【HOJ1356】【Miller_rabin素性测试】Prime Judge

Given a positive integer, your job is writing a program to determine whether it is a prime number or not.

Input

There are several tests. Each test consists of a positive integer n(no more than 2^31) on a single line. Input is terminated by end of file.

Output

For each integer in the input, print a "YES" if it is a prime number, otherwise print a "NO" instead.

Sample Input

4
5
6

Sample Output

NO
YES
NO
【分析】
素性测试最基本的应用，主要精髓在于费马小定理和二次探测理论。

 /*
 五代李煜
 《清平乐·别来春半》
 别来春半，触目柔肠断。砌下落梅如雪乱，拂了一身还满。
 雁来音信无凭，路遥归梦难成。离恨恰如春草，更行更远还生。
 */
 #include <cstdio>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 #include <queue>
 #include <vector>
 #include <iostream>
 #include <string>
 #include <ctime>
 #define LOCAL
 const int MAXN =  + ;
 using namespace std;
 typedef long long ll;
 ll n;

 ll pow(ll a, ll b, ll p){
     if (b == ) return a % p;
     ll tmp = pow(a, b / , p);
     if (b %  == ) return (tmp * tmp) % p;
     else return (((tmp * tmp) % p) * (a % p)) % p;
 }
 //二次探测
 bool Sec_Check(ll a, ll p){
     ll tmp = pow(a, p, n);
     if (tmp !=  && tmp != (n - )) return ;//不通过
     if (tmp == (n - ) || (p %  != )) return ;
     return Sec_Check(a, p / );
 }
 bool miller_rabin(ll n){
     ll cnt = ;
     while (cnt--){
         ll a = (rand()%(n - )) + ;
         if (!Sec_Check(a, n - )) return ;
     }
     return ;
 }

 int main(){
     srand(time());

     while (scanf("%lld", &n) != EOF){
         if (n == ) printf("NO\n");
         else if (miller_rabin(n)) printf("YES\n");
         else printf("NO\n");
     }
     return ;
 }