poj 1181(大数判素数 ，分解)

//miller_rabin 判断一个大数是否是素数
//pollard_rho 大数因子分解
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>

using namespace std;

#define LL long long
const LL Max = (LL) 1 << 62;
LL p[10]={2,3,5,7,11,13,17,19,23,29};

//计算a*b%n
inline LL multi_mod(LL a,LL b,LL mod)
{
    LL sum=0;
    while(b)
    {
        if(b&1)    sum = (sum + a) % mod;
        a <<= 1;
        b >>= 1;
        if (a >= mod) a %= mod;
    }
    return sum;
}

//计算a^b%n;
inline LL quick_mod(LL a,LL b,LL mod)
{
    LL sum = 1;
    while(b)
    {
        if(b & 1) sum = multi_mod(sum, a, mod);
        a = multi_mod(a, a, mod);
        b >>= 1;
    }
    return sum;
}

bool miller_rabin(LL n)
{
    LL u,m,buf;
    int k = 0;
    //将n分解为m*2^k
    if(n==2)   return true;
    if(n<2 || !(n&1))    return false;
    m = n - 1;
    while(!(m&1))
        k++,m >>= 1;
    for(int i = 0; i < 9; ++i)
    {
        if(p[i] >= n) return true;
        u = quick_mod(p[i], m, n);
        if(u==1) continue;
        for(int j = 0; j < k; ++j)
        {
            buf = multi_mod(u, u, n);
            if(buf == 1 && u != 1 && u != n - 1)
                return false;
            u = buf;
        }
        //如果p[i]^(n-1)%n!=1那么n为合数
        if(u - 1) return false;
    }
    return true;
}

LL gcd(LL a, LL b)
{
    return b == 0 ? a: gcd(b, a%b);
}
//寻找n的一个因子，该因子并不一定是最小的，所以下面要二分查找最小的那个因子
LL pollard(LL n )
{
   LL x,y,c=0,d,i=1,k=2;
   while(c==0 || c==2 ) c = abs( rand())%(n-1) + 1;
   x = y = (rand( )%( n-1 )) + 1;
   do
   {
      i++;
      d = gcd( y + n - x, n );
      if( d >1 && d < n )
          return d; 
      if( i == k )
      {
         y = x; k <<= 1;        
      }    
      x = (multi_mod( x , x, n )+n-c )%n;
    }while( x != y );
    return n; 
}

LL pollard_min(LL n)
{
    LL p,a,b=Max;
    if(n==1)    return Max;
    if(miller_rabin(n))    return n;
    p = pollard(n);
    a = pollard_min(p);//二分查找
    b = pollard_min(n / p);
    return a < b ? a : b;
}

int main(void)
{
    LL T;
    LL n;
    scanf("%lld",&T);
    while(T--)
    {
        scanf("%lld",&n);
        if(miller_rabin(n))
        {
            puts("Prime");
        }
        else printf("%lld\n",pollard_min(n));
    }
    return 0;
}