{"id":989010,"date":"2024-12-27T08:07:32","date_gmt":"2024-12-27T00:07:32","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/989010.html"},"modified":"2024-12-27T08:07:36","modified_gmt":"2024-12-27T00:07:36","slug":"python%e4%b8%ad%e8%b4%a8%e6%95%b0%e5%a6%82%e4%bd%95%e5%88%a4%e6%96%ad","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/989010.html","title":{"rendered":"python\u4e2d\u8d28\u6570\u5982\u4f55\u5224\u65ad"},"content":{"rendered":"

\"python\u4e2d\u8d28\u6570\u5982\u4f55\u5224\u65ad\"<\/p>\n

\u5728Python\u4e2d\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u7528\u7684\u5305\u62ec\u7d20\u6570\u7684\u5b9a\u4e49\u5224\u65ad\u3001\u8bd5\u9664\u6cd5\u548c\u4f18\u5316\u7684\u8bd5\u9664\u6cd5<\/strong>\u7b49\u3002\u7d20\u6570\u7684\u5b9a\u4e49\u662f\u5927\u4e8e1\u7684\u81ea\u7136\u6570\u4e2d\uff0c\u53ea\u67091\u548c\u81ea\u8eab\u4e24\u4e2a\u56e0\u6570\u7684\u6570\u3002\u4ee5\u4e0b\u662f\u5176\u4e2d\u4e00\u79cd\u65b9\u6cd5\u7684\u8be6\u7ec6\u63cf\u8ff0\uff1a\u8bd5\u9664\u6cd5<\/strong>\u3002\u8bd5\u9664\u6cd5\u662f\u6700\u5e38\u7528\u7684\u8d28\u6570\u5224\u65ad\u65b9\u6cd5\u4e4b\u4e00\uff0c\u5176\u57fa\u672c\u601d\u60f3\u662f\u68c0\u67e5\u4e00\u4e2a\u6570n\u662f\u5426\u80fd\u88ab\u5c0f\u4e8e\u7b49\u4e8e\u5b83\u5e73\u65b9\u6839\u7684\u6574\u6570\u6574\u9664\u3002\u5982\u679cn\u4e0d\u80fd\u88ab\u8fd9\u4e9b\u6570\u6574\u9664\uff0c\u90a3\u4e48n\u5c31\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u7d20\u6570\u7684\u5b9a\u4e49\u5224\u65ad<\/p>\n<\/p>\n

\u8d28\u6570\u662f\u6307\u4e00\u4e2a\u5927\u4e8e1\u7684\u81ea\u7136\u6570\uff0c\u9664\u4e861\u548c\u5b83\u672c\u8eab\u4ee5\u5916\u6ca1\u6709\u5176\u4ed6\u56e0\u6570\u3002\u6839\u636e\u8fd9\u4e2a\u5b9a\u4e49\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u6700\u7b80\u5355\u7684\u65b9\u6cd5\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002\u5177\u4f53\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

def is_prime(n):<\/p>\n
    if n <= 1:<\/p>\n
        return False<\/p>\n
    for i in range(2, n):<\/p>\n
        if n % i == 0:<\/p>\n
            return False<\/p>\n
    return True<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u4e2a\u65b9\u6cd5\u867d\u7136\u76f4\u89c2\uff0c\u4f46\u6548\u7387\u4e0d\u9ad8\u3002\u5bf9\u4e8e\u5927\u6570\u6765\u8bf4\uff0c\u9700\u8981\u68c0\u67e5\u7684\u53ef\u80fd\u6027\u592a\u591a\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u8bd5\u9664\u6cd5<\/p>\n<\/p>\n
\u8bd5\u9664\u6cd5\u662f\u901a\u8fc7\u5bf9\u4e00\u4e2a\u6570\u8fdb\u884c\u9664\u6cd5\u8fd0\u7b97\u6765\u5224\u65ad\u5b83\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u3002\u5176\u57fa\u672c\u601d\u8def\u662f\uff1a\u4ece2\u5f00\u59cb\uff0c\u5c1d\u8bd5\u9664\u4ee5\u6bcf\u4e00\u4e2a\u6574\u6570\u3002\u5982\u679c\u5728\u67d0\u4e2a\u6570\u4e0a\u6574\u9664\uff0c\u90a3\u4e48\u5b83\u5c31\u4e0d\u662f\u8d28\u6570\uff1b\u5982\u679c\u76f4\u5230\u5b83\u7684\u5e73\u65b9\u6839\u90fd\u6ca1\u6709\u627e\u5230\u80fd\u6574\u9664\u7684\u6570\uff0c\u90a3\u4e48\u5b83\u5c31\u662f\u8d28\u6570\u3002<\/p>\n<\/p>\n
