{"id":1008093,"date":"2024-12-27T10:59:39","date_gmt":"2024-12-27T02:59:39","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1008093.html"},"modified":"2024-12-27T10:59:41","modified_gmt":"2024-12-27T02:59:41","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e6%9f%a5%e6%89%be%e7%b4%a0%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1008093.html","title":{"rendered":"\u5982\u4f55\u7528python\u67e5\u627e\u7d20\u6570"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25083532\/6c050b3f-5fc3-4ba8-b7c1-c8fae584c843.webp\" alt=\"\u5982\u4f55\u7528python\u67e5\u627e\u7d20\u6570\" \/><\/p>\n<p><p> <strong>\u8981\u7528Python\u67e5\u627e\u7d20\u6570\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\uff0c\u4f8b\u5982\u7b80\u5355\u7684\u5faa\u73af\u68c0\u67e5\u6cd5\u3001Sieve of Eratosthenes\u7b97\u6cd5\u3001\u8bd5\u9664\u6cd5\u7b49\u3002\u4f7f\u7528\u5faa\u73af\u68c0\u67e5\u6cd5\u662f\u6700\u76f4\u89c2\u7684\u65b9\u6cd5\uff0c\u4f46\u6548\u7387\u8f83\u4f4e\uff1bSieve of Eratosthenes\u7b97\u6cd5\u66f4\u4e3a\u9ad8\u6548\uff0c\u4f46\u9700\u8981\u66f4\u591a\u7684\u5185\u5b58\uff1b\u800c\u8bd5\u9664\u6cd5\u901a\u8fc7\u51cf\u5c11\u68c0\u67e5\u7684\u6b21\u6570\u6765\u63d0\u9ad8\u6548\u7387\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528\u8fd9\u4e9b\u65b9\u6cd5\u6765\u67e5\u627e\u7d20\u6570\u3002<\/strong><\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff0c<strong>Sieve of Eratosthenes\u7b97\u6cd5<\/strong>\u662f\u4e00\u79cd\u7ecf\u5178\u7684\u3001\u9ad8\u6548\u7684\u67e5\u627e\u7d20\u6570\u7684\u65b9\u6cd5\u3002\u5b83\u7684\u57fa\u672c\u601d\u60f3\u662f\u4ece2\u5f00\u59cb\uff0c\u9010\u6b65\u6807\u8bb0\u5176\u500d\u6570\u4e3a\u975e\u7d20\u6570\uff0c\u7136\u540e\u627e\u5230\u4e0b\u4e00\u4e2a\u672a\u88ab\u6807\u8bb0\u7684\u6570\uff0c\u7ee7\u7eed\u6807\u8bb0\u5176\u500d\u6570\uff0c\u76f4\u5230\u5230\u8fbe\u6307\u5b9a\u8303\u56f4\u7684\u4e0a\u9650\u3002\u8fd9\u6837\u4e00\u8f6e\u904d\u5386\u4e0b\u6765\uff0c\u672a\u88ab\u6807\u8bb0\u7684\u6570\u5c31\u662f\u7d20\u6570\u3002\u4e0b\u9762\u6211\u4eec\u6df1\u5165\u63a2\u8ba8\u8fd9\u79cd\u7b97\u6cd5\uff0c\u5e76\u7ed9\u51faPython\u5b9e\u73b0\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u4ec0\u4e48\u662f\u7d20\u6570\uff1f<\/p>\n<\/p>\n<p><p>\u7d20\u6570\u662f\u6307\u5927\u4e8e1\u7684\u81ea\u7136\u6570\u4e2d\uff0c\u53ea\u80fd\u88ab1\u548c\u5b83\u672c\u8eab\u6574\u9664\u7684\u6570\u3002\u4f8b\u5982\uff0c2\u30013\u30015\u30017\u300111\u7b49\u90fd\u662f\u7d20\u6570\u3002\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u7684\u6700\u57fa\u672c\u65b9\u6cd5\u662f\uff0c\u68c0\u67e5\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\u4e4b\u95f4\uff0c\u662f\u5426\u6709\u6570\u80fd\u6574\u9664\u5b83\u3002\u5982\u679c\u5b58\u5728\u8fd9\u6837\u7684\u6570\uff0c\u5219\u5b83\u4e0d\u662f\u7d20\u6570\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u4f7f\u7528\u5faa\u73af\u68c0\u67e5\u6cd5\u67e5\u627e\u7d20\u6570<\/p>\n<\/p>\n<p><p>\u5faa\u73af\u68c0\u67e5\u6cd5\u662f\u6700\u76f4\u89c2\