POJ 1811

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <stdlib.h>
#include <time.h>
#define LL __int64
using namespace std;
LL ans;
const LL C=201;
LL random(LL n){
	return (LL)((double)rand()/RAND_MAX*n+0.5);
}

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

LL multi(LL a,LL b,LL m){  a*b%m这个函数写得真心好，很好地避免了超出范围的情    况
	LL ret=0;
	while(b>0){
		if(b&1)
		ret=(ret+a)%m;
		b>>=1;
		a=(a<<1)%m;
	}
	return ret;
}

LL Pollard_rho(LL n, LL c){
	LL x,y,d,i=1,k=2;
	x=random(n-1)+1;
	y=x;
	while(true){
		i++;
		x=(multi(x,x,n)+c)%n;
		d=gcd(y-x,n);
		if(d>1&&d<n) return d;
		if(y==x) return n;
		if(i==k){
			y=x;
			k=k<<1;
		}
	}
}

LL quick(LL a,LL k,LL m){
	LL ans=1;
	a%=m;
	while(k){
		if(k&1){
			ans=multi(ans,a,m);
		}
		k=k>>1;
		a=multi(a,a,m);   // 这里如果不写函数直接乘会超范围
	}
	return ans;
}

bool Witness(LL a, LL n){
	LL m=n-1;
	int j=0;
	while(!(m&1)){
		j++;
		m=m>>1;
	}
	LL x= quick(a,m,n);
	if(x==1||x==n-1)
	return false;
	while(j--){
		x=multi(x,x,n);
		if(x==n-1)
		return false;
	}
	return true;
}

bool Miller_Rabin(LL n){
	if(n<2) return false;
	if(n==2) return true;
	if(!(n&1)) return false;
	for(int i=1;i<=10;i++){
		LL a=random(n-2)+1;
		if(Witness(a,n)) return false;
	}
	return true;
}

void find(LL n){
	if(n==1) return ;
	if(Miller_Rabin(n)){
		if(n<ans)
		ans=n;
		return ;
	}
	LL p=n;
	while(p>=n)
	p=Pollard_rho(p,random(n-2)+1);
	find(p);
	find(n/p);
}

int main(){
	LL n; int T;
	srand(time(0));
	scanf("%d",&T);
	while(T--){
		scanf("%I64d",&n);
		if(Miller_Rabin(n)){
			printf("Prime\n");
			continue;
		}
		ans=(1LL<<60);
		find(n);
		printf("%I64d\n",ans);
	}
	return 0;
}