import math<\/p>\n
def is_prime(n):<\/p>\n
    if n <= 1:<\/p>\n
        return False<\/p>\n
    if n <= 3:<\/p>\n
        return True<\/p>\n
    if n % 2 == 0 or n % 3 == 0:<\/p>\n
        return False<\/p>\n
    i = 5<\/p>\n
    while i * i <= n:<\/p>\n
        if n % i == 0 or n % (i + 2) == 0:<\/p>\n
            return False<\/p>\n
        i += 6<\/p>\n
    return True<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4f18\u5316\u540e\u7684\u8bd5\u9664\u6cd5<\/strong>\u901a\u8fc7\u51cf\u5c11\u9700\u8981\u68c0\u67e5\u7684\u6570\uff0c\u63d0\u9ad8\u4e86\u6548\u7387\u3002\u6b64\u65b9\u6cd5\u5229\u7528\u4e86\u4ee5\u4e0b\u51e0\u70b9\uff1a<\/p>\n<\/p>\n
    \n
  1. \u5927\u4e8e2\u7684\u5076\u6570\u90fd\u4e0d\u662f\u8d28\u6570\u3002<\/li>\n
  2. \u53ea\u9700\u68c0\u67e5\u5230\u5e73\u65b9\u6839\uff0c\u56e0\u4e3a\u5982\u679cn = a * b\uff0c\u90a3\u4e48a\u548cb\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2a\u5c0f\u4e8e\u7b49\u4e8e\u221an\u3002<\/li>\n
  3. \u68c0\u67e56\u7684\u500d\u6570\u9644\u8fd1\u7684\u6570\uff086k \u00b1 1\uff09\uff0c\u56e0\u4e3a\u8d28\u6570\u5927\u4e8e3\u7684\uff0c\u5fc5\u5b9a\u57286\u7684\u500d\u6570\u7684\u4e24\u4fa7\u3002<\/li>\n<\/ol>\n
    \u4e09\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5<\/p>\n<\/p>\n
    \u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u627e\u51fa\u6240\u6709\u5c0f\u4e8e\u67d0\u4e2a\u6570\u7684\u8d28\u6570\u7684\u9ad8\u6548\u7b97\u6cd5\u3002\u5b83\u7684\u57fa\u672c\u539f\u7406\u662f\uff1a\u4ece2\u5f00\u59cb\uff0c\u5c06\u6bcf\u4e2a\u8d28\u6570\u7684\u500d\u6570\u6807\u8bb0\u4e3a\u5408\u6570\u3002\u6700\u7ec8\uff0c\u672a\u88ab\u6807\u8bb0\u7684\u6570\u5c31\u662f\u8d28\u6570\u3002\u4ee5\u4e0b\u662f\u5177\u4f53\u5b9e\u73b0\uff1a<\/p>\n<\/p>\n
    def sieve_of_eratosthenes(max_num):<\/p>\n
        is_prime = [True] * (max_num + 1)<\/p>\n
        p = 2<\/p>\n
        while (p * p <= max_num):<\/p>\n
            if is_prime[p]:<\/p>\n
                for i in range(p * p, max_num + 1, p):<\/p>\n
                    is_prime[i] = False<\/p>\n
            p += 1<\/p>\n
        prime_numbers = [p for p in range(2, max_num) if is_prime[p]]<\/p>\n
        return prime_numbers<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u6548\u7387\u8f83\u9ad8\uff0c\u4f46\u9700\u8981\u989d\u5916\u7684\u7a7a\u95f4\u6765\u5b58\u50a8\u6807\u8bb0\u3002<\/p>\n<\/p>\n
    \u56db\u3001\u4f7f\u7528Python\u5e93\u8fdb\u884c\u8d28\u6570\u5224\u65ad<\/p>\n<\/p>\n
    Python\u6709\u8bb8\u591a\u79d1\u5b66\u8ba1\u7b97\u5e93\u53ef\u4ee5\u7528\u6765\u8fdb\u884c\u8d28\u6570\u5224\u65ad\uff0c\u6bd4\u5982SymPy\u3002SymPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684Python\u5e93\uff0c\u4e13\u95e8\u7528\u4e8e\u7b26\u53f7\u6570\u5b66\u8ba1\u7b97\u3002\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2aisprime\u51fd\u6570\u53ef\u4ee5\u76f4\u63a5\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\uff1a<\/p>\n<\/p>\n
    from sympy import isprime<\/p>\n