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u901a\u8fc7\u904d\u5386\u6bcf\u4e00\u4e2a\u5c0f\u4e8e\u5f53\u524d\u6570\u7684\u6574\u6570\uff0c\u5224\u65ad\u5b83\u4eec\u662f\u5426\u80fd\u6574\u9664\u5f53\u524d\u6570\uff0c\u4ece\u800c\u5224\u65ad\u5f53\u524d\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u5b9e\u73b0\u6b65\u9aa4<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u4ece2\u5f00\u59cb\uff0c\u9010\u4e2a\u904d\u5386\u6bcf\u4e2a\u6574\u6570\u3002<\/li>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u6574\u6570\uff0c\u68c0\u67e5\u5b83\u662f\u5426\u80fd\u88ab\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u6240\u6709\u6574\u6570\u6574\u9664\u3002<\/li>\n<li>\u5982\u679c\u4e0d\u80fd\u88ab\u4efb\u4f55\u6570\u6574\u9664\uff0c\u5219\u5b83\u662f\u4e00\u4e2a\u7d20\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>Python\u5b9e\u73b0<\/strong><\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">def is_prime(num):<\/p>\n<p>    if num &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    for i in range(2, int(num0.5) + 1):<\/p>\n<p>        if num % i == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p>def find_primes(limit):<\/p>\n<p>    primes = []<\/p>\n<p>    for num in range(2, limit + 1):<\/p>\n<p>        if is_prime(num):<\/p>\n<p>            primes.append(num)<\/p>\n<p>    return primes<\/p>\n<p>print(find_primes(100))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e09\u3001\u4f7f\u7528Sieve of Eratosthenes\u7b97\u6cd5\u67e5\u627e\u7d20\u6570<\/p>\n<\/p>\n<p><p>Sieve of Eratosthenes\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u67e5\u627e\u7d20\u6570\u7684\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u8f83\u5927\u8303\u56f4\u7684\u7d20\u6570\u67e5\u627e\u3002<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u7b97\u6cd5\u539f\u7406<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u521b\u5efa\u4e00\u4e2a\u4ece2\u5230n\u7684\u5217\u8868\uff0c\u5e76\u5c06\u6240\u6709\u6570\u6807\u8bb0\u4e3a\u7d20\u6570\u3002<\/li>\n<li>\u4ece2\u5f00\u59cb\uff0c\u9010\u4e2a\u5c06\u5176\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u7d20\u6570\u3002<\/li>\n<li>\u91cd\u590d\u4e0a\u8ff0\u6b65\u9aa4\uff0c\u76f4\u5230\u904d\u5386\u5230n\u7684\u5e73\u65b9\u6839\u3002<\/li>\n<li>\u5269\u4e0b\u672a\u88ab\u6807\u8bb0\u7684\u6570\u5373\u4e3a\u7d20\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>Python\u5b9e\u73b0<\/strong><\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">def sieve_of_eratosthenes(limit):<\/p>\n<p>    is_prime = [True] * (limit + 1)<\/p>\n<p>    p = 2<\/p>\n<p>    while p2 &lt;= limit:<\/p>\n<p>        if is_prime[p]:<\/p>\n<p>            for i in range(p * p, limit + 1, p):<\/p>\n<p>                is_prime[i] = False<\/p>\n<p>        p += 1<\/p>\n<p>    primes = [p for p in range(2, limit + 1) if is_prime[p]]<\/p>\n<p>    return primes<\/p>\n<p>print(sieve_of_eratosthenes(100))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u56db\u3001\u4f7f\u7528\u8bd5\u9664\u6cd5\u67e5\u627e\u7d20\u6570<\/p>\n<\/p>\n<p><p>\u8bd5\u9664\u6cd5\u662f\u4ecb\u4e8e\u7b80\u5355\u7684\u5faa\u73af\u68c0\u67e5\u548cSieve