计蒜客——Goldbach

• Goldbach
• 判断大素数

#include<cstdio>
#include<cstdlib>
using namespace std;
#define N 10000
typedef unsigned long long ll;

ll ModMul(ll a, ll b, ll n) { //快速积取模 a*b%n
    ll ans = 0;
    while(b) {
        if(b & 1)
            ans = (ans + a) % n;
        a = (a + a) % n;
        b >>= 1;
    }
    return ans;
}
ll ModExp(ll a, ll b, ll n) { //快速幂取模 a^b%n
    ll ans = 1;
    while(b) {
        if(b & 1)
            ans = ModMul(ans, a, n);
        a = ModMul(a, a, n);
        b >>= 1;
    }
    return ans;
}
bool miller_rabin(ll n) { //Miller-Rabin素数检测算法
    ll i, j, a, x, y, t, u, s = 10;
    if(n == 2)
        return true;
    if(n < 2 || !(n & 1))
        return false;
    for(t = 0, u = n - 1; !(u & 1); t++, u >>= 1); //n-1=u*2^t
    for(i = 0; i < s; i++) {
        a = rand() % (n - 1) + 1;
        x = ModExp(a, u, n);
        for(j = 0; j < t; j++) {
            y = ModMul(x, x, n);
            if(y == 1 && x != 1 && x != n - 1)
                return false;
            x = y;
        }
        if(x != 1)
            return false;
    }
    return true;
}

//以上都是模板，以下为核心算法
int main()
{
    ll n, t;
    scanf("%llu",&t);
    while(t--){
        scanf("%llu", &n);
        //通过数学规律可以发现第一个素数最大不超过10000
        for(ll i = 1; i < N; i++){
            if(miller_rabin(i) && miller_rabin(n-i)){
                printf("%llu %llu\n",i, n-i);
                break;
            }
        }
    }
    return 0;
}

参考：https://blog.csdn.net/a1097304791/article/details/81586513