    def check_prime(n):<\/p>\n
        return isprime(n)<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u4f7f\u7528\u5e93\u65b9\u6cd5\u53ef\u4ee5\u5927\u5927\u7b80\u5316\u4ee3\u7801\uff0c\u4f46\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u4e0d\u5982\u624b\u52a8\u5b9e\u73b0\u7684\u5feb\u3002<\/p>\n<\/p>\n
    \u4e94\u3001\u7d20\u6027\u6d4b\u8bd5\u548c\u5927\u6570\u8d28\u6570\u5224\u65ad<\/p>\n<\/p>\n
    \u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\uff0c\u5e38\u7528\u7684\u8d28\u6570\u5224\u65ad\u65b9\u6cd5\u53ef\u80fd\u4e0d\u591f\u9ad8\u6548\u6216\u51c6\u786e\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u7d20\u6027\u6d4b\u8bd5\uff08\u5982Miller-Rabin\u6d4b\u8bd5\uff09\u6765\u5224\u65ad\u3002\u7d20\u6027\u6d4b\u8bd5\u4e0d\u80fd100%\u786e\u5b9a\u4e00\u4e2a\u6570\u662f\u8d28\u6570\uff0c\u4f46\u53ef\u4ee5\u5728\u6982\u7387\u4e0a\u7ed9\u51fa\u5f88\u9ad8\u7684\u51c6\u786e\u7387\u3002<\/p>\n<\/p>\n
    def miller_rabin(n, k=5):<\/p>\n
        if n <= 1:<\/p>\n
            return False<\/p>\n
        if n <= 3:<\/p>\n
            return True<\/p>\n
        if n % 2 == 0:<\/p>\n
            return False<\/p>\n
        r, d = 0, n - 1<\/p>\n
        while d % 2 == 0:<\/p>\n
            r += 1<\/p>\n
            d \/\/= 2<\/p>\n
        def check(a, d, n, r):<\/p>\n
            x = pow(a, d, n)<\/p>\n
            if x == 1 or x == n - 1:<\/p>\n
                return True<\/p>\n
            for _ in range(r - 1):<\/p>\n
                x = pow(x, 2, n)<\/p>\n
                if x == n - 1:<\/p>\n
                    return True<\/p>\n
            return False<\/p>\n
        import random<\/p>\n
        for _ in range(k):<\/p>\n
            a = random.randint(2, n - 2)<\/p>\n
            if not check(a, d, n, r):<\/p>\n
                return False<\/p>\n
        return True<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    Miller-Rabin\u7d20\u6027\u6d4b\u8bd5\u662f\u4e00\u79cd\u968f\u673a\u5316\u7b97\u6cd5\uff0c\u901a\u8fc7\u591a\u6b21\u6d4b\u8bd5\u6765\u964d\u4f4e\u9519\u8bef\u7387\u3002<\/p>\n<\/p>\n
    \u901a\u8fc7\u4ee5\u4e0a\u51e0\u79cd\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002\u6839\u636e\u5b9e\u9645\u9700\u6c42\uff0c\u53ef\u4ee5\u9009\u62e9\u6700\u5408\u9002\u7684\u7b97\u6cd5\u8fdb\u884c\u5b9e\u73b0\u3002<\/p>\n<\/p>\n
    \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
     \u5982\u4f55\u5728Python\u4e2d\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\uff1f<\/strong>
    \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\u8d28\u6570\u3002\u8d28\u6570\u662f\u6307\u5927\u4e8e1\u7684\u81ea\u7136\u6570\uff0c\u4e14\u53ea\u80fd\u88ab1\u548c\u5176\u81ea\u8eab\u6574\u9664\u3002\u53ef\u4ee5\u4f7f\u7528\u5faa\u73af\u548c\u6761\u4ef6\u8bed\u53e5\u6765\u5b9e\u73b0\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u68c0\u67e5\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u6240\u6709\u6574\u6570\uff0c\u82e5\u8be5\u6570\u80fd\u88ab\u5176\u4e2d\u4efb\u4f55\u4e00\u4e2a\u6574\u9664\uff0c\u5219\u5b83\u4e0d\u662f\u8d28\u6570\u3002<\/p>\n
