POJ1811
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<string>
#include<ctime>
#include<cmath>
#define ll long long
using namespace std;
const int s=8;
//记得把龟速乘换成快速乘
ll mult_mod(ll a,ll b,ll c)
{
a%=c,b%=c;
ll ret=0,temp=a;
while(b)
{
if(b&1)
{
ret=(ret+temp);
if(ret>c) ret-=c;
}
temp<<=1;
if(temp>c) temp-=c;
b>>=1;
}
return ret;
}
ll pow_mod(ll a,ll b,ll c)
{
ll ret=1,temp=a%c;
while(b)
{
if(b&1) ret=mult_mod(ret,temp,c);
temp=mult_mod(temp,temp,c);
b>>=1;
}
return ret;
}
bool check(ll a,ll n,ll x,ll t)
{
ll ret=pow_mod(a,x,n);
ll 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(ll n)
{
if(n<2) return false;
if(n==2) return true;
if((n&1)==0) return false;
ll x=n-1;
ll t=0;
while((x&1)==0)
{
x>>=1;
t++;
}
srand(time(NULL));
for(int i=0;i<s;i++)
{
ll a=rand()%(n-1)+1;
if(check(a,n,x,t))
return false;
}
return true;
}
ll factor[100];
int tot=0;
ll gcd(ll a,ll b)
{
ll t;
while(b)
{
t=a;
a=b;
b=t%b;
}
if(a>=0) return a;
else return -a;
}
ll Pollard_rho(ll x,ll c)
{
ll i=1,k=2;
srand(time(NULL));
ll x0=rand()%(x-1)+1;
ll y=x0;
while(1)
{
i++;
x0=(mult_mod(x0,x0,x)+c)%x;
ll 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(ll n,int k)
{
if(n==1) return ;
if(Miller_Rabin(n))
{
factor[tot++]=n;
return ;
}
ll p=n;
int c=k;
while(p>=n) p=Pollard_rho(p,c--);
findfac(p,k);
findfac(n/p,k);
}
int main(void)
{
int t;
cin>>t;
while(t--)
{
ll n;
scanf("%lld",&n);
if(Miller_Rabin(n))
{
printf("Prime\n");
continue;
}
tot=0;
findfac(n,107);
ll maxx=factor[0];
for(int i=1;i<tot;i++)
maxx=min(maxx,factor[i]);
printf("%lld\n",maxx);
}
return 0;
}