setTimeout((()=>{e.apply(this,arguments),n=null}),t)}},volantis.requestAnimationFrame=e=>(window.requestAnimationFrame||(window.requestAnimationFrame=window.requestAnimationFrame||window.mozRequestAnimationFrame||window.webkitRequestAnimationFrame||function(e){return window.setTimeout(e,1e3/60)}),window.requestAnimationFrame(e)),volantis.layoutHelper=(e,t,n)=>{function o(e,t,n){volantis.tempDiv=document.createElement("div"),volantis.tempDiv.innerHTML=t;let o=document.querySelector("#layoutHelper-"+e);o&&(n&&(o.innerHTML=""),o.append(volantis.tempDiv))}n=Object.assign({clean:!1,pjax:!0},n),o(e,t,n.clean),n.pjax&&volantis.pjax.push((()=>{o(e,t,n.clean)}),"layoutHelper-"+e)},volantis.scroll={engine:new RunItem,unengine:new RunItem},volantis.scroll=Object.assign(volantis.scroll,{push:volantis.scroll.engine.push}),volantis.scroll.getScrollTop=()=>{let e;return window.pageYOffset?e=window.pageYOffset:document.compatMode&&"BackCompat"!=document.compatMode?e=document.documentElement.scrollTop:document.body&&(e=document.body.scrollTop),e},volantis.scroll.scrollHeight=function(){return Math.max(document.body.scrollHeight,document.documentElement.scrollHeight)},volantis.scroll.offsetHeight=function(){return Math.min(document.body.offsetHeight,document.documentElement.offsetHeight,document.body.clientHeight,document.documentElement.clientHeight)},volantis.scroll.progress=function(){return volantis.scroll.getScrollTop()/(volantis.scroll.scrollHeight()-volantis.scroll.offsetHeight())},volantis.scroll.handleScrollEvents=()=>{volantis.scroll.lastScrollTop=volantis.scroll.getScrollTop(),volantis.requestAnimationFrame((function e(){const t=volantis.scroll.getScrollTop();volantis.scroll.lastScrollTop!==t?(volantis.scroll.del=t-volantis.scroll.lastScrollTop,volantis.scroll.lastScrollTop=t,volantis.scroll.unengine.list=[],volantis.scroll.engine.start()):volantis.scroll.unengine.start(),volantis.requestAnimationFrame(e)}))},volantis.scroll.handleScrollEvents(),volantis.scroll.ele=null,volantis.scroll.to=(e,t={})=>{e&&(volantis.scroll.ele=e,opt={top:e.getBoundingClientRect().top+document.documentElement.scrollTop,behavior:"smooth"},"top"in t&&(opt.top=t.top),"behavior"in t&&(opt.behavior=t.behavior),"addTop"in t&&(opt.top+=t.addTop),"observerDic"in t||(t.observerDic=100),window.scrollTo(opt),t.observer&&setTimeout((()=>{volantis.scroll.ele==e&&volantis.scroll.unengine.push((()=>{let n=e.getBoundingClientRect().top;n>=-t.observerDic&&n<=t.observerDic||volantis.scroll.to(e,t),volantis.scroll.unengine.remove("unengineObserver")}),"unengineObserver")}),1e3))},volantis.cleanContentVisibility=()=>{document.querySelector(".post-story")&&(console.log("cleanContentVisibility"),document.querySelectorAll(".post-story").forEach((e=>{e.classList.remove("post-story")})))};const nativeSetTimeout=window.setTimeout,nativeSetInterval=window.setInterval,nativeClearTimeout=window.clearTimeout,nativeClearInterval=window.clearInterval;volantis.activeTimeout=[],volantis.activeInterval=[],window.setTimeout=function(e,t,...n){const o=nativeSetTimeout((function(...t){try{return e.apply(this,t)}finally{const e=volantis.activeTimeout.indexOf(o);-1!==e&&volantis.activeTimeout.splice(e,1)}}),t,...n);return volantis.activeTimeout.push(o),o},window.setInterval=function(e,t,...n){const o=nativeSetInterval(e,t,...n);return volantis.activeInterval.push(o),o},window.clearTimeout=function(e){nativeClearTimeout(e);const t=volantis.activeTimeout.indexOf(e);-1!==t&&volantis.activeTimeout.splice(t,1)},window.clearInterval=function(e){nativeClearInterval(e);const t=volantis.activeInterval.indexOf(e);-1!==t&&volantis.activeInterval.splice(t,1)},volantis.getActiveInterval=function(){return[...volantis.activeInterval]},volantis.getActiveTimeout=function(){return[...volantis.activeTimeout]},volantis.clearAllTimers=function(){volantis.getActiveInterval().forEach((function(e){clearInterval(e)})),volantis.getActiveTimeout().forEach((function(e){clearTimeout(e)}))},volantis.pjax.send(volantis.clearAllTimers,"clearAllTimers")</script><script>volantis.GLOBAL_CONFIG={root:"/",debug:!1,default:{avatar:"https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/avatar/round/3442075.svg",link:"https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/link/8f277b4ee0ecd.svg",cover:"https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/cover/76b86c0226ffd.svg",image:"https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/placeholder/image/2659360.svg"},lastupdate:new Date(1779510804521),cdn:{izitoast_css:"https://cdn.bootcdn.net/ajax/libs/izitoast/1.4.0/css/iziToast.min.css",izitoast_js:"https://cdn.bootcdn.net/ajax/libs/izitoast/1.4.0/js/iziToast.min.js",fancybox_css:"https://cdn.bootcdn.net/ajax/libs/fancyapps-ui/4.0.31/fancybox.min.css",fancybox_js:"https://cdn.bootcdn.net/ajax/libs/fancyapps-ui/4.0.31/fancybox.umd.min.js"},sidebar:{for_page:["blogger","navigation","webinfo"],for_post:["toc"],webinfo:{lastupd:{enable:!1,friendlyShow:!0},runtime:{data:"2019/08/19",unit:"天"}}},plugins:{message:{enable:!1,icon:{default:"fa-solid fa-info-circle light-blue",quection:"fa-solid fa-question-circle light-blue"},time:{default:5e3,quection:2e4},position:"topRight",transitionIn:"bounceInLeft",transitionOut:"fadeOutRight",titleColor:"var(--color-text)",messageColor:"var(--color-text)",backgroundColor:"var(--color-card)",zindex:2147483647,copyright:{enable:!0,title:"知识共享许可协议",message:"请遵守 CC BY-NC-SA 4.0 协议。",icon:"far fa-copyright light-blue"},aplayer:{enable:!0,play:"fa-solid fa-play",pause:"fa-solid fa-pause"},rightmenu:{enable:!0,notice:!0}},aplayer:{id:1480000098,enable:!0}},search:{dataPath:("/".endsWith("/")?"/":"//")+"content.json"},languages:{search:{hits_empty:"找不到您查询的内容：${query}",hits_stats:"找到 ${hits} 条结果，用时 ${time} 毫秒"}}}</script><script type="application/ld+json">[{"@context":"http://schema.org","@type":"Organization","name":"MHuiG Magicland","url":"https://blog.mhuig.top/","logo":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png","width":192,"height":192}},{"@context":"http://schema.org","@type":"Person","name":"MHuiG","image":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png"},"url":"https://blog.mhuig.top/","sameAs":["https://github.com/MHuiG","https://twitter.com/iMHuiG","https://t.me/MHuiG","https://keybase.io/MHuiG"],"description":"「Be Yourself, Make a Difference.」"},{"@context":"http://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https://blog.mhuig.top/","name":"Magicland"}},{"@type":"ListItem","position":2,"item":{"@id":"https://blog.mhuig.top/categories/数学/","name":"数学"}},{"@type":"ListItem","position":2,"item":{"@id":"https://blog.mhuig.top/categories/数学/Zeta/","name":"Zeta"}},{"@type":"ListItem","position":3,"item":{"@id":"https://blog.mhuig.top/notes/Zeta/10.html","name":"埃拉托斯特尼筛法"}}]},{"@context":"http://schema.org","@type":"WebSite","name":"MHuiG Magicland","url":"https://blog.mhuig.top/","keywords":"MHuiG, @MHuiG, Blog, 博客, Magicland, 魔法世界","description":"宠辱不惊，看庭前花开花落；去留无意，望天上云卷云舒。「Be Yourself, Make a Difference.」 - Magic Island","author":{"@type":"Person","name":"MHuiG","image":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png"},"url":"https://blog.mhuig.top/","description":"「Be Yourself, Make a Difference.」"},"publisher":{"@type":"Organization","name":"MHuiG Magicland","url":"https://blog.mhuig.top/","logo":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png","width":192,"height":192}},"potentialAction":{"@type":"SearchAction","name":"Coco | The Cat of MHuiG","target":{"@type":"EntryPoint","urlTemplate":"https://blog.mhuig.top/havefun/Coco/?s={search_term_string}"},"query-input":"required name=search_term_string"}},{"@context":"http://schema.org","@type":"BlogPosting","headline":"埃拉托斯特尼筛法","description":"该文档详解古希腊数学家埃拉托斯特尼提出的素数识别算法，核心步骤为剔除不大于根号n的素数倍数，以100以内整数为例演示操作过程，通过保留2、3、5、7并删除其倍数得到素数，清晰呈现该经典算法的基本原理。","inLanguage":"zh-Hans","mainEntityOfPage":{"@type":"WebPage","@id":"https://blog.mhuig.top/notes/Zeta/10"},"author":{"@type":"Person","name":"MHuiG","image":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png"},"url":"https://blog.mhuig.top/"},"publisher":{"@type":"Organization","name":"MHuiG Magicland","logo":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png","width":192,"height":192}},"url":"https://blog.mhuig.top/notes/Zeta/10","wordCount":0,"datePublished":"2025-09-15T02:28:00.000Z","dateModified":"2025-11-20T10:18:00.000Z","articleSection":"数学","keywords":"Math,埃拉托斯特尼筛法,素数识别,算法原理","image":{"@type":"ImageObject","url":"/lib/favicon/android-chrome-192x192.png","width":192,"height":192}}]</script></head><body itemscope="" itemtype="http://schema.org/WebPage"><pjax></pjax><header itemscope="" itemtype="http://schema.org/WPHeader" id="l_header" class="l_header auto shadow floatable blur show" style="opacity:0"><div class="container"><div id="wrapper"><div class="nav-sub"><p class="title"></p><ul class="switcher nav-list-h m-phone" id="pjax-header-nav-list"><li><a id="s-comment" class="fa-solid fa-comments fa-fw" target="_self" title="comment"></a></li><li><a id="s-toc" class="s-toc fa-solid fa-list fa-fw" target="_self" title="toc"></a></li></ul></div><div class="nav-main"> <a class="title flat-box" target="_self" href="/">MHuiG</a><div class="menu navigation"><ul class="nav-list-h m-pc"><li><a class="menuitem flat-box faa-parent animated-hover" title="索引"><i class="fa-duotone fa-list-alt fa-fw"></i> 索引</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/notes/" title="便签" active-action="action-notes"><i class="fa-duotone