miller-rabin

素数的判定，poj3641

#include<iostream>
using namespace std;
long long pow_mod(long long a,long long b,long long m)
{
    long long t=a%m,res=1;
    while(b)
    {
        if(b&1) res=(res*t)%m;
        t=(t*t)%m;
        b/=2;
    }
    return res;
}
bool miller(long long k,long long d,long long n,long long a)
{
    if(n==2||n==a) return true;
    if(!(n&1)) return false;
    long long i,t=pow_mod(a,d,n);
    if(t==1) return true;
    for(i=0;i<k;i++)
    {
        if(t==n-1) return true;
        t=(t*t)%n;
    }
    return false;
}
bool judge(long long n)
{
    if(n<2) return false;
    long long k=0,d=n-1;
    while(!(d&1))
    {
        k++;
        d>>=1;
    }
    if(n<1373653)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)) return true;
        return false;
    }
    if(n<9080191)
    {
        if(miller(k,d,n,31)&&miller(k,d,n,73)) return true;
        return false;
    }
    if(n<4759123141)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,11)) return true;
        return false;
    }
    if(n<2152302898747)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,7)&&miller(k,d,n,11)) return true;
        return false;
    }
    else
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,7)&&miller(k,d,n,11)&&miller(k,d,n,31)&&miller(k,d,n,61)&&miller(k,d,n,73)) return true;
        return false;
    }
}
int main()
{
    long long a,p;
    while(cin>>p>>a&&a)
    {
        if(judge(p)) cout<<"no"<<endl;
        else
        {
            if(pow_mod(a,p,p)==a) cout<<"yes"<<endl;
            else cout<<"no"<<endl;
        }
    }
}

#include<iostream>
using namespace std; typedef long long ll;
ll txt[]={2,3,5,7,11,31,61};
long long pow_mod(long long a,long long b,long long m)
{
    long long t=a%m,res=1;
    while(b)
    {
        if(b&1) res=(res*t)%m;
        t=(t*t)%m;
        b/=2;
    }
    return res;
}
bool miller(ll a,ll d,ll k,ll n)
{
    if(n==2||n==a) return true;
    if(!(n&1)) return false;
    ll i,t=pow_mod(a,d,n);
    if(t==1) return true;
    for(i=0;i<k;i++)
    {
        if(t==n-1)
            return true;
        t=(t*t)%n;
    }
    return false;
}
bool judge(long long n)
{
    if(n<2) return false;
    bool f;
    ll i,d=n-1,k=0;
    while(!(d&1))
    {
        k++;
        d>>=1;
    }
    for(i=0;i<7;i++)
        if(!miller(txt[i],d,k,n)) return false;
    return true;
}
int main()
{
    long long p,a;
    while(cin>>p>>a&&a)
    {
        if(judge(p)) cout<<"no"<<endl;
        else
        {
            if(pow_mod(a,p,p)==a) cout<<"yes"<<endl;
            else cout<<"no"<<endl;
        }
    }
}