{"id":1007648,"date":"2024-12-27T10:55:33","date_gmt":"2024-12-27T02:55:33","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1007648.html"},"modified":"2024-12-27T10:55:39","modified_gmt":"2024-12-27T02:55:39","slug":"python%e5%87%bd%e6%95%b0%e5%a6%82%e4%bd%95%e5%88%a4%e6%96%ad%e8%b4%a8%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1007648.html","title":{"rendered":"Python\u51fd\u6570\u5982\u4f55\u5224\u65ad\u8d28\u6570"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25083303\/4de41f90-3c4e-4416-b51e-94ac74f00346.webp\" alt=\"Python\u51fd\u6570\u5982\u4f55\u5224\u65ad\u8d28\u6570\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\u5224\u65ad\u8d28\u6570\u7684\u51fd\u6570\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u6cd5\u5b9e\u73b0\uff0c\u5e38\u89c1\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u904d\u5386\u68c0\u67e5\u6cd5\u3001\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u3001\u8bd5\u9664\u6cd5\u3002\u6211\u4eec\u5c06\u8be6\u7ec6\u5c55\u5f00\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\uff0c\u56e0\u4e3a\u5b83\u5728\u6027\u80fd\u4e0a\u4f18\u4e8e\u904d\u5386\u68c0\u67e5\u6cd5\u3002<\/strong><\/p>\n<\/p>\n<p><p>\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\uff1a\u4e00\u4e2a\u6570n\u5982\u679c\u4e0d\u662f\u8d28\u6570\uff0c\u90a3\u4e48\u5b83\u5fc5\u5b9a\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u56e0\u6570a\u548cb\uff0c\u5176\u4e2da\u548cb\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u5c0f\u4e8e\u6216\u7b49\u4e8e\u221an\u3002\u56e0\u6b64\uff0c\u53ea\u9700\u68c0\u67e5n\u662f\u5426\u80fd\u88ab2\u5230\u221an\u4e4b\u95f4\u7684\u4efb\u4f55\u6570\u6574\u9664\u5373\u53ef\u3002\u5982\u679c\u4e0d\u80fd\uff0c\u5219n\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n<p><p>\u4ee5\u4e0b\u662f\u5b9e\u73b0\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u7684\u8be6\u7ec6\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u7684\u5b9e\u73b0<\/strong><\/p>\n<\/p>\n<ol>\n<li>\n<p>\u9996\u5148\uff0c\u6392\u9664\u5c0f\u4e8e2\u7684\u6570\u5b57\uff0c\u56e0\u4e3a\u8d28\u6570\u5b9a\u4e49\u4e3a\u5927\u4e8e1\u7684\u81ea\u7136\u6570\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u7136\u540e\uff0c\u68c0\u67e5\u6570\u5b572\uff0c\u56e0\u4e3a2\u662f\u6700\u5c0f\u7684\u8d28\u6570\uff0c\u4e5f\u662f\u552f\u4e00\u7684\u5076\u6570\u8d28\u6570\u3002\u5bf9\u4e8e\u5927\u4e8e2\u7684\u5076\u6570\uff0c\u76f4\u63a5\u8fd4\u56deFalse\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u5bf9\u4e8e\u5947\u6570\uff0c\u68c0\u67e5\u4ece3\u5230\u221an\u7684\u6240\u6709\u5947\u6570\u3002\u5982\u679cn\u80fd\u591f\u88ab\u8fd9\u4e9b\u6570\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u6574\u9664\uff0c\u5219n\u4e0d\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import math<\/p>\n<p>def is_prime(n):<\/p>\n<p>    &quot;&quot;&quot;\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570&quot;&quot;&quot;<\/p>\n<p>    if n &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    if n == 2:<\/p>\n<p>        return True<\/p>\n<p>    if n % 2 == 0:<\/p>\n<p>        return False<\/p>\n<p>    max_divisor = math.isqrt(n)<\/p>\n<p>    for i in range(3, max_divisor + 1, 2):<\/p>\n<p>        if n % i == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e8c\u3001\u904d\u5386\u68c0\u67e5\u6cd5<\/p>\n<\/p>\n<p><p>\u904d\u5386\u68c0\u67e5\u6cd5\u662f\u6700\u7b80\u5355\u7684\u8d28\u6570\u5224\u65ad\u65b9\u6cd5\u3002\u5b83\u901a\u8fc7\u68c0\u67e5\u4ece2\u5230n-1\u7684\u6bcf\u4e00\u4e2a\u6570\u662f\u5426\u80fd\u6574\u9664n\u6765\u5224\u65adn\u662f\u5426\u4e3a\u8d28\u6570\u3002\u867d\u7136\u8fd9\u79cd\u65b9\u6cd5\u76f4\u89c2\u4e14\u6613\u4e8e\u7406\u89e3\uff0c\u4f46\u5bf9\u4e8e\u5927\u7684\u6570\u5b57\uff0c\u5b83\u7684\u6548\u7387\u8f83\u4f4e\u3002<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u5b9e\u73b0\u904d\u5386\u68c0\u67e5\u6cd5<\/strong><\/p>\n<\/p>\n<ol>\n<li>\n<p>\u76f4\u63a5\u4ece2\u5f00\u59cb\uff0c\u9010\u4e2a\u68c0\u67e5\u6bcf\u4e2a\u6570\u5b57\u662f\u5426\u80fd\u6574\u9664n\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u6570\u5b57\u80fd\u6574\u9664n\uff0c\u5219n\u4e0d\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">def is_prime_basic(n):<\/p>\n<p>    &quot;&quot;&quot;\u4f7f\u7528\u904d\u5386\u68c0\u67e5\u6cd5\u5224\u65ad\u8d28\u6570&quot;&quot;&quot;<\/p>\n<p>    if n &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    for i in range(2, n):<\/p>\n<p>        if n % i == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e09\u3001\u8bd5\u9664\u6cd5<\/p>\n<\/p>\n<p><p>\u8bd5\u9664\u6cd5\u662f\u5bf9\u904d\u5386\u68c0\u67e5\u6cd5\u7684\u6539\u8fdb\u3002\u5b83\u901a\u8fc7\u53ea\u68c0\u67e5\u5230n\u7684\u4e00\u534a\u7684\u6570\u5b57\u6765\u63d0\u9ad8\u6548\u7387\u3002\u56e0\u4e3a\u5982\u679cn = a * b\uff0c\u5176\u4e2da\u548cb\u90fd\u662f\u5927\u4e8en\/2\u7684\u6570\uff0c\u90a3\u4e48a\u548cb\u5fc5\u987b\u90fd\u5927\u4e8e1\u4e14\u5c0f\u4e8en\u3002<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u5b9e\u73b0\u8bd5\u9664\u6cd5<\/strong><\/p>\n<\/p>\n<ol>\n<li>\n<p>\u68c0\u67e5\u4ece2\u5230n\/2\u7684\u6570\u5b57\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u6570\u5b57\u80fd\u6574\u9664n\uff0c\u5219n\u4e0d\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">def is_prime_trial(n):<\/p>\n<p>    &quot;&quot;&quot;\u4f7f\u7528\u8bd5\u9664\u6cd5\u5224\u65ad\u8d28\u6570&quot;&quot;&quot;<\/p>\n<p>    if n &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    for i in range(2, n\/\/2 + 1):<\/p>\n<p>        if n % i == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u56db\u3001\u6027\u80fd\u6bd4\u8f83\u4e0e\u4f18\u5316\u5efa\u8bae<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u6027\u80fd\u6bd4\u8f83<\/strong><\/p>\n<\/p>\n<ol>\n<li>\n<p>\u5728\u5bf9\u8d28\u6570\u8fdb\u884c\u5224\u65ad\u65f6\uff0c\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u76f8\u8f83\u4e8e\u5176\u4ed6\u65b9\u6cd5\u6027\u80fd\u66f4\u597d\u3002\u56e0\u4e3a\u5b83\u51cf\u5c11\u4e86\u9700\u8981\u68c0\u67e5\u7684\u53ef\u80fd\u56e0\u6570\u7684\u6570\u91cf\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u5bf9\u4e8e\u8f83\u5c0f\u7684\u6570\u5b57\uff0c\u904d\u5386\u68c0\u67e5\u6cd5\u548c\u8bd5\u9664\u6cd5\u7684\u6027\u80fd\u5dee\u522b\u4e0d\u5927\u3002\u4f46\u968f\u7740\u6570\u5b57\u7684\u589e\u5927\uff0c\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u7684\u6548\u7387\u4f18\u52bf\u9010\u6e10\u663e\u73b0\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<p><strong>\u4f18\u5316\u