fa-books fa-fw"></i> 便签</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/categories/" title="分类" active-action="action-categories"><i class="fa-duotone fa-folder-open fa-fw"></i> 分类</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/tags/" title="标签" active-action="action-tags"><i class="fa-duotone fa-tags fa-fw"></i> 标签</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/archives/" title="归档" active-action="action-archives"><i class="fa-duotone fa-archive fa-fw"></i> 归档</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/friends/" title="友链" active-action="action-pagesfriends"><i class="fa-duotone fa-link fa-fw"></i> 友链</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="https://www.travellings.cn/go-by-clouds.html" title="Travelling" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway fa-fw"></i> Travelling</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/about/" title="关于" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie fa-fw"></i> 关于</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/time-machine/" title="时光机" active-action="action-pagestime-machine"><i class="fa-duotone fa-clock fa-fw"></i> 时光机</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="noopener" href="https://mhuig.top/privacy-policy/" title="隐私政策" active-action="action-https:mhuigtopprivacy-policy"><i class="fa-duotone fa-user-secret fa-fw"></i> 隐私政策</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" title="更多"><i class="fa-duotone fa-fan fa-spin fa-fw"></i> 更多</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/beer/" title="Sponsor" active-action="action-pagesbeer"><i class="fa-duotone fa-heart-square fa-fw"></i> Sponsor</a></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" title="博客管理"><i class="fa-duotone fa-user-shield fa-fw"></i> 博客管理</a><ul class="list-v"><li><a class="menuitem flat-box header toggle-mode-btn"><i class="fa-duotone fa-bat fa-fw"></i> 暗黑模式</a></li><li></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/rss/" title="RSS订阅" active-action="action-pagesrss"><i class="fa-duotone fa-rss fa-fw"></i> RSS订阅</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/sitemap.xml" title="站点地图" active-action="action-sitemapxml"><i class="fa-duotone fa-sitemap fa-fw"></i> 站点地图</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://mhuig.instatus.com/" title="Monitors" active-action="action-https:mhuiginstatuscom"><i class="fa-duotone fa-telescope fa-fw"></i> Monitors</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://ssl.mhuig.top/" title="SSL Status" active-action="action-https:sslmhuigtop"><i class="fa-brands fa-expeditedssl fa-fw"></i> SSL Status</a></li></ul></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" title="工具箱"><i class="fa-duotone fa-tools fa-fw"></i> 工具箱</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://rssbox.mhuig.top/" title="RSS Box" active-action="action-https:rssboxmhuigtop"><i class="fa-duotone fa-conveyor-belt-boxes fa-fw"></i> RSS Box</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/havefun/Coco/" title="My Cat" active-action="action-havefunCoco"><i class="fa-duotone fa-cat fa-fw"></i> My Cat</a></li><li><a class="menuitem flat-box"><i class="fa-duotone fa-compact-disc fa-spin fa-fw music"></i> Music</a><ul class="list-v"><li><div class="aplayer-container"><div class="aplayer-local"></div></div></li></ul></li><li></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/talk/" title="碎言碎语" active-action="action-pagestalk"><i class="fa-duotone fa-comments fa-fw"></i> 碎言碎语</a></li></ul></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" title="GitHub" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github fa-fw"></i> GitHub</a></li></ul></li></ul></div><div class="m_search"><form name="searchform" class="form u-search-form"><i class="icon fa-solid fa-search fa-fw"></i> <input type="text" class="input u-search-input" placeholder="Search..."></form></div><ul class="switcher nav-list-h m-phone"><li><a class="s-search fa-solid fa-search fa-fw" target="_self" title="search"></a></li><li><a class="s-menu fa-solid fa-bars fa-fw" target="_self" title="menu"></a><ul class="menu-phone list-v navigation white-box"><li><a class="menuitem flat-box faa-parent animated-hover" title="索引"><i class="fa-duotone fa-list-alt fa-fw"></i> 索引</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/notes/" title="便签" active-action="action-notes"><i class="fa-duotone fa-books fa-fw"></i> 便签</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/categories/" title="分类" active-action="action-categories"><i class="fa-duotone fa-folder-open fa-fw"></i> 分类</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/tags/" title="标签" active-action="action-tags"><i class="fa-duotone fa-tags fa-fw"></i> 标签</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/archives/" title="归档" active-action="action-archives"><i class="fa-duotone fa-archive fa-fw"></i> 归档</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/friends/" title="友链" active-action="action-pagesfriends"><i class="fa-duotone fa-link fa-fw"></i> 友链</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="https://www.travellings.cn/go-by-clouds.html" title="Travelling" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway fa-fw"></i> Travelling</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/about/" title="关于" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie fa-fw"></i> 关于</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/time-machine/" title="时光机" active-action="action-pagestime-machine"><i class="fa-duotone fa-clock fa-fw"></i> 时光机</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="noopener" href="https://mhuig.top/privacy-policy/" title="隐私政策" active-action="action-https:mhuigtopprivacy-policy"><i class="fa-duotone fa-user-secret fa-fw"></i> 隐私政策</a></li></ul></li><li><a class="menuitem flat-box faa-parent animated-hover" title="更多"><i class="fa-duotone fa-fan fa-spin fa-fw"></i> 更多</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/beer/" title="Sponsor" active-action="action-pagesbeer"><i class="fa-duotone fa-heart-square fa-fw"></i> Sponsor</a></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" title="博客管理"><i class="fa-duotone fa-user-shield fa-fw"></i> 博客管理</a><ul class="list-v"><li><a class="menuitem flat-box header toggle-mode-btn"><i class="fa-duotone fa-bat fa-fw"></i> 暗黑模式</a></li><li></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/rss/" title="RSS订阅" active-action="action-pagesrss"><i class="fa-duotone fa-rss fa-fw"></i> RSS订阅</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/sitemap.xml" title="站点地图" active-action="action-sitemapxml"><i class="fa-duotone fa-sitemap fa-fw"></i> 站点地图</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://mhuig.instatus.com/" title="Monitors" active-action="action-https:mhuiginstatuscom"><i class="fa-duotone fa-telescope fa-fw"></i> Monitors</a></li><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://ssl.mhuig.top/" title="SSL Status" active-action="action-https:sslmhuigtop"><i class="fa-brands fa-expeditedssl fa-fw"></i> SSL Status</a></li></ul></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" title="工具箱"><i class="fa-duotone fa-tools fa-fw"></i> 工具箱</a><ul class="list-v"><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://rssbox.mhuig.top/" title="RSS Box" active-action="action-https:rssboxmhuigtop"><i class="fa-duotone fa-conveyor-belt-boxes fa-fw"></i> RSS Box</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/havefun/Coco/" title="My Cat" active-action="action-havefunCoco"><i class="fa-duotone fa-cat fa-fw"></i> My Cat</a></li><li><a class="menuitem flat-box faa-parent animated-hover" href="/pages/talk/" title="碎言碎语" active-action="action-pagestalk"><i class="fa-duotone fa-comments fa-fw"></i> 碎言碎语</a></li></ul></li><hr><li><a class="menuitem flat-box faa-parent animated-hover" target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" title="GitHub" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github fa-fw"></i> GitHub</a></li></ul></li></ul></li></ul></div></div></div></header><div id="l_body"><div id="l_cover"><div id="none" class="cover-wrapper docs featured" style="display:none"><div class="cover-bg lazyload placeholder" data-bg=""></div><div class="cover-body"><div class="top"><p class="title">Magicland</p><p class="subtitle">「看庭前花开花落,望天上云卷云舒」</p></div><div class="bottom"><div class="menu navigation"><div class="list-h"><a target="_blank" rel="external nofollow noopener noreferrer" href="https://github.com/MHuiG" active-action="action-https:githubcomMHuiG"><i class="fa-brands fa-github color-github fa-fw"></i><p>Github</p></a><a href="/pages/friends/" active-action="action-pagesfriends"><i class="fa-duotone fa-link color-friends fa-fw"></i><p>友链</p></a><a href="/pages/about/" active-action="action-pagesabout"><i class="fa-duotone fa-user-tie color-about fa-fw"></i><p>关于</p></a><a href="https://www.travellings.cn/go-by-clouds.html" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway color-travellings fa-fw"></i><p>Travelling</p></a></div></div></div></div><div id="scroll-down" style="display:none"><i class="fa fa-chevron-down scroll-down-effects"></i></div></div></div><div id="safearea"><div class="body-wrapper"><div id="l_main" class=""><article itemscope="" itemtype="http://schema.org/Article" class="article post white-box reveal md shadow floatable blur article-type-docs" id="docs" itemprop="blogPost"><link itemprop="mainEntityOfPage" href="https://blog.mhuig.top/notes/Zeta/10"><span hidden="" itemprop="publisher" itemscope="" itemtype="http://schema.org/Organization"><meta itemprop="name" content="Magicland"></span><span hidden="" itemprop="post" itemscope="" itemtype="http://schema.org/CreativeWork"><meta itemprop="name" content="埃拉托斯特尼筛法"><meta itemprop="description" content="该文档详解古希腊数学家埃拉托斯特尼提出的素数识别算法，核心步骤为剔除不大于根号n的素数倍数，以100以内整数为例演示操作过程，通过保留2、3、5、7并删除其倍数得到素数，清晰呈现该经典算法的基本原理。"