    \u6709\u54ea\u4e9b\u5e38\u89c1\u7684\u7b97\u6cd5\u53ef\u4ee5\u7528\u6765\u5224\u65ad\u8d28\u6570\uff1f<\/strong>
    \u5224\u65ad\u8d28\u6570\u7684\u5e38\u89c1\u7b97\u6cd5\u5305\u62ec\u8bd5\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u548c\u7c73\u52d2-\u62c9\u5bbe\u6d4b\u8bd5\u7b49\u3002\u8bd5\u9664\u6cd5\u662f\u6700\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u6cd5\uff0c\u800c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u5219\u9002\u5408\u7528\u4e8e\u5bfb\u627e\u8303\u56f4\u5185\u7684\u6240\u6709\u8d28\u6570\u3002\u7c73\u52d2-\u62c9\u5bbe\u6d4b\u8bd5\u5219\u662f\u4e00\u79cd\u6982\u7387\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u975e\u5e38\u5927\u7684\u6570\u5b57\u3002<\/p>\n
    \u662f\u5426\u6709\u73b0\u6210\u7684Python\u5e93\u53ef\u4ee5\u7528\u6765\u5224\u65ad\u8d28\u6570\uff1f<\/strong>
    \u662f\u7684\uff0cPython\u7684\u4e00\u4e9b\u7b2c\u4e09\u65b9\u5e93\uff0c\u5982SymPy\u548cNumPy\uff0c\u63d0\u4f9b\u4e86\u5224\u65ad\u8d28\u6570\u7684\u51fd\u6570\u3002\u4f7f\u7528\u8fd9\u4e9b\u5e93\u53ef\u4ee5\u7b80\u5316\u4ee3\u7801\u7684\u7f16\u5199\uff0c\u5e76\u63d0\u9ad8\u8fd0\u884c\u6548\u7387\u3002\u4f8b\u5982\uff0cSymPy\u5e93\u4e2d\u7684isprime()<\/code>\u51fd\u6570\u53ef\u4ee5\u76f4\u63a5\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\uff0c\u975e\u5e38\u65b9\u4fbf\u3002<\/p>\n
    \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5224\u65ad\u8d28\u6570\u6709\u4ec0\u4e48\u91cd\u8981\u6027\uff1f<\/strong>
    \u8d28\u6570\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u5bc6\u7801\u5b66\u548c\u6570\u8bba\u4e2d\u6709\u7740\u91cd\u8981\u5e94\u7528\u3002\u5c24\u5176\u662f\u5728\u52a0\u5bc6\u7b97\u6cd5\u4e2d\uff0c\u8bb8\u591a\u5b89\u5168\u534f\u8bae\u4f9d\u8d56\u4e8e\u5927\u8d28\u6570\u7684\u751f\u6210\u4e0e\u5206\u89e3\u3002\u56e0\u6b64\uff0c\u638c\u63e1\u8d28\u6570\u7684\u5224\u65ad\u65b9\u5f0f\u5bf9\u4e8e\u7406\u89e3\u76f8\u5173\u9886\u57df\u7684\u57fa\u7840\u77e5\u8bc6\u81f3\u5173\u91cd\u8981\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u7528\u7684\u5305\u62ec\u7d20\u6570\u7684\u5b9a\u4e49\u5224\u65ad\u3001\u8bd5\u9664\u6cd5\u548c\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u7b49\u3002\u7d20\u6570\u7684\u5b9a\u4e49 […]","protected":false},"author":3,"featured_media":989022,"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\/989010"}],"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=989010"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/989010\/revisions"}],"predecessor-version":[{"id":989023,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/989010\/revisions\/989023"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/989022"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=989010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=989010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=989010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}