C# 中快速素性测试的示例代码 [重复]

Question

可能重复：
Fastest algorithm for primality test

希望参考 C# 中快速素性测试的示例代码，最好使用 BigInteger 或其他可变大小类型。

Answer 1

这是 c# 中的 Miller Rabin 测试：

    bool MillerRabin(ulong n)
    {
        ulong[] ar;
        if (n < 4759123141) ar = new ulong[] { 2, 7, 61 };
        else if (n < 341550071728321) ar = new ulong[] { 2, 3, 5, 7, 11, 13, 17 };
        else ar = new ulong[] { 2, 3, 5, 7, 11, 13, 17, 19, 23 };
        ulong d = n - 1;
        int s = 0;
        while ((d & 1) == 0) { d >>= 1; s++; }
        int i, j;
        for (i = 0; i < ar.Length; i++)
        {
            ulong a   = Math.Min(n - 2, ar[i]);
            ulong now = pow(a, d, n);
            if (now == 1) continue;
            if (now == n - 1) continue;
            for (j = 1; j < s; j++)
            {
                now = mul(now, now, n);
                if (now == n - 1) break;
            }
            if (j == s) return false;
        }
        return true;
    }

    ulong mul(ulong a, ulong b, ulong mod)
    {
        int i;
        ulong now = 0;
        for (i = 63; i >= 0; i--) if (((a >> i) & 1) == 1) break;
        for (; i >= 0; i--)
        {
            now <<= 1;
            while (now > mod) now -= mod;
            if (((a >> i) & 1) == 1) now += b;
            while (now > mod) now -= mod;
        }
        return now;
    }

    ulong pow(ulong a, ulong p, ulong mod)
    {
        if (p == 0) return 1;
        if (p % 2 == 0) return pow(mul(a, a, mod), p / 2, mod);
        return mul(pow(a, p - 1, mod), a, mod);
    }