></span><span hidden=""><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><span hidden="" itemprop="name headline"></span></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p> <span class="p logo center large">埃拉托斯特尼筛法</span></p><br><h1 hidden="">埃拉托斯特尼筛法</h1><p>The Greek mathematician Eratosthenes proposed a simple algorithm for identifying prime numbers. To obtain all prime numbers less than or equal to a natural number<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="n"><g data-mml-node="mi" data-latex="n"><path data-c="1D45B" d="M537 137C514 58 481 18 440 18 427 18 420 28 420 47 420 61 426 84 438 115 478 224 498 296 498 333 498 403 451 442 381 442 322 442 271 416 230 363 222 407 187 442 136 442 80 442 58 390 44 345 34 313 29 294 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 151 413 160 399 160 371 160 358 155 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 111-11 130-11 144-1 151 19 153 24 159 49 170 92L191 181 221 295C232 318 249 341 270 365 299 397 335 413 378 413 411 413 427 391 427 348 427 310 406 234 363 120 356 102 353 87 353 74 353 25 390-11 438-11 482-11 517 14 542 64 561 104 571 131 571 144 571 153 566 158 555 158 552 158 537 149 537 137Z"></path></g></g></g></svg></mjx-container>, one must eliminate all multiples of prime numbers not greater than<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.491ex" xmlns="http://www.w3.org/2000/svg" width="3.287ex" height="2.398ex" role="img" focusable="false" viewBox="0 -843 1453 1060"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\sqrt{n}"><g data-mml-node="msqrt" data-latex="\sqrt{n}"><g data-mml-node="mo" transform="translate(0,743)"><path data-c="221A" d="M847-2C851 7 853 13 853 16 853 32 845 40 829 40 820 40 813 36 809 27 666-259 595-403 595-405L595-406C595-413 527-558 390-843L217-461C212-450 207-445 201-445 198-445 192-448 184-454L86-528C77-535 73-540 73-545 73-555 78-560 87-560 90-560 95-557 103-551L151-516 345-943C350-954 357-960 367-960 379-960 387-955 392-946Z"></path></g><g transform="translate(853,0)"><g data-mml-node="mi" data-latex="n"><path data-c="1D45B" d="M537 137C514 58 481 18 440 18 427 18 420 28 420 47 420 61 426 84 438 115 478 224 498 296 498 333 498 403 451 442 381 442 322 442 271 416 230 363 222 407 187 442 136 442 80 442 58 390 44 345 34 313 29 294 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 151 413 160 399 160 371 160 358 155 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 111-11 130-11 144-1 151 19 153 24 159 49 170 92L191 181 221 295C232 318 249 341 270 365 299 397 335 413 378 413 411 413 427 391 427 348 427 310 406 234 363 120 356 102 353 87 353 74 353 25 390-11 438-11 482-11 517 14 542 64 561 104 571 131 571 144 571 153 566 158 555 158 552 158 537 149 537 137Z"></path></g></g><rect width="600" height="60" x="853" y="723"></rect></g></g></g></svg></mjx-container>, and the remaining numbers will be prime.</p><p>希腊数学家埃拉托斯特尼所提出一种简单检定素数的算法。要得到自然数<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 600 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="n"><g data-mml-node="mi" data-latex="n"><path data-c="1D45B" d="M537 137C514 58 481 18 440 18 427 18 420 28 420 47 420 61 426 84 438 115 478 224 498 296 498 333 498 403 451 442 381 442 322 442 271 416 230 363 222 407 187 442 136 442 80 442 58 390 44 345 34 313 29 294 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 151 413 160 399 160 371 160 358 155 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 111-11 130-11 144-1 151 19 153 24 159 49 170 92L191 181 221 295C232 318 249 341 270 365 299 397 335 413 378 413 411 413 427 391 427 348 427 310 406 234 363 120 356 102 353 87 353 74 353 25 390-11 438-11 482-11 517 14 542 64 561 104 571 131 571 144 571 153 566 158 555 158 552 158 537 149 537 137Z"></path></g></g></g></svg></mjx-container> 以内的全部素数，必须把不大于<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.491ex" xmlns="http://www.w3.org/2000/svg" width="3.287ex" height="2.398ex" role="img" focusable="false" viewBox="0 -843 1453 1060"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\sqrt{n}"><g data-mml-node="msqrt" data-latex="\sqrt{n}"><g data-mml-node="mo" transform="translate(0,743)"><path data-c="221A" d="M847-2C851 7 853 13 853 16 853 32 845 40 829 40 820 40 813 36 809 27 666-259 595-403 595-405L595-406C595-413 527-558 390-843L217-461C212-450 207-445 201-445 198-445 192-448 184-454L86-528C77-535 73-540 73-545 73-555 78-560 87-560 90-560 95-557 103-551L151-516 345-943C350-954 357-960 367-960 379-960 387-955 392-946Z"></path></g><g transform="translate(853,0)"><g data-mml-node="mi" data-latex="n"><path data-c="1D45B" d="M537 137C514 58 481 18 440 18 427 18 420 28 420 47 420 61 426 84 438 115 478 224 498 296 498 333 498 403 451 442 381 442 322 442 271 416 230 363 222 407 187 442 136 442 80 442 58 390 44 345 34 313 29 294 29 287 29 278 34 273 45 273 50 273 53 274 56 276 61 285 64 292 65 299 83 375 106 413 133 413 151 413 160 399 160 371 160 358 155 331 144 290L87 63C84 50 78 24 78 19 78-1 89-11 111-11 130-11 144-1 151 19 153 24 159 49 170 92L191 181 221 295C232 318 249 341 270 365 299 397 335 413 378 413 411 413 427 391 427 348 427 310 406 234 363 120 356 102 353 87 353 74 353 25 390-11 438-11 482-11 517 14 542 64 561 104 571 131 571 144 571 153 566 158 555 158 552 158 537 149 537 137Z"></path></g></g><rect width="600" height="60" x="853" y="723"></rect></g></g></g></svg></mjx-container> 的所有素数的倍数剔除，剩下的就是素数。</p><p>Next, I will manually demonstrate how to obtain all the prime numbers within a certain range.</p><p>下面我将手动演示如何获得某个区间的所有素数。</p><p>Write integers of about<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="3.394ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 1500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="100"><g data-mml-node="mn" data-latex="100"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(500,0)"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(1000,0)"></path></g></g></g></svg></mjx-container>.</p><p>写出大约<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="3.394ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 1500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="100"><g data-mml-node="mn" data-latex="100"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(500,0)"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(1000,0)"></path></g></g></g></svg></mjx-container> 的整数。</p><p><img src="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-1.jpeg" class="lazyload" data-srcset="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-1.jpeg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="Eratosthenes"></p><p>Leaving<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> unchanged, remove all the numbers in the number table that are multiples of<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> to get:</p><p>保持<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> 不变，删掉所有<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> 的倍数，得到：</p><p><img src="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-2.jpeg" class="lazyload" data-srcset="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-2.jpeg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="Eratosthenes"></p><p>The first number after<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> is<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container>. Keep<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> and<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> unchanged, and remove all the numbers in the number table that are multiples of<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> to get:</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> 之后的第一个数字是<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> ，保持<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container> 和<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> 不变，删掉所有<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> 的倍数，得到：</p><p><img src="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-3.jpeg" class="lazyload" data-srcset="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-3.jpeg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="Eratosthenes"></p><p>The first unaffected number after<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> is<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container>. Leaving<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container>, and<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container> unchanged, and discarding all multiples of<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container> in the number table, we get:</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container> 之后的第一个不受影响的数字是<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container> ，保持<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container> 不变，删掉所有<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container> 的倍数，得到：</p><p><img src="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-4.jpeg" class="lazyload" data-srcset="https://bookmak.github.io/Zeta-Archive/Eratosthenes/Eratosthenes-4.jpeg" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="Eratosthenes"></p><p>The first number not affected is<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container>. The next step is to leave<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container> unchanged, and eliminate all the numbers in the table that are multiples of<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container>.