poj1811

Given a big integer number, you are required to find out whether it's a prime number.

Input

The first line contains the number of test cases T (1 <= T <= 20 ), then the following T lines each contains an integer number N (2 <= N < 2 ⁵⁴).

Output

For each test case, if N is a prime number, output a line containing the word "Prime", otherwise, output a line containing the smallest prime factor of N.

Sample Input

2
5
10

Sample Output

Prime
2

//============================================================================
// Name        : HDU3864.cpp
// Author      : 
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <algorithm>
#include <string.h>
#include <time.h>
using namespace std;
const int S=15;
long long mult_mod(long long a,long long b,long long c)
{
    a%=c;
    b%=c;
    long long ret=0;
    while(b)
    {
        if(b&1){ret+=a;ret%=c;}
        a<<=1;
        if(a>=c)a%=c;
        b>>=1;
    }
    return ret;
}
long long pow_mod(long long x,long long n,long long mod)
{
    if(n==1)return x%mod;
    x%=mod;
    long long tmp=x;
    long long ret=1;
    while(n)
    {
        if(n&1)ret=mult_mod(ret,tmp,mod);
        tmp=mult_mod(tmp,tmp,mod);
        n>>=1;
    }
    return ret;
}
long long check(long long a,long long n,long long x,long long t)
{
    long long ret=pow_mod(a,x,n);
    long long last=ret;
    for(int i=1;i<=t;i++)
    {
        ret=mult_mod(ret,ret,n);
        if(ret==1 && last!=1 &&last!=n-1)return true;
        last=ret;
    }
    if(ret!=1)return true;
    return false;
}
bool Miller_Rabin(long long n)
{
    if(n<2)return false;
    if(n==2)return true;
    if((n&1)==0)return false;
    long long x=n-1;
    long long t=0;
    while((x&1)==0){x>>=1;t++;}
    for(int i=0;i<S;i++)
    {
        long long a=rand()%(n-1)+1;
        if(check(a,n,x,t))
            return false;
    }
    return true;
}

long long factor[100];
int tol;
long long gcd(long long a,long long b)
{
    if(a==0)return 1;
    if(a<0)return gcd(-a,b);
    while(b)
    {
        long long t=a%b;
        a=b;
        b=t;
    }
    return a;
}

long long Pollard_rho(long long x,long long c)
{
    long long i=1,k=2;
    long long x0=rand()%x;
    long long y=x0;
    while(1)
    {
        i++;
        x0=(mult_mod(x0,x0,x)+c)%x;
        long long d=gcd(y-x0,x);
        if(d!=1&&d!=x)return d;
        if(y==x0)return x;
        if(i==k)
        {
            y=x0;
            k+=k;
        }
    }
}

void findfac(long long n)
{
    if(Miller_Rabin(n))
    {
        factor[tol++]=n;
        return;
    }
    long long p=n;
    while(p>=n)p=Pollard_rho(p,rand()%(n-1)+1);
    findfac(p);
    findfac(n/p);
}

int main()
{
    srand(time(NULL));
    long long n;
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld",&n);
        tol=0;
        findfac(n);
        if(tol==1)
        {
            printf("Prime
");
            continue;
        }
        sort(factor,factor+tol);
        printf("%lld
",factor[0]);
    }
    return 0;
}