of Eratosthenes\u4e4b\u95f4\u7684\u65b9\u6cd5\uff0c\u6548\u7387\u6bd4\u7b80\u5355\u5faa\u73af\u68c0\u67e5\u9ad8\u3002<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u7b97\u6cd5\u539f\u7406<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u4ece2\u5f00\u59cb\uff0c\u4ec5\u68c0\u67e5\u5c0f\u4e8e\u8be5\u6570\u5e73\u65b9\u6839\u7684\u7d20\u6570\u3002<\/li>\n<li>\u5982\u679c\u4e0d\u80fd\u88ab\u4efb\u4f55\u8fd9\u4e9b\u7d20\u6570\u6574\u9664\uff0c\u5219\u5b83\u662f\u4e00\u4e2a\u7d20\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>Python\u5b9e\u73b0<\/strong><\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">def is_prime_trial_division(num, primes):<\/p>\n<p>    if num &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    for prime in primes:<\/p>\n<p>        if prime * prime &gt; num:<\/p>\n<p>            break<\/p>\n<p>        if num % prime == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p>def find_primes_trial_division(limit):<\/p>\n<p>    primes = []<\/p>\n<p>    for num in range(2, limit + 1):<\/p>\n<p>        if is_prime_trial_division(num, primes):<\/p>\n<p>            primes.append(num)<\/p>\n<p>    return primes<\/p>\n<p>print(find_primes_trial_division(100))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e94\u3001\u4f18\u5316\u548c\u5e94\u7528\u573a\u666f<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u4f18\u5316<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u5bf9\u4e8eSieve of Eratosthenes\uff0c\u53ef\u4ee5\u4f7f\u7528\u4f4d\u6570\u7ec4\uff08bit array\uff09\u6765\u8282\u7701\u5185\u5b58\u3002<\/li>\n<li>\u4f7f\u7528\u5e76\u884c\u8ba1\u7b97\u52a0\u901f\u7d20\u6570\u67e5\u627e\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u5e94\u7528\u573a\u666f<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u7d20\u6570\u5728\u5bc6\u7801\u5b66\u4e2d\u6709\u5e7f\u6cdb\u5e94\u7528\uff0c\u5982RSA\u52a0\u5bc6\u3002<\/li>\n<li>\u5206\u6790\u5927\u6570\u636e\u65f6\uff0c\u7d20\u6570\u7528\u4e8e\u751f\u6210\u552f\u4e00\u6807\u8bc6\u7b26\u3002<\/li>\n<li>\u79d1\u5b66\u7814\u7a76\u4e2d\uff0c\u7d20\u6570\u7528\u4e8e\u6570\u8bba\u548c\u6570\u5b66\u6a21\u578b\u5206\u6790\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p><p>\u901a\u8fc7\u4ee5\u4e0a\u65b9\u6cd5\u548c\u4f18\u5316\u7b56\u7565\uff0c\u53ef\u4ee5\u9ad8\u6548\u5730\u67e5\u627e\u7d20\u6570\uff0c\u5e76\u5e94\u7528\u4e8e\u5b9e\u9645\u7684\u8ba1\u7b97\u4efb\u52a1\u4e2d\u3002\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u5e94\u7528\u573a\u666f\u548c\u8ba1\u7b97\u8d44\u6e90\u7684\u9650\u5236\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u4f7f\u7528Python\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u7f16\u5199\u4e00\u4e2a\u7b80\u5355\u7684\u51fd\u6570\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u901a\u5e38\uff0c\u7d20\u6570\u5b9a\u4e49\u4e3a\u5927\u4e8e1\u4e14\u53ea\u80fd\u88ab1\u548c\u81ea\u8eab