</p><p>之后的第一个不受影响的数字是<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container> ，保持<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:0" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.507ex" role="img" focusable="false" viewBox="0 -666 500 666"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="2"><g data-mml-node="mn" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="3"><g data-mml-node="mn" data-latex="3"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 500 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="5"><g data-mml-node="mn" data-latex="5"><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"></path></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container> 不变，删掉所有<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="1.579ex" role="img" focusable="false" viewBox="0 -676 500 698"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="7"><g data-mml-node="mn" data-latex="7"><path data-c="37" d="M475 604C482 613 485 626 485 644L243 644C174 644 135 648 128 657 125 660 122 667 120 676L89 676 55 464 88 464C98 520 106 550 112 555 115 558 146 560 205 560L401 560 295 410C214 295 174 171 174 36 174-3 190-22 223-22 256-22 272-3 272 36L272 87C272 239 296 349 343 416Z"></path></g></g></g></svg></mjx-container> 的倍数。</p><p>…………</p><p>The last remaining numbers are prime numbers.</p><p>最后剩下的数字是素数。</p><p>This is the Sieve of Eratosthenes.</p><p>这是埃拉托斯特尼筛法。</p></div><div class="footer"></div><div class="article-meta" id="bottom"><div class="new-meta-box"></div></div><div class="prev-next"><a class="prev" href="/notes/Zeta/9"><p class="title"><i class="fa-solid fa-chevron-left" aria-hidden="true"></i>Euclid素数无限定理</p><p class="content">欧几里得在《几何原本》第九卷命题20中提出素数无限定理，通过反证法构造矛盾证明素数无穷多：假设有限素数集合，构造所有素数乘积加1的数q，q若为素数则形成新素数，若为合数则其素因子必不在原集合，从而推翻假设。公元888年阿雷萨斯书记员斯蒂芬抄写的手稿现存牛津大学博德利图书馆，该证明开创数论构造性证明范式，现代数学仍沿用其核心逻辑，是初等数论与数学推理的经典范例。</p></a><a class="next" href="/notes/Zeta/11"><p class="title">Euler对无穷级数的若干观察<i class="fa-solid fa-chevron-right" aria-hidden="true"></i></p><p class="content">该文章系统探讨欧拉在无穷级数领域的研究成果，包括级数收敛性分析及Zeta函数贡献，提供多语言PDF版本，为数学爱好者和研究者呈现欧拉无穷级数研究的历史文献与学术价值。欧拉跨学科的思维方式和对形式化方法的大胆运用，至今仍是数学创新的典范。</p></a></div><div class="recommended-article"><div class="recommended-article-header"><i class="fa-solid fa-bookmark fa-fw" aria-hidden="true"></i> <span>推荐阅读</span></div><div class="recommended-article-group"> <a class="recommended-article-item" href="/notes/Zeta/12.html" title="欧拉乘积公式" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/62.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/62.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="欧拉乘积公式"> <span class="title">欧拉乘积公式</span></a> <a class="recommended-article-item" href="/p/564714f9/" title="时间之箭" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/58.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/58.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="时间之箭"> <span class="title">时间之箭</span></a> <a class="recommended-article-item" href="/notes/P-2000/3.html" title="P-2000 Problem" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/114.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/114.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="P-2000 Problem"> <span class="title">P-2000 Problem</span></a> <a class="recommended-article-item" href="/notes/Zeta/2.html" title="On the Number of Primes Less Than a Given Magnitude" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/48.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/48.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="On the Number of Primes Less Than a Given Magnitude"> <span class="title">On the Number of Primes Less Than a Given Magnitude</span></a> <a class="recommended-article-item" href="/notes/Zeta/58.html" title="筛法的奇偶障碍" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/22.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/22.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="筛法的奇偶障碍"> <span class="title">筛法的奇偶障碍</span></a> <a class="recommended-article-item" href="/notes/Zeta/121.html" title="第n个素数的通项公式：从历史探索到现代理论" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/86.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/86.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="第n个素数的通项公式：从历史探索到现代理论"> <span class="title">第n个素数的通项公式：从历史探索到现代理论</span></a></div></div></article><article class="post white-box shadow floatable blur" id="comments"><span hidden=""><meta itemprop="discussionUrl" content="/notes/Zeta/10#comments"></span><p ct=""><i class="fa-duotone fa-comments"></i> 留言区</p><div id="layoutHelper-comments"></div></article></div><aside id="l_side" itemscope="" itemtype="http://schema.org/WPSideBar"><section class="widget text desktop mobile pjax"><header><a href="/notes/"><i class="fa-duotone fa-book fa-fw" aria-hidden="true"></i> <span class="name">Notes</span></a></header><div class="content"></div></section><section class="widget list group desktop mobile pjax"><header><i class="fa-duotone fa-square-z fa-fw" aria-hidden="true"></i> <span class="name">Zeta Archive</span></header><div class="content"><ul class="list entry navigation"><li><a class="flat-box" title="/notes/Zeta/" href="/notes/Zeta/" active-action="action-notesZeta"><div class="name"> Welcome</div></a></li><li><a class="flat-box" title="/notes/Zeta/1" href="/notes/Zeta/1" active-action="action-notesZeta1"><div class="name"> Leibniz</div></a></li><li><a class="flat-box" title="/notes/Zeta/2" href="/notes/Zeta/2" active-action="action-notesZeta2"><div class="name"> On the Number of Primes Less Than a Given Magnitude</div></a></li><li><a class="flat-box" title="/notes/Zeta/3" href="/notes/Zeta/3" active-action="action-notesZeta3"><div class="name"> Clebsch's fair copy of Riemann's publication</div></a></li><li><a class="flat-box" title="/notes/Zeta/4" href="/notes/Zeta/4" active-action="action-notesZeta4"><div class="name"> Clebsch's fair copy of Riemann's publication</div></a></li><li><a class="flat-box" title="/notes/Zeta/5" href="/notes/Zeta/5" active-action="action-notesZeta5"><div class="name"> Riemann’s 1859 Manuscript</div></a></li><li><a class="flat-box" title="/notes/Zeta/6" href="/notes/Zeta/6" active-action="action-notesZeta6"><div class="name"> Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse</div></a></li><li><a class="flat-box" title="/notes/Zeta/7" href="/notes/Zeta/7" active-action="action-notesZeta7"><div class="name"> On the Number of Primes Less Than a Given Quantity</div></a></li><li><a class="flat-box" title="/notes/Zeta/8" href="/notes/Zeta/8" active-action="action-notesZeta8"><div class="name"> Riemann’s Zeta Function</div></a></li><li><a class="flat-box" title="/notes/Zeta/9" href="/notes/Zeta/9" active-action="action-notesZeta9"><div class="name"> Euclid素数无限定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/10" href="/notes/Zeta/10" active-action="action-notesZeta10"><div class="name"> 埃拉托斯特尼筛法</div></a></li><li><a class="flat-box" title="/notes/Zeta/11" href="/notes/Zeta/11" active-action="action-notesZeta11"><div class="name"> Euler对无穷级数的若干观察</div></a></li><li><a class="flat-box" title="/notes/Zeta/12" href="/notes/Zeta/12" active-action="action-notesZeta12"><div class="name"> 欧拉乘积公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/13" href="/notes/Zeta/13" active-action="action-notesZeta13"><div class="name"> 牛顿广义二项式定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/14" href="/notes/Zeta/14" active-action="action-notesZeta14"><div class="name"> 二年级之梦</div></a></li><li><a class="flat-box" title="/notes/Zeta/15" href="/notes/Zeta/15" active-action="action-notesZeta15"><div class="name"> 罗素悖论</div></a></li><li><a class="flat-box" title="/notes/Zeta/16" href="/notes/Zeta/16" active-action="action-notesZeta16"><div class="name"> 哥德尔不完备性定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/17" href="/notes/Zeta/17" active-action="action-notesZeta17"><div class="name"> 停机问题</div></a></li><li><a class="flat-box" title="/notes/Zeta/18" href="/notes/Zeta/18" active-action="action-notesZeta18"><div class="name"> 素数定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/19" href="/notes/Zeta/19" active-action="action-notesZeta19"><div class="name"> 对数运算法则</div></a></li><li><a class="flat-box" title="/notes/Zeta/20" href="/notes/Zeta/20" active-action="action-notesZeta20"><div class="name"> 本福特定律</div></a></li><li><a class="flat-box" title="/notes/Zeta/21" href="/notes/Zeta/21" active-action="action-notesZeta21"><div class="name"> 狄利克雷Eta函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/22" href="/notes/Zeta/22" active-action="action-notesZeta22"><div class="name"> 留数定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/23" href="/notes/Zeta/23" active-action="action-notesZeta23"><div class="name"> 多项式分式前n项和变换为积分</div></a></li><li><a class="flat-box" title="/notes/Zeta/24" href="/notes/Zeta/24" active-action="action-notesZeta24"><div class="name"> 梅林变换</div></a></li><li><a class="flat-box" title="/notes/Zeta/25" href="/notes/Zeta/25" active-action="action-notesZeta25"><div class="name"> 佩龙公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/26" href="/notes/Zeta/26" active-action="action-notesZeta26"><div