说实话，我知道每一步都干啥，但我完全不知道为啥这么做，也不知道为什么是正确的，反正会用就行了~
#include <cmath>
#include <cstdio>
#include <algorithm>
#define ll long long
#define ull unsigned long long
#define setIO(s) freopen(s".in","r",stdin)
using namespace std;
int array[20]={2,3,5,7,11,13,17,19};
ll Max;
ll mult(ll x,ll y,ll mod)
{
ll tmp=(long double)x/mod*y;
return ((ull)x*y-(ull)tmp*mod+mod)%mod;
}
ll qpow(ll base,ll k,ll mod)
{
ll tmp=1;
for(;k;k>>=1,base=mult(base,base,mod)) if(k&1) tmp=mult(tmp,base,mod);
return tmp;
}
ll F(ll x,ll c,ll mod)
{
return (mult(x,x,mod)+c)%mod;
}
int isprime(ll x)
{
if(x<=1) return 1;
int k,i,j;
ll cur,a,pre;
for(k=0,cur=x-1;cur%2==0;cur>>=1) ++k;
for(i=0;i<8;++i)
{
if(x==array[i]) return 1;
pre=a=qpow(array[i],cur,x);
for(j=1;j<=k;++j)
{
a=mult(a,a,x);
if(a==1&&pre!=1&&pre!=x-1) return 0;
pre=a;
}
if(a!=1) return 0;
}
return 1;
}
ll pollard_rho(ll x)
{
ll s=0,t=0,c=rand()%(x-1)+1,val=1,d;
int k,step;
for(k=1;;k<<=1,s=t,val=1)
{
for(step=1;step<=k;++step)
{
t=F(t,c,x);
val=mult(val,abs(s-t),x);
if(step%127==0)
{
d=__gcd(val,x);
if(d>1) return d;
}
}
d=__gcd(val,x);
if(d>1) return d;
}
}
void solve(ll x)
{
if(x<=Max||x<2) return;
if(isprime(x))
{
Max=max(Max,x);
return;
}
ll p=x;
for(;p>=x;) p=pollard_rho(x);
for(;x%p==0;) x/=p;
solve(x),solve(p);
}
int main()
{
int T,i,j;
// setIO("input");
scanf("%d",&T);
for(i=1;i<=T;++i)
{
ll a;
scanf("%lld",&a),Max=0,solve(a);
if(Max==a) printf("Prime
");
else printf("%lld
",Max);
}
return 0;
}