先用Miller_Rabin演算法進行素數判斷，再用Pollard_rho分解素因子。

今天做TC時，遇到一道大素數判定和質因子分解的模板題。想到了質因子分解，但沒想到用這個模板。賽後，還是自己理解一遍，然後手敲吧。。

#include <stdio.h>
#include <iostream>
#include <map>
#include <set>
#include <stack>
#include <vector>
#include <math.h>
#include <string.h>
#include <queue>
#include <string>
#include <stdlib.h>
#include <algorithm>

#define LL long long
#define _LL __int64
#define eps 1e-12
#define PI acos(-1.0)
#define C 240
#define S 20
using namespace std;

LL fac[100];
int tol;

LL gcd(LL a, LL b)
{
	if(a == 0)
		return 1;
	if(a < 0)
		return gcd(-a,b);
	if(b == 0)
		return a;
	return gcd(b,a%b);
}

LL MultMod(LL a, LL b, LL n)
{
	a %= n;
	b %= n;
	LL ret = 0;

	while(b)
	{
		if(b&1)
		{
			ret += a;
			if(ret >= n)
				ret -= n;
		}
		a <<= 1;
		if(a >= n)
			a -= n;
		b >>= 1;
	}
	return ret;
}

LL PowMod(LL a, LL n, LL m)
{
	LL ret = 1;
	a %= m;

	while(n)
	{
		if(n&1)
			ret = MultMod(ret,a,m);
		a = MultMod(a,a,m);
		n >>= 1;
	}
	return ret;
}

/// 大素數判定
bool Witness(LL a, LL n)
{
	LL t = 0;
	LL u = n-1;
	while(!(u&1))
	{
		t++;
		u = u/2;
	}

	LL x0 = PowMod(a,u,n);

	for(int i = 1; i <= t; i++)
	{
		LL x1 = MultMod(x0,x0,n);
		if(x1 == 1 && x0 != 1 && x0 != (n-1) )
			return true;
		x0 = x1; //之前少了這一句
	}
	if(x0 != 1)
		return true;
	return false;
}

bool Miller_Rabin(LL n)
{
	if(n == 2)
		return true;
	if((n&1) == 0)
		return false;
	//srand(time(NULL));
	for(int i = 0; i < S; i++)
	{
		LL a = rand()%(n-1) + 1;
		if(Witness(a,n))
			return false;
	}
	return true;
}

///質因子分解
LL Pollar_Rho(LL n, LL c)
{
	LL i = 1,x = rand()%n, y = x,k = 2;
	while(1)
	{
		i++;
		x = ( MultMod(x,x,n)+c)%n;
		LL d = gcd(y-x,n);
		if(d != 1 && d != n)
			return d;
		if(x == y)
			return n;
		if(i == k)
		{
			y = x;
			k = k*2;
		}

	}
}

void get_small(LL n, LL c)
{
	if(n == 1)
		return;
	if(Miller_Rabin(n))
	{
		fac[tol++] = n;
		return;
	}
	LL p = n;
	while(p >= n)
		p = Pollar_Rho(p,c--);
	get_small(p,c);
	get_small(n/p,c);
}

int main()
{
	int test;
	LL n;
	scanf("%d",&test);
	while(test--)
	{
		scanf("%lld",&n);
		if(Miller_Rabin(n))
		{
			printf("Prime\n");
			continue;
		}
		tol = 0;
		get_small(n,C);
		LL ans = fac[0];
		for(int i = 1; i < tol; i++)
			ans = min(ans,fac[i]);
		printf("%lld\n",ans);
	}
	return 0;
}