class="name"> 曼戈尔特函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/27" href="/notes/Zeta/27" active-action="action-notesZeta27"><div class="name"> 黎曼素数计数函数J(x)</div></a></li><li><a class="flat-box" title="/notes/Zeta/28" href="/notes/Zeta/28" active-action="action-notesZeta28"><div class="name"> 莫比乌斯反演</div></a></li><li><a class="flat-box" title="/notes/Zeta/29" href="/notes/Zeta/29" active-action="action-notesZeta29"><div class="name"> 斯蒂尔杰斯积分</div></a></li><li><a class="flat-box" title="/notes/Zeta/30" href="/notes/Zeta/30" active-action="action-notesZeta30"><div class="name"> 威尔斯特拉斯无穷乘积展开</div></a></li><li><a class="flat-box" title="/notes/Zeta/31" href="/notes/Zeta/31" active-action="action-notesZeta31"><div class="name"> 不知名的碎片1</div></a></li><li><a class="flat-box" title="/notes/Zeta/32" href="/notes/Zeta/32" active-action="action-notesZeta32"><div class="name"> 不知名的碎片2</div></a></li><li><a class="flat-box" title="/notes/Zeta/33" href="/notes/Zeta/33" active-action="action-notesZeta33"><div class="name"> 不知名的碎片3</div></a></li><li><a class="flat-box" title="/notes/Zeta/34" href="/notes/Zeta/34" active-action="action-notesZeta34"><div class="name"> 根号2的无理性证明</div></a></li><li><a class="flat-box" title="/notes/Zeta/35" href="/notes/Zeta/35" active-action="action-notesZeta35"><div class="name"> e的无理性证明</div></a></li><li><a class="flat-box" title="/notes/Zeta/36" href="/notes/Zeta/36" active-action="action-notesZeta36"><div class="name"> π的无理性证明</div></a></li><li><a class="flat-box" title="/notes/Zeta/37" href="/notes/Zeta/37" active-action="action-notesZeta37"><div class="name"> Zeta的无理性之谜</div></a></li><li><a class="flat-box" title="/notes/Zeta/38" href="/notes/Zeta/38" active-action="action-notesZeta38"><div class="name"> Niven的无理数</div></a></li><li><a class="flat-box" title="/notes/Zeta/39" href="/notes/Zeta/39" active-action="action-notesZeta39"><div class="name"> 柯西方法</div></a></li><li><a class="flat-box" title="/notes/Zeta/40" href="/notes/Zeta/40" active-action="action-notesZeta40"><div class="name"> 积性函数蕴含迭代结构</div></a></li><li><a class="flat-box" title="/notes/Zeta/41" href="/notes/Zeta/41" active-action="action-notesZeta41"><div class="name"> 黎曼 Zeta 函数是分形</div></a></li><li><a class="flat-box" title="/notes/Zeta/42" href="/notes/Zeta/42" active-action="action-notesZeta42"><div class="name"> 沃罗宁定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/43" href="/notes/Zeta/43" active-action="action-notesZeta43"><div class="name"> 迭代积分</div></a></li><li><a class="flat-box" title="/notes/Zeta/44" href="/notes/Zeta/44" active-action="action-notesZeta44"><div class="name"> 高阶导数</div></a></li><li><a class="flat-box" title="/notes/Zeta/45" href="/notes/Zeta/45" active-action="action-notesZeta45"><div class="name"> 阿贝尔变换</div></a></li><li><a class="flat-box" title="/notes/Zeta/46" href="/notes/Zeta/46" active-action="action-notesZeta46"><div class="name"> 泊松求和公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/47" href="/notes/Zeta/47" active-action="action-notesZeta47"><div class="name"> Theta函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/48" href="/notes/Zeta/48" active-action="action-notesZeta48"><div class="name"> 魔群</div></a></li><li><a class="flat-box" title="/notes/Zeta/49" href="/notes/Zeta/49" active-action="action-notesZeta49"><div class="name"> 朗兰兹纲领</div></a></li><li><a class="flat-box" title="/notes/Zeta/50" href="/notes/Zeta/50" active-action="action-notesZeta50"><div class="name"> 黎曼Zeta函数的解析延拓</div></a></li><li><a class="flat-box" title="/notes/Zeta/51" href="/notes/Zeta/51" active-action="action-notesZeta51"><div class="name"> 积分与求和交换顺序</div></a></li><li><a class="flat-box" title="/notes/Zeta/52" href="/notes/Zeta/52" active-action="action-notesZeta52"><div class="name"> 魏尔斯特拉斯判别法</div></a></li><li><a class="flat-box" title="/notes/Zeta/53" href="/notes/Zeta/53" active-action="action-notesZeta53"><div class="name"> Zeta函数的函数方程</div></a></li><li><a class="flat-box" title="/notes/Zeta/54" href="/notes/Zeta/54" active-action="action-notesZeta54"><div class="name"> Zeta函数解析延拓的经典方法</div></a></li><li><a class="flat-box" title="/notes/Zeta/55" href="/notes/Zeta/55" active-action="action-notesZeta55"><div class="name"> 黎曼Xi函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/56" href="/notes/Zeta/56" active-action="action-notesZeta56"><div class="name"> 黎曼关于Zeta函数零点分布的三个核心论断</div></a></li><li><a class="flat-box" title="/notes/Zeta/57" href="/notes/Zeta/57" active-action="action-notesZeta57"><div class="name"> 黎曼的整体思路</div></a></li><li><a class="flat-box" title="/notes/Zeta/58" href="/notes/Zeta/58" active-action="action-notesZeta58"><div class="name"> 筛法的奇偶障碍</div></a></li><li><a class="flat-box" title="/notes/Zeta/59" href="/notes/Zeta/59" active-action="action-notesZeta59"><div class="name"> 黎曼非平凡零点计数渐近公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/60" href="/notes/Zeta/60" active-action="action-notesZeta60"><div class="name"> Zeta非平凡零点虚部渐近公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/61" href="/notes/Zeta/61" active-action="action-notesZeta61"><div class="name"> 黎曼Zeta函数非平凡零点虚部研究的历史脉络</div></a></li><li><a class="flat-box" title="/notes/Zeta/62" href="/notes/Zeta/62" active-action="action-notesZeta62"><div class="name"> 黎曼Zeta函数非平凡零点虚部的表达式</div></a></li><li><a class="flat-box" title="/notes/Zeta/63" href="/notes/Zeta/63" active-action="action-notesZeta63"><div class="name"> 黎曼-西格尔公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/64" href="/notes/Zeta/64" active-action="action-notesZeta64"><div class="name"> On Riemann’s Nachlass for Analytic Number Theory Siegel(1932)</div></a></li><li><a class="flat-box" title="/notes/Zeta/65" href="/notes/Zeta/65" active-action="action-notesZeta65"><div class="name"> 论黎曼解析数论遗稿 西格尔(1932)[中文]</div></a></li><li><a class="flat-box" title="/notes/Zeta/66" href="/notes/Zeta/66" active-action="action-notesZeta66"><div class="name"> 不知名的碎片4</div></a></li><li><a class="flat-box" title="/notes/Zeta/67" href="/notes/Zeta/67" active-action="action-notesZeta67"><div class="name"> 不知名的碎片5</div></a></li><li><a class="flat-box" title="/notes/Zeta/68" href="/notes/Zeta/68" active-action="action-notesZeta68"><div class="name"> 不知名的碎片6</div></a></li><li><a class="flat-box" title="/notes/Zeta/69" href="/notes/Zeta/69" active-action="action-notesZeta69"><div class="name"> 不知名的碎片7</div></a></li><li><a class="flat-box" title="/notes/Zeta/70" href="/notes/Zeta/70" active-action="action-notesZeta70"><div class="name"> Zeta(3)</div></a></li><li><a class="flat-box" title="/notes/Zeta/71" href="/notes/Zeta/71" active-action="action-notesZeta71"><div class="name"> 与RH等价的命题</div></a></li><li><a class="flat-box" title="/notes/Zeta/72" href="/notes/Zeta/72" active-action="action-notesZeta72"><div class="name"> 黎曼ξ函数的对数表示与其零点乘积形式</div></a></li><li><a class="flat-box" title="/notes/Zeta/73" href="/notes/Zeta/73" active-action="action-notesZeta73"><div class="name"> 黎曼ξ函数对数展开的历史</div></a></li><li><a class="flat-box" title="/notes/Zeta/74" href="/notes/Zeta/74" active-action="action-notesZeta74"><div class="name"> 阿达马因子分解定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/75" href="/notes/Zeta/75" active-action="action-notesZeta75"><div class="name"> 戴森与蒙哥马利的跨学科邂逅</div></a></li><li><a class="flat-box" title="/notes/Zeta/76" href="/notes/Zeta/76" active-action="action-notesZeta76"><div class="name"> 希尔伯特-波利亚猜想</div></a></li><li><a class="flat-box" title="/notes/Zeta/77" href="/notes/Zeta/77" active-action="action-notesZeta77"><div class="name"> 蒙哥马利-奥德利兹科定律</div></a></li><li><a class="flat-box" title="/notes/Zeta/78" href="/notes/Zeta/78" active-action="action-notesZeta78"><div class="name"> 黎曼Zeta函数的表示方法</div></a></li><li><a class="flat-box" title="/notes/Zeta/79" href="/notes/Zeta/79" active-action="action-notesZeta79"><div class="name"> 拉马努金主定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/80" href="/notes/Zeta/80" active-action="action-notesZeta80"><div class="name"> 不知名的碎片8</div></a></li><li><a class="flat-box" title="/notes/Zeta/81" href="/notes/Zeta/81" active-action="action-notesZeta81"><div class="name"> 不知名的碎片9</div></a></li><li><a class="flat-box" title="/notes/Zeta/82" href="/notes/Zeta/82" active-action="action-notesZeta82"><div class="name"> 不知名的碎片10</div></a></li><li><a class="flat-box" title="/notes/Zeta/83" href="/notes/Zeta/83" active-action="action-notesZeta83"><div class="name"> 不知名的碎片11</div></a></li><li><a class="flat-box" title="/notes/Zeta/84" href="/notes/Zeta/84" active-action="action-notesZeta84"><div class="name"> 哈代定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/85" href="/notes/Zeta/85" active-action="action-notesZeta85"><div class="name"> 解析延拓的局限性</div></a></li><li><a class="flat-box" title="/notes/Zeta/86" href="/notes/Zeta/86" active-action="action-notesZeta86"><div class="name"> P对NP问题：计算复杂性的终极谜题</div></a></li><li><a class="flat-box" title="/notes/Zeta/87" href="/notes/Zeta/87" active-action="action-notesZeta87"><div class="name"> 广义化思维：从特殊到一般</div></a></li><li><a class="flat-box" title="/notes/Zeta/88" href="/notes/Zeta/88" active-action="action-notesZeta88"><div class="name"> 问题的归约</div></a></li><li><a class="flat-box" title="/notes/Zeta/89" href="/notes/Zeta/89" active-action="action-notesZeta89"><div class="name"> Shor算法</div></a></li><li><a class="flat-box" title="/notes/Zeta/90" href="/notes/Zeta/90" active-action="action-notesZeta90"><div class="name"> 子集和问题的NPC属性证明</div></a></li><li><a