Rubin-Miller与Pollard Rho

两个没什么卵用的算法。

只放一下模板：

BZOJ3667

//BZOJ 3667
//by Cydiater
//2017.2.20
#include <iostream>
#include <queue>
#include <map>
#include <ctime>
#include <cmath>
#include <cstring>
#include <string>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <iomanip>
#include <bitset>
#include <set>
#include <vector>
#include <complex>
using namespace std;
#define ll long long
#define up(i,j,n)	for(ll i=j;i<=n;i++)
#define down(i,j,n)	for(ll i=j;i>=n;i--)
#define cmax(a,b)	a=max(a,b)
#define cmin(a,b)	a=min(a,b)
inline ll read(){
	char ch=getchar();ll x=0,f=1;
	while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
ll N,ans=0,a[]={2,3,5,7,11,13,17,19,23,29};
namespace solution{
	ll gcd(ll a,ll b){return !b?a:gcd(b,a%b);}
	ll mul(ll x,ll y,ll mod){
		ll tmp=0;
		while(y){
			if(y&1)(tmp+=x)%=mod;
			(x+=x)%=mod;y>>=1;
		}
		return tmp;
	}
	ll quick_pow(ll base,ll ind,ll mod){
		ll tmp=1;
		while(ind){
			if(ind&1)tmp=mul(tmp,base,mod);
			base=mul(base,base,mod);ind>>=1;
		}
		return tmp;
	}
	bool OK(ll base,ll num){
		if(!(num&1)||num==1)return 0;
		ll ind=num-1;
		while(!(ind&1))ind>>=1;
		ll Num=quick_pow(base,ind,num);
		if(Num==1)return 1;
		while(ind<num){
			if(Num==num-1)return 1;
			Num=mul(Num,Num,num);ind<<=1;
		}
		return 0;
	}
	bool isPrime(ll num){
		up(i,0,9){
			if(num==a[i])return 1;
			if(!OK(a[i],num))return 0;
		}
		return 1;
	}
	ll rho(ll num,ll c){
		ll i=1,k=2,x=rand()%(num-1)+1,y=x;
		while(true){
			i++;
			x=(mul(x,x,num)+c)%num;
			ll d=gcd((y-x+num)%num,num);
			if(d>1&&d<num)return d;
			if(x==y)return num;
			if(i==k){y=x;k<<=1;}
		}
	}
	void find(ll num,ll k){
		if(num==1||num<=ans)return;
		if(isPrime(num)){
			cmax(ans,num);
			return;
		}
		ll p=num,c=k;
		while(p>=num)p=rho(num,k--);
		find(p,c);find(num/p,c);
	}
	void Solve(){
		N=read();ans=0;
		while(N--){
			ll num=read();ans=0;
			find(num,120);
			if(ans==num)puts("Prime");
			else printf("%lld\n",ans);
		}
}
int main(){
	freopen("input.in","r",stdin);
	using namespace solution;
	Solve();
	return 0;
}