学步园

 

#include<iostream>
#include<algorithm>
using namespace std;
long long factor[110], cnt;
long long Mul_Mod(long long a, long long b, long long c) {
if (b == 0)
return 0;
long long ans = Mul_Mod(a, b / 2, c);
    ans = (ans * 2) % c;
if (b % 2)
        ans = (ans + a) % c;
return ans;
}
long long Pow_Mod(long long a, long long b, long long c) {
if (b == 0)
return 1;
long long x = Pow_Mod(a, b / 2, c);
if (x == 0)
return 0;
long long y = Mul_Mod(x, x, c);
if (y == 1 && x != 1 && x != c - 1)
return 0;
if (b % 2)
        y = Mul_Mod(y, a, c);
return y;
}
bool Miller_rabin(long long n, int timenum = 10) {
if (n < 2)
return false;
if (n == 2)
return true;
while (timenum--) {
if (Pow_Mod(rand() % (n - 2) + 2, n - 1, n) != 1)
return false;
    }
return true;
}
long long Gcd(long long a, long long b) {
long long t;
while (b) {
        t = a;
        a = b;
        b = t % b;
    }
return a;
}
void Pollard(long long n);

void Factor(long long n) {
long long d = 2;
while (true) {
if (n % d == 0) {
            Pollard(d);
            Pollard(n / d);
return;
        }
        d++;
    }
}
void Pollard(long long n) {
if (n <= 0)
        printf("error\n");
if (n == 1)
return;
if (Miller_rabin(n)) {
        factor[cnt++] = n;
return;
    }
long long i = 0, k = 2, x, y, d;
    x = y = rand() % (n - 1) + 1;
while (i++ < 123456) {
        x = (Mul_Mod(x, x, n) + n - 1) % n;
        d = Gcd((y - x + n) % n, n);
if (d != 1) {
            Pollard(d);
            Pollard(n / d);
return;
        }
if (i == k) {
            y = x;
            k *= 2;
        }
    }
    Factor(n);
}
int main() {
int Case;
long long n;
    scanf("%d", &Case);
while (Case--) {
        scanf("%lld", &n);
if (Miller_rabin(n))
            printf("Prime\n");
else {
            cnt = 0;
            Pollard(n);
            sort(factor, factor + cnt);
            printf("%lld\n", factor[0]);
        }
    }
return 0;
}