class="flat-box" title="/notes/Zeta/91" href="/notes/Zeta/91" active-action="action-notesZeta91"><div class="name"> 函数零点问题的等价转化及黎曼猜想的方法论困境</div></a></li><li><a class="flat-box" title="/notes/Zeta/92" href="/notes/Zeta/92" active-action="action-notesZeta92"><div class="name"> 黎曼素数计数函数 J(x) 的自然截断现象与截断点分析</div></a></li><li><a class="flat-box" title="/notes/Zeta/93" href="/notes/Zeta/93" active-action="action-notesZeta93"><div class="name"> 拉普拉斯变换</div></a></li><li><a class="flat-box" title="/notes/Zeta/94" href="/notes/Zeta/94" active-action="action-notesZeta94"><div class="name"> 莫比乌斯函数与黎曼 Zeta 函数的深刻联系</div></a></li><li><a class="flat-box" title="/notes/Zeta/95" href="/notes/Zeta/95" active-action="action-notesZeta95"><div class="name"> 特殊函数倍乘公式的统一性</div></a></li><li><a class="flat-box" title="/notes/Zeta/96" href="/notes/Zeta/96" active-action="action-notesZeta96"><div class="name"> 塞尔伯格渐近公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/97" href="/notes/Zeta/97" active-action="action-notesZeta97"><div class="name"> 塞尔伯格Zeta函数非平凡零点的正密率</div></a></li><li><a class="flat-box" title="/notes/Zeta/98" href="/notes/Zeta/98" active-action="action-notesZeta98"><div class="name"> 塞尔伯格磨光函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/99" href="/notes/Zeta/99" active-action="action-notesZeta99"><div class="name"> 磨光技术</div></a></li><li><a class="flat-box" title="/notes/Zeta/100" href="/notes/Zeta/100" active-action="action-notesZeta100"><div class="name"> 黎曼Zeta函数临界线幅角函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/101" href="/notes/Zeta/101" active-action="action-notesZeta101"><div class="name"> 玻尔-兰道定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/102" href="/notes/Zeta/102" active-action="action-notesZeta102"><div class="name"> 哈代-利特尔伍德临界线定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/103" href="/notes/Zeta/103" active-action="action-notesZeta103"><div class="name"> 塞尔伯格临界线定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/104" href="/notes/Zeta/104" active-action="action-notesZeta104"><div class="name"> 莱文森临界线定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/105" href="/notes/Zeta/105" active-action="action-notesZeta105"><div class="name"> 康瑞临界线定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/106" href="/notes/Zeta/106" active-action="action-notesZeta106"><div class="name"> Zeta函数非平凡零点虚部的无理性与超越性之谜</div></a></li><li><a class="flat-box" title="/notes/Zeta/107" href="/notes/Zeta/107" active-action="action-notesZeta107"><div class="name"> 塞尔伯格迹公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/108" href="/notes/Zeta/108" active-action="action-notesZeta108"><div class="name"> 复制函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/109" href="/notes/Zeta/109" active-action="action-notesZeta109"><div class="name"> 塞尔伯格筛法</div></a></li><li><a class="flat-box" title="/notes/Zeta/110" href="/notes/Zeta/110" active-action="action-notesZeta110"><div class="name"> 庞加莱猜想与奇点手术</div></a></li><li><a class="flat-box" title="/notes/Zeta/111" href="/notes/Zeta/111" active-action="action-notesZeta111"><div class="name"> 先磨光再解析延拓</div></a></li><li><a class="flat-box" title="/notes/Zeta/112" href="/notes/Zeta/112" active-action="action-notesZeta112"><div class="name"> 朗道-西格尔零点猜想</div></a></li><li><a class="flat-box" title="/notes/Zeta/113" href="/notes/Zeta/113" active-action="action-notesZeta113"><div class="name"> 等差数列上的素数分布</div></a></li><li><a class="flat-box" title="/notes/Zeta/114" href="/notes/Zeta/114" active-action="action-notesZeta114"><div class="name"> 大筛法</div></a></li><li><a class="flat-box" title="/notes/Zeta/115" href="/notes/Zeta/115" active-action="action-notesZeta115"><div class="name"> 模性定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/116" href="/notes/Zeta/116" active-action="action-notesZeta116"><div class="name"> 相邻素数间的有界间隔</div></a></li><li><a class="flat-box" title="/notes/Zeta/117" href="/notes/Zeta/117" active-action="action-notesZeta117"><div class="name"> 克拉梅尔模型与孪生素数猜想</div></a></li><li><a class="flat-box" title="/notes/Zeta/118" href="/notes/Zeta/118" active-action="action-notesZeta118"><div class="name"> Zeta函数的洛朗展开</div></a></li><li><a class="flat-box" title="/notes/Zeta/119" href="/notes/Zeta/119" active-action="action-notesZeta119"><div class="name"> Zeta函数与欧拉常数的关系</div></a></li><li><a class="flat-box" title="/notes/Zeta/120" href="/notes/Zeta/120" active-action="action-notesZeta120"><div class="name"> 黎曼Zeta函数的矩问题</div></a></li><li><a class="flat-box" title="/notes/Zeta/121" href="/notes/Zeta/121" active-action="action-notesZeta121"><div class="name"> 第n个素数的通项公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/122" href="/notes/Zeta/122" active-action="action-notesZeta122"><div class="name"> AKS算法证明素数判定属于P类问题</div></a></li><li><a class="flat-box" title="/notes/Zeta/123" href="/notes/Zeta/123" active-action="action-notesZeta123"><div class="name"> 米勒-拉宾素性检验</div></a></li><li><a class="flat-box" title="/notes/Zeta/124" href="/notes/Zeta/124" active-action="action-notesZeta124"><div class="name"> 中国剩余定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/125" href="/notes/Zeta/125" active-action="action-notesZeta125"><div class="name"> 二次互反律</div></a></li><li><a class="flat-box" title="/notes/Zeta/126" href="/notes/Zeta/126" active-action="action-notesZeta126"><div class="name"> 不知名的碎片12</div></a></li><li><a class="flat-box" title="/notes/Zeta/127" href="/notes/Zeta/127" active-action="action-notesZeta127"><div class="name"> 斯特林公式</div></a></li><li><a class="flat-box" title="/notes/Zeta/128" href="/notes/Zeta/128" active-action="action-notesZeta128"><div class="name"> 梅森素数</div></a></li><li><a class="flat-box" title="/notes/Zeta/129" href="/notes/Zeta/129" active-action="action-notesZeta129"><div class="name"> 全一素数</div></a></li><li><a class="flat-box" title="/notes/Zeta/130" href="/notes/Zeta/130" active-action="action-notesZeta130"><div class="name"> 华里士公式与欧拉 Beta 函数</div></a></li><li><a class="flat-box" title="/notes/Zeta/131" href="/notes/Zeta/131" active-action="action-notesZeta131"><div class="name"> Bombieri-Vinogradov 定理</div></a></li><li><a class="flat-box" title="/notes/Zeta/132" href="/notes/Zeta/132" active-action="action-notesZeta132"><div class="name"> EH猜想</div></a></li><li><a class="flat-box" title="/notes/Zeta/133" href="/notes/Zeta/133" active-action="action-notesZeta133"><div class="name"> Sarnak纲领性猜想：轨道上的素数分布理论</div></a></li><li><a class="flat-box" title="/notes/Zeta/134" href="/notes/Zeta/134" active-action="action-notesZeta134"><div class="name"> 圆法</div></a></li><li><a class="flat-box" title="/notes/Zeta/135" href="/notes/Zeta/135" active-action="action-notesZeta135"><div class="name"> Bourgain-Gamburd-Sarnak猜想</div></a></li><li><a class="flat-box" title="/notes/Zeta/136" href="/notes/Zeta/136" active-action="action-notesZeta136"><div class="name"> 从L函数到动力系统的深层联系</div></a></li><li><a class="flat-box" title="/notes/Zeta/137" href="/notes/Zeta/137" active-action="action-notesZeta137"><div class="name"> 量子唯一遍历性</div></a></li><li><a class="flat-box" title="/notes/Zeta/138" href="/notes/Zeta/138" active-action="action-notesZeta138"><div class="name"> 投资组合优化 Markowitz 模型</div></a></li><li><a class="flat-box" title="/notes/Zeta/139" href="/notes/Zeta/139" active-action="action-notesZeta139"><div class="name"> 凝聚态物理 谢林顿-柯克帕特里克模型</div></a></li><li><a class="flat-box" title="/notes/Zeta/140" href="/notes/Zeta/140" active-action="action-notesZeta140"><div class="name"> 神经网络 Hopfield 模型</div></a></li><li><a class="flat-box" title="/notes/Zeta/141" href="/notes/Zeta/141" active-action="action-notesZeta141"><div class="name"> 跨学科视角下的二次优化模型</div></a></li><li><a class="flat-box" title="/notes/Zeta/142" href="/notes/Zeta/142" active-action="action-notesZeta142"><div class="name"> 不知名的碎片13</div></a></li><li><a class="flat-box" title="/notes/Zeta/143" href="/notes/Zeta/143" active-action="action-notesZeta143"><div class="name"> 马尔可夫过程</div></a></li><li><a class="flat-box" title="/notes/Zeta/144" href="/notes/Zeta/144" active-action="action-notesZeta144"><div class="name"> 玻尔兹曼机</div></a></li><li><a class="flat-box" title="/notes/Zeta/145" href="/notes/Zeta/145" active-action="action-notesZeta145"><div class="name"> 乌拉姆素数螺旋</div></a></li><li><a class="flat-box" title="/notes/Zeta/146" href="/notes/Zeta/146" active-action="action-notesZeta146"><div class="name"> 计算不可约性</div></a></li><li><a class="flat-box" title="/notes/Zeta/147" href="/notes/Zeta/147" active-action="action-notesZeta147"><div class="name"> TREE(3)</div></a></li><li><a class="flat-box" title="/notes/Zeta/148" href="/notes/Zeta/148" active-action="action-notesZeta148"><div class="name"> 数学自循环演化系统 [胡说八道]</div></a></li><li><a class="flat-box" title="/notes/Zeta/149" href="/notes/Zeta/149" active-action="action-notesZeta149"><div class="name"> 不知名的碎片14</div></a></li><li><a class="flat-box" title="/notes/Zeta/150" href="/notes/Zeta/150" active-action="action-notesZeta150"><div class="name"> L-函数的分析构造与自守形式的联系</div></a></li></ul></div></section><div class="widget-sticky pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div></aside><pjax><script>window.pdata={},pdata.ispage=!1,pdata.commentPath="",pdata.commentPlaceholder="",pdata.commentConfig={};var l_header=document.getElementById("l_header");l_header.classList.add("show");var cover_wrapper=document.querySelector("#l_cover .cover-wrapper"),scroll_down=document.getElementById("scroll-down");cover_wrapper.id="none",cover_wrapper.style.display="none",scroll_down.style.display="none"</script></pjax></div><footer