5efa\u8bae<\/strong><\/p>\n<\/p>\n<ol>\n<li>\n<p>\u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\u5b57\uff0c\u53ef\u4ee5\u4f7f\u7528\u66f4\u9ad8\u7ea7\u7684\u7b97\u6cd5\u5982Miller-Rabin\u7d20\u6027\u6d4b\u8bd5\uff0c\u5c3d\u7ba1\u8be5\u7b97\u6cd5\u662f\u6982\u7387\u6027\u7684\uff0c\u4f46\u5bf9\u4e8e\u5927\u591a\u6570\u5e94\u7528\u573a\u666f\u5df2\u7ecf\u8db3\u591f\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5982\u679c\u9700\u8981\u5927\u91cf\u5224\u65ad\u8d28\u6570\uff0c\u53ef\u4ee5\u7ed3\u5408\u7f13\u5b58\u6280\u672f\u51cf\u5c11\u91cd\u590d\u8ba1\u7b97\uff0c\u63d0\u9ad8\u6548\u7387\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><p>\u4e94\u3001Python\u4e2d\u7684\u5e94\u7528\u573a\u666f<\/p>\n<\/p>\n<ol>\n<li>\n<p><strong>\u8d28\u6570\u5728\u52a0\u5bc6\u4e2d\u7684\u5e94\u7528<\/strong><\/p>\n<\/p>\n<p><p>\u8d28\u6570\u5728\u73b0\u4ee3\u52a0\u5bc6\u7b97\u6cd5\u4e2d\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5c24\u5176\u662f\u5728\u516c\u94a5\u52a0\u5bc6\u7b97\u6cd5\u5982RSA\u4e2d\u3002RSA\u5229\u7528\u4e24\u4e2a\u5927\u8d28\u6570\u7684\u4e58\u79ef\u751f\u6210\u4e00\u4e2a\u516c\u94a5\u548c\u79c1\u94a5\u5bf9\uff0c\u5176\u4e2d\u5927\u8d28\u6570\u7684\u6027\u8d28\u786e\u4fdd\u4e86\u52a0\u5bc6\u7684\u5b89\u5168\u6027\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u7b97\u6cd5\u7ade\u8d5b\u4e0e\u6570\u5b66\u95ee\u9898<\/strong><\/p>\n<\/p>\n<p><p>\u5224\u65ad\u8d28\u6570\u662f\u8bb8\u591a\u7b97\u6cd5\u7ade\u8d5b\u548c\u6570\u5b66\u95ee\u9898\u7684\u57fa\u7840\uff0c\u5feb\u901f\u5224\u65ad\u8d28\u6570\u7684\u80fd\u529b\u53ef\u4ee5\u4e3a\u590d\u6742\u95ee\u9898\u7684\u89e3\u51b3\u63d0\u4f9b\u5e2e\u52a9\u3002<\/p>\n<\/p>\n<\/li>\n<li>\n<p><strong>\u6570\u636e\u5206\u6790\u4e0e\u79d1\u5b66\u8ba1\u7b97<\/strong><\/p>\n<\/p>\n<p><p>\u5728\u6570\u636e\u5206\u6790\u548c\u79d1\u5b66\u8ba1\u7b97\u4e2d\uff0c\u6709\u65f6\u9700\u8981\u5bf9\u6570\u636e\u8fdb\u884c\u7b5b\u9009\u548c\u4f18\u5316\uff0c\u8d28\u6570\u5224\u65ad\u53ef\u4ee5\u4f5c\u4e3a\u6570\u636e\u5904\u7406\u7684\u4e00\u90e8\u5206\uff0c\u5e2e\u52a9\u7814\u7a76\u4eba\u5458\u8bc6\u522b\u548c\u8fc7\u6ee4\u6570\u636e\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n<p><p>\u516d\u3001\u603b\u7ed3<\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u672c\u7bc7\u6587\u7ae0\u7684\u8ba8\u8bba\uff0c\u6211\u4eec\u4e86\u89e3\u4e86Python\u4e2d\u5224\u65ad\u8d28\u6570\u7684\u591a\u79cd\u65b9\u6cd5\uff0c\u5305\u62ec<strong>\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u3001\u904d\u5386\u68c0\u67e5\u6cd5\u3001\u8bd5\u9664\u6cd5<\/strong>\uff0c\u5e76\u91cd\u70b9\u5206\u6790\u4e86\u5e73\u65b9\u6839\u4f18\u5316\u6cd5\u7684\u5b9e\u73b0\u7ec6\u8282\u53ca\u5176\u6027\u80fd\u4f18\u52bf\u3002\u540c\u65f6\uff0c\u7ed3\u5408\u5b9e\u9645\u5e94\u7528\u573a\u666f\uff0c\u6211\u4eec\u8ba4\u8bc6\u5230\u8d28\u6570\u5224\u65ad\u5728\u73b0\u4ee3\u8ba1\u7b97\u4e2d\u7684\u91cd\u8981\u6027\u3002\u56e0\u6b64\uff0c\u5728\u7f16\u5199Python\u7a0b\u5e8f\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u8d28\u6570\u5224\u65ad\u65b9\u6cd5\u53ef\u4ee5\u63d0\u9ad8\u7a0b\u5e8f\u7684\u6548\u7387\u548c\u51c6\u786e\u6027\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> 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