米勒-拉宾素性测试

#include<bits/stdc++.h>
using namespace std;

/**
//普通快速幂
LL pow_mod(LL a, LL x, LL p) {
    LL res = 1;
    while(x) {
        if (x & 1) res = (unsigned long long)res * a % p;
        x >>= 1;
        a = (unsigned long long)a * a % p;
    }
    return res;
}
**/

///Miller-Rabin测试,时间复杂度O(logn)
typedef long long LL;

LL gcd(LL a, LL b)
{
    return b == 0 ? a : gcd(b, a%b);
}

LL mul_mod(LL a, LL x, LL n)            ///乘法快速幂
{
    LL t = 0;
    while(x)
    {
        if(x & 1)
        {
            t += a;
            if(t >= n) t -= n;
        }
        a <<= 1;
        if(a >= n) a -= n;
        x >>= 1;
    }
    return t;
}

///直接的快速幂取模在数据很大的时候有平方,这个平方long long都会存不下,所以需要乘方快速幂
LL pow2_mod(LL a, LL x, LL n)           ///乘方快速幂
{
    LL t = 1;
    a %= n;
    while(x)
    {
        if(x & 1) t = mul_mod(t, a, n);
        a = mul_mod(a, a, n);
        x >>= 1;
    }
    return t;
}

bool test(LL n, LL a, LL d)
{
    if(n == 2) return true;
    if(n == a) return true;
    if((n&1) == 0) return false;
    while(!(d&1)) d /= 2;
    LL t = pow2_mod(a, d, n);
    while((d != n-1) && (t != 1) && (t != n-1))
    {
//        t = (LL)t*t%n;
        t = mul_mod(t, t, n);
        d = d<<1;
    }
    return (t == n-1 || (d&1) == 1);
}

bool isPrime(LL n)
{
    ///有些题目把1看作质数，但是负数不会是质数
    if(n < 2) return false;
    LL a[] = {2, 3, 61};
    for(int i = 0; i <= 2; i++) if(!test(n, a[i], n-1)) return false;
    return true;
}

int main()
{
    ///freopen("in.txt","r",stdin);
    if(isPrime(3203431780337ll))
        puts("YES");
    else puts("NO");
    return 0;
}