class="footer clearfix" itemscope="" itemtype="http://schema.org/WPFooter"><br><br><div class="aplayer-container"><div class="aplayer-local"></div></div><br><div class="social-wrapper" itemprop="about" itemscope="" itemtype="http://schema.org/Thing"><a href="/atom.xml" class="social fa-duotone fa-rss flat-btn" target="_blank" rel="external nofollow noopener noreferrer" itemprop="url"></a><a href="https://mhuig.top/contact/" class="social fa-duotone fa-envelope flat-btn" target="_blank" rel="external nofollow noopener noreferrer" itemprop="url"></a><a href="https://github.com/MHuiG" class="social fa-brands fa-github flat-btn" target="_blank" rel="external nofollow noopener noreferrer" itemprop="url"></a><a href="https://t.me/MHuiG" class="social fa-brands fa-telegram flat-btn" target="_blank" rel="external nofollow noopener noreferrer" itemprop="url"></a></div><div><p>博客内容遵循 <a target="_blank" rel="external nofollow noopener noreferrer" href="https://creativecommons.org/licenses/by-nc-sa/4.0/deed.zh-hans">署名-非商业性使用-相同方式共享 4.0 国际 (CC BY-NC-SA 4.0) 协议</a></p></div><div class="copyright"><p><a href="https://icp.gov.moe" target="_blank" rel="external nofollow noopener noreferrer">萌ICP备</a> <a href="https://icp.gov.moe/?keyword=2020012138" target="_blank" rel="external nofollow noopener noreferrer">2020012138号</a><br><a target="_blank" rel="noopener" href="https://mhuig.top/">Copyright © Since 2018 MHuiG</a></p></div></footer><a id="s-top" class="fa-solid fa-arrow-up fa-fw" title="top"></a></div></div><div><script>volantis.dom.bodyAnchor=volantis.dom.$(document.getElementById("safearea")),volantis.dom.topBtn=volantis.dom.$(document.getElementById("s-top")),volantis.dom.wrapper=volantis.dom.$(document.getElementById("wrapper")),volantis.dom.coverAnchor=volantis.dom.$(document.querySelector("#l_cover .cover-wrapper")),volantis.dom.switcher=volantis.dom.$(document.querySelector("#l_header .switcher .s-search")),volantis.dom.header=volantis.dom.$(document.getElementById("l_header")),volantis.dom.search=volantis.dom.$(document.querySelector("#l_header .m_search")),volantis.dom.mPhoneList=volantis.dom.$(document.querySelectorAll("#l_header .m-phone .list-v"))</script><script>volantis.css("https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/libs/@fortawesome/fontawesome-pro/css/all.min.css")</script><script src="/js/app.js"></script><script>const rootElement=document.documentElement,darkModeStorageKey="color-scheme",rootElementDarkModeAttributeName="color-scheme",setLS=(e,t)=>{localStorage.setItem(e,t)},removeLS=e=>{localStorage.removeItem(e)},getLS=e=>localStorage.getItem(e),getModeFromCSSMediaQuery=()=>window.matchMedia("(prefers-color-scheme: dark)").matches?"dark":"light",resetRootDarkModeAttributeAndLS=()=>{rootElement.removeAttribute("color-scheme"),removeLS("color-scheme")},validColorModeKeys={dark:!0,light:!0},applyCustomDarkModeSettings=e=>{const t=e||getLS("color-scheme");getCustomDarkMode(),t===getModeFromCSSMediaQuery()?resetRootDarkModeAttributeAndLS():validColorModeKeys[t]?rootElement.setAttribute("color-scheme",t):resetRootDarkModeAttributeAndLS()},invertDarkModeObj={dark:"light",light:"dark"},getCustomDarkMode=()=>{let e=getLS("color-scheme");if(validColorModeKeys[e])e=invertDarkModeObj[e];else{if(null!==e)return;e=invertDarkModeObj[getModeFromCSSMediaQuery()]}volantis.dark.mode="dark"==e?"light":"dark"},toggleCustomDarkMode=()=>{let e=getLS("color-scheme");if(validColorModeKeys[e])e=invertDarkModeObj[e];else{if(null!==e)return;e=invertDarkModeObj[getModeFromCSSMediaQuery()]}return setLS("color-scheme",e),e};function bindToggleButton(){document.querySelectorAll("#wrapper .toggle-mode-btn,#rightmenu-wrapper .toggle-mode-btn").forEach((function(e){volantis.dom.$(e).on("click",volantis.dark.toggle)}))}volantis.dark.toggle=()=>{const e=toggleCustomDarkMode();applyCustomDarkModeSettings(e),volantis.dark.method.toggle.start()},applyCustomDarkModeSettings(),document.addEventListener("DOMContentLoaded",(()=>{volantis.requestAnimationFrame(bindToggleButton)})),volantis.pjax.push(bindToggleButton);const darkModelListeners={dark:e=>{e.matches&&(volantis.dark.mode="dark"),volantis.dark.method.toggle.start()},light:e=>{e.matches&&(volantis.dark.mode="light"),volantis.dark.method.toggle.start()}};window.matchMedia("(prefers-color-scheme: dark)").addListener(darkModelListeners.dark),window.matchMedia("(prefers-color-scheme: light)").addListener(darkModelListeners.light)</script><script>function loadIssuesJS(){null!=document.getElementById("sites-api")&&"undefined"==typeof SitesJS&&volantis.js("/js/plugins/tags/sites.js");null!=document.getElementById("friends-api")&&"undefined"==typeof FriendsJS&&volantis.js("/js/plugins/tags/friends.js");null!=document.getElementById("contributors-api")&&"undefined"==typeof ContributorsJS&&volantis.js("/js/plugins/tags/contributors.js")}loadIssuesJS(),volantis.pjax.push((()=>{loadIssuesJS()}))</script><script defer="" src="https://cdn.bootcdn.net/ajax/libs/vanilla-lazyload/17.1.0/lazyload.min.js"></script><script>window.lazyLoadOptions={elements_selector:".lazyload",threshold:0},window.addEventListener("LazyLoad::Initialized",(function(n){window.lazyLoadInstance=n.detail.instance}),!1),document.addEventListener("DOMContentLoaded",(function(){lazyLoadInstance.update()})),document.addEventListener("pjax:complete",(function(){lazyLoadInstance.update()}))</script><script>window.FPConfig={delay:0,ignoreKeywords:["#"],maxRPS:6,hoverDelay:0}</script><script defer="" src="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/libs/flying-pages/flying-pages.min.js"></script><script>volantis.css("https://cdn.bootcdn.net/ajax/libs/aplayer/1.10.1/APlayer.min.css"),volantis.js("https://cdn.bootcdn.net/ajax/libs/aplayer/1.10.1/APlayer.min.js").then((()=>{function e(){document.querySelector(".aplayer-local-min")&&document.querySelectorAll(".aplayer-local-min").forEach((e=>{new APlayer(Object.assign({container:e,mini:!0,order:"list",volume:"0.7",autoplay:!1,loop:"all",theme:"#1BCDFC",listMaxHeight:"320px",listFolded:"true",preload:"auto",lrcType:3,audio:[{name:"虹之间",artist:"钢琴版伴奏",url:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.mp3",lrc:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.lrc",cover:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.jpg"},{name:"Avem",artist:"Alan Walker",url:"https://blog.mhuig.top/music-Archive/Avem.mp3",lrc:"https://blog.mhuig.top/music-Archive/Avem.lrc",cover:"https://blog.mhuig.top/music-Archive/Avem.jpg"},{name:"Fly",artist:"Marshmello / Leau Culver",url:"https://blog.mhuig.top/music-Archive/fly.mp3",lrc:"https://blog.mhuig.top/music-Archive/fly.lrc",cover:"https://blog.mhuig.top/music-Archive/fly.jpg"},{name:"Alone",artist:"Marshmello",url:"https://blog.mhuig.top/music-Archive/alone.mp3",lrc:"https://blog.mhuig.top/music-Archive/alone.lrc",cover:"https://blog.mhuig.top/music-Archive/alone.jpg"}]},JSON.parse(e.querySelector(".aplayer-local-min-conf").innerText)))}))}document.querySelectorAll(".aplayer-local").forEach((e=>{new APlayer({container:e,fixed:!1,order:"list",volume:"0.7",autoplay:!1,loop:"all",theme:"#1BCDFC",listMaxHeight:"320px",listFolded:"true",preload:"auto",lrcType:3,audio:[{name:"虹之间",artist:"钢琴版伴奏",url:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.mp3",lrc:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.lrc",cover:"https://blog.mhuig.top/music-Archive/BetweenTheRainbow.jpg"},{name:"Avem",artist:"Alan Walker",url:"https://blog.mhuig.top/music-Archive/Avem.mp3",lrc:"https://blog.mhuig.top/music-Archive/Avem.lrc",cover:"https://blog.mhuig.top/music-Archive/Avem.jpg"},{name:"Fly",artist:"Marshmello / Leau Culver",url:"https://blog.mhuig.top/music-Archive/fly.mp3",lrc:"https://blog.mhuig.top/music-Archive/fly.lrc",cover:"https://blog.mhuig.top/music-Archive/fly.jpg"},{name:"Alone",artist:"Marshmello",url:"https://blog.mhuig.top/music-Archive/alone.mp3",lrc:"https://blog.mhuig.top/music-Archive/alone.lrc",cover:"https://blog.mhuig.top/music-Archive/alone.jpg"}]})})),e(),volantis.pjax.push(e,"aplayerMin")}))</script><script>function check_giscus(){return"dark"===volantis.dark.mode?volantis.giscus.Theme="dark":volantis.giscus.Theme="light",document.getElementById("giscus_container")}function pjax_giscus(){const t=check_giscus();if(!t)return;let s=Object.assign({theme:{light:"light",dark:"dark"},repo:"MHuiG/talk","repo-id":"MDEwOlJlcG9zaXRvcnkyODQ4NDg1NTg=",category:"Giscus","category-id":"DIC_kwDOEPpxrs4B_X67",mapping:"pathname","reactions-enabled":"1","emit-metadata":"1",lang:"zh-CN","input-position":"top"},pdata.commentConfig);const e=document.createElement("script");e.setAttribute("src","https://giscus.app/client.js"),Object.keys(s).forEach((t=>{"theme"!