\u6574\u9664\u7684\u6570\u3002\u53ef\u4ee5\u4f7f\u7528\u5faa\u73af\u6765\u68c0\u67e5\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u6240\u6709\u6574\u6570\uff0c\u770b\u770b\u662f\u5426\u6709\u80fd\u6574\u9664\u8be5\u6570\u7684\u6570\u3002\u5982\u679c\u6ca1\u6709\u627e\u5230\u8fd9\u6837\u7684\u6570\uff0c\u5219\u8be5\u6570\u4e3a\u7d20\u6570\u3002<\/p>\n<p><strong>Python\u4e2d\u6709\u54ea\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u67e5\u627e\u6307\u5b9a\u8303\u56f4\u5185\u7684\u7d20\u6570\uff1f<\/strong><br \/>\u53ef\u4ee5\u4f7f\u7528\u201c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u201d\u6765\u9ad8\u6548\u67e5\u627e\u6307\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002\u8fd9\u4e2a\u7b97\u6cd5\u901a\u8fc7\u8fed\u4ee3\u5730\u6807\u8bb0\u5408\u6570\uff0c\u53ef\u4ee5\u5728O(n log log n)\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u627e\u5230\u6240\u6709\u7d20\u6570\u3002\u4f60\u53ef\u4ee5\u4f7f\u7528\u5217\u8868\u6765\u5b58\u50a8\u7ed3\u679c\uff0c\u5e76\u901a\u8fc7\u8fed\u4ee3\u7684\u65b9\u5f0f\u6765\u5b9e\u73b0\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u67e5\u627e\u7d20\u6570\u65f6\uff0c\u5e38\u89c1\u7684\u6027\u80fd\u4f18\u5316\u6709\u54ea\u4e9b\uff1f<\/strong><br \/>\u5bf9\u4e8e\u67e5\u627e\u7d20\u6570\u7684\u6027\u80fd\u4f18\u5316\uff0c\u53ef\u4ee5\u8003\u8651\u4ee5\u4e0b\u51e0\u79cd\u7b56\u7565\uff1a  <\/p>\n<ol>\n<li>\u53ea\u68c0\u67e5\u5947\u6570\uff0c\u56e0\u4e3a\u5076\u6570\uff08\u9664\u4e862\uff09\u4e0d\u53ef\u80fd\u662f\u7d20\u6570\u3002<\/li>\n<li>\u5c06\u68c0\u67e5\u8303\u56f4\u9650\u5236\u5728\u6570\u7684\u5e73\u65b9\u6839\u4e4b\u5185\uff0c\u4ece\u800c\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u8ba1\u7b97\u3002<\/li>\n<li>\u4f7f\u7528\u96c6\u5408\u6216\u5b57\u5178\u6765\u5b58\u50a8\u5df2\u627e\u5230\u7684\u7d20\u6570\uff0c\u907f\u514d\u91cd\u590d\u8ba1\u7b97\u548c\u67e5\u627e\u3002<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u65b9\u6cd5\u4e0d\u4ec5\u63d0\u9ad8\u4e86\u6027\u80fd\uff0c\u8fd8\u80fd\u4f7f\u4ee3\u7801\u66f4\u7b80\u6d01\u6613\u8bfb\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u8981\u7528Python\u67e5\u627e\u7d20\u6570\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u65b9\u6cd5\uff0c\u4f8b\u5982\u7b80\u5355\u7684\u5faa\u73af\u68c0\u67e5\u6cd5\u3001Sieve of Eratosthenes\u7b97 [&hellip;]","protected":false},"author":3,"featured_media":1008103,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1008093"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1008093"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1008093\/revisions"}],"predecessor-version":[{"id":1008105,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1008093\/revisions\/1008105"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1008103"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1008093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1008093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1008093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}