=t&&e.setAttribute("data-"+t,s[t])})),e.setAttribute("data-theme",volantis.giscus.Theme),e.setAttribute("crossorigin","anonymous"),t.appendChild(e)}function dark_giscus(){if(!check_giscus())return;const t={setConfig:{theme:volantis.giscus.Theme}};document.querySelector("iframe.giscus-frame").contentWindow.postMessage({giscus:t},"https://giscus.app")}volantis.layoutHelper("comments",'<div id="giscus_container"></div>'),volantis.giscus={},pjax_giscus(),volantis.pjax.push(pjax_giscus),volantis.dark.push(dark_giscus)</script><script>async function loadSearchScript(){return volantis.js("/js/search/hexo.js")}function loadSearchService(){loadSearchScript(),document.querySelectorAll(".input.u-search-input").forEach((e=>{e.removeEventListener("focus",loadSearchService,!1)})),document.querySelectorAll(".u-search-form").forEach((e=>{e.addEventListener("submit",(e=>{e.preventDefault()}),!1)}))}function OpenSearch(e){"undefined"==typeof SearchService?loadSearchScript().then((()=>{SearchService.setQueryText(e),SearchService.search()})):(SearchService.setQueryText(e),SearchService.search())}if(window.location.search&&/^\?s=/g.test(window.location.search)){OpenSearch(decodeURI(window.location.search).replace(/\ /g,"-").replace(/^\?s=/g,""))}document.querySelectorAll(".input.u-search-input").forEach((e=>{e.addEventListener("focus",loadSearchService,!1)}))</script><script>function pjax_highlightjs_copyCode(){(document.querySelector(".highlight .code pre")||document.querySelector(".article pre code"))&&VolantisApp.utilCopyCode(".highlight .code pre, .article pre code")}volantis.requestAnimationFrame(pjax_highlightjs_copyCode),volantis.pjax.push(pjax_highlightjs_copyCode)</script><script>function load_swiper(){document.querySelectorAll(".swiper-container")[0]&&(volantis.css("https://cdn.bootcdn.net/ajax/libs/Swiper/8.3.2/swiper-bundle.min.css"),volantis.js("https://cdn.bootcdn.net/ajax/libs/Swiper/8.3.2/swiper-bundle.min.js").then((()=>{pjax_swiper()})))}function pjax_swiper(){volantis.swiper=new Swiper(".swiper-container",{slidesPerView:"auto",spaceBetween:8,centeredSlides:!0,loop:!0,pagination:{el:".swiper-pagination",clickable:!0},navigation:{nextEl:".swiper-button-next",prevEl:".swiper-button-prev"}})}load_swiper(),volantis.pjax.push((()=>{document.querySelectorAll(".swiper-container")[0]&&(void 0===volantis.swiper?load_swiper():pjax_swiper())}))</script><script>volantis.css("https://cdn.bootcdn.net/ajax/libs/pace/1.2.4/themes/blue/pace-theme-minimal.min.css"),volantis.js("https://cdn.bootcdn.net/ajax/libs/pace/1.2.4/pace.min.js").then((()=>{Pace.options.restartOnPushState=!1,volantis.pjax.send(Pace.restart,"Pace.restart"),volantis.scroll.push(volantis.debounce((()=>{Pace.stop(),Pace.trigger("start"),Pace.bar.update(100*volantis.scroll.progress()),document.body.className=document.body.className.replaceAll("pace-running ","")})),"阅读进度")}))</script><pjax></pjax><script>function listenSidebarTOC(){const t=document.querySelectorAll(".toc li");if(!t.length)return;const e=[];Array.from(t).forEach((t=>{const n=t.querySelector(".toc-link"),i=document.getElementById(n.getAttribute("href")?decodeURI(n.getAttribute("href")).replace("#",""):n.getAttribute("toc-action").split("toc-")[1]);return e.push(i),n.getAttribute("href")&&(n.setAttribute("toc-action","toc-"+decodeURI(n.getAttribute("href")).replace("#","")),n.removeAttribute("href")),i&&i.id&&n.addEventListener("click",(t=>{t.preventDefault(),volantis.scroll.to(i,{addTop:5,observer:!0}),history.pushState(null,document.title,"#"+i.id)})),i}));function n(t){if(t.classList.contains("active-current"))return;document.querySelectorAll(".toc .active").forEach((t=>{t.classList.remove("active","active-current")})),t.classList.add("active","active-current");let e=t.parentNode;for(;!e.matches(".toc");)e.matches("li")&&e.classList.add("active"),e=e.parentNode}volantis.activateNavIndex=0,n(t[volantis.activateNavIndex]),e[0]&&volantis.scroll.push(volantis.debounce((()=>{if(e[0].getBoundingClientRect().top>=0)volantis.activateNavIndex=0;else if(e[e.length-1].getBoundingClientRect().top<0)volantis.activateNavIndex=e.length-1;else for(let t=0;t<e.length;t++){const n=e[t],i=e[(t+1)%e.length];if(n.getBoundingClientRect().top<0&&i.getBoundingClientRect().top>=0){volantis.activateNavIndex=t;break}}n(t[volantis.activateNavIndex])})),"sidebar-toc")}document.addEventListener("DOMContentLoaded",(()=>{volantis.requestAnimationFrame(listenSidebarTOC)})),volantis.pjax.push(listenSidebarTOC,"listenSidebarTOC")</script><script>try{let e=(e,t,n=2)=>Math.abs(e-t)<=n,t=(t,n)=>!e(t.width,n.width)||!e(t.height,n.height),n=new WeakMap,i=(e,i=e.getClientBoundingRect())=>{let o=n.get(e);o&&!t(o,i)||(n.set(e,i),e.style["contain-intrinsic-size"]=`${i.width}px ${i.height}px`)},o=new IntersectionObserver(((e,t)=>{e.forEach((e=>{i(e.target,e.boundingClientRect)}))}),{rootMargin:"500px 0px 500px 0px"}),r=new ResizeObserver(((e,t)=>{e.forEach((e=>{i(e.target,e.contentRect)}))})),s=e=>{let t=document.querySelectorAll(e);t.length&&(t.forEach((e=>{o.observe(e),r.observe(e)})),requestAnimationFrame((()=>{requestAnimationFrame((()=>{t[0].style["content-visibility"]="auto"}))})))},a=()=>{"content-visibility"in document.documentElement.style&&s(".post-story")};a(),volantis.pjax.push(a)}catch(e){console.log(e)}</script><script>document.onreadystatechange=function(){if("complete"==document.readyState){const{saveData:e,effectiveType:t}=navigator.connection||navigator.mozConnection||navigator.webkitConnection||{};("none"==getComputedStyle(document.querySelector("#safearea"),null).display||e||/2g/.test(t))&&(document.querySelectorAll(".reveal").forEach((function(e){e.style.opacity="1"})),document.querySelector("#safearea").style.display="block")}}</script><script src="https://cdn.bootcdn.net/ajax/libs/pjax/0.2.8/pjax.min.js"></script><script>const performanceMonitor={slowThreshold:800,slowCount:0,maxSlowAllowed:1,requestStartTime:0,start(){this.requestStartTime=Date.now()},check(){Date.now()-this.requestStartTime>this.slowThreshold?this.slowCount++:this.slowCount=0},res(){return this.slowCount>=this.maxSlowAllowed}};var pjax;document.addEventListener("DOMContentLoaded",(function(){pjax=new Pjax({elements:'a[href]:not([href^="#"]):not([href="javascript:void(0)"]):not([pjax-fancybox]):not([onclick="return false;"]):not([onclick="return!1"]):not([target="_blank"]):not([target="view_window"]):not([href$=".xml"])',selectors:["head title","head meta[name=keywords]","head meta[name=description]","#l_main","#pjax-header-nav-list",".pjax","pjax","meta[name=robots]","link[rel=canonical]","meta[property='og:title']","meta[property='og:description']","meta[property='og:url']","meta[property='og:image']","script[type='application/ld+json']"],cacheBust:!1,timeout:900})})),document.addEventListener("pjax:send",(function(e){window.stop(),performanceMonitor.start();try{var t=window.location.pathname,o=e.triggerElement.href,n=[""];""!=n[0]&&n.forEach((e=>{-1==t.indexOf(e)&&-1==o.indexOf(e)||(window.location.href=o)})),performanceMonitor.res()&&(window.location.href=o)}catch(e){}volantis.pjax.method.send.start()})),document.addEventListener("pjax:complete",(function(){performanceMonitor.check(),document.querySelectorAll("script[data-pjax], .pjax-reload script").forEach((e=>{const t=e.text||e.textContent||e.innerHTML||"",o=document.createElement("script");Object.keys(e.attributes).forEach((t=>{o.setAttribute(e.attributes[t].nodeName,e.attributes[t].nodeValue)})),t&&o.appendChild(document.createTextNode(t)),e.parentNode.replaceChild(o,e)})),volantis.pjax.method.complete.start()})),document.addEventListener("pjax:error",(function(e){"pjax"===volantis.debug?(console.error(e),console.log("pjax error: \n"+JSON.stringify(e))):(volantis.pjax.method.error.start(),window.location.href=e.triggerElement.href)}))</script></div><pjax> <a style="display:none" target="_blank" rel="external nofollow noopener noreferrer" href="https://bot-trap.mhuig.top/">Are You A Robot?</a></pjax><script>(()=>{function t(){if("localhost:4000"!=window.location.host&&!/blog\.mhuig\.top/.test(window.location.host)){const t=document.createElement("meta");t.name="robots",t.content=atob("bm9pbmRleCwgbm9mb2xsb3csIG5vYXJjaGl2ZQ=="),document.head.appendChild(t)}}function o(){document.querySelector("figcaption")&&document.querySelectorAll("figcaption").forEach((t=>{volantis.dom.$(t).on("click",(function(){const t=!window.CodeBlockFullscreen;window.CodeBlockFullscreen=t;const o=document.getElementById("post")||document.getElementById("docs")||document.getElementById("page");if(!o)return;const e=this.parentElement,n=e.parentElement,l=document.documentElement,c=document.querySelectorAll(".highlight > table .gutter");o.classList.toggle("code-block-fullscreen",t),e.classList.toggle("code-block-fullscreen",t),n.classList.toggle("code-block-fullscreen",t),e.classList.toggle("code-block-fullscreen-overflow-auto",t),l.classList.toggle("code-block-fullscreen-html-scroll",t),c.forEach((o=>{o.classList.toggle("code-block-fullscreen-gutter",t)}))}))}))}t(),volantis.pjax.push(t),top.location!=self.location&&(top.location=self.location),"mhuig.github.io"==window.location.host||"localhost:4000"==window.location.host||/mhuig\.top$/.test(window.location.host)||/kix\.moe$/.test(window.location.host)||/mhuig/.test(window.location.host)||/ipfs/.test(window.location.host)||(window.location.href=atob("aHR0cHM6Ly9ibG9nLm1odWlnLnRvcC8=")),o(),volantis.pjax.push(o);const e=[{month:12,day:13},function(){const t=(new Date).getFullYear(),o=t%100,e=t>=2e3?4.81:5.59,n=Math.floor(o/4),l=Math.floor(.2422*o+e)-n;return{month:4,day:Math.max(4,l)}}(),{month:7,day:7},{month:9,day:18},{month:9,day:30}];function n(){document.documentElement.classList.remove("mourning-mode");if(!["/","/index.html","/index.htm","/index"].includes(window.location.pathname))return;const t=new Date,o=t.getMonth()+1,n=t.getDate();e.some((t=>t.month===o&&t.day===n))&&document.documentElement.classList.add("mourning-mode")}const l=document.createElement("style");l.textContent="\n html.mourning-mode {\n filter: grayscale(100%);\n -webkit-filter: grayscale(100%);\n transition: filter 0.5s ease;\n }\n ",document.head.appendChild(l),n(),document.addEventListener("pjax:complete",n)})()</script></body></html>