采用费马素性测试和二次探测定理判断质数
#include <bits/stdc++.h>
#define io cin.tie(0), cout.tie(0), ios::sync_with_stdio(false)
#define LL long long
#define ULL unsigned long long
#define EPS 1e-8
#define INF 0x7fffffff
#define SUB -INF - 1
using namespace std;
LL fast_pow(LL x, LL y, int m)
{
LL res = 1;
x %= m;
while (y)
{
if (y & 1)
res = (res * x) % m;
x = (x * x) % m;
y >>= 1;
}
return res;
}
bool witness(LL a, LL n)
{
LL u = n - 1;
int t = 0;
while (u & 1 == 0)
u = u >> 1, t++;
LL x1, x2;
x1 = fast_pow(a, u, n);
for (int i = 1; i <= t; i++)
{
x2 = fast_pow(x1, 2, n);
if (x2 == 1 && x1 != 1 && x1 != n - 1)
return true;
x1 = x2;
}
if (x1 != 1)
return true;
return false;
}
int miller_rabin(LL n, int s)
{
if (n < 2)
return 0;
if (n == 2)
return 1;
if (n % 2 == 0)
return 0;
for (int i = 0; i < s && i < n; i++)
{
LL a = rand() % (n - 1) + 1;
if (witness(s, n))
return 0;
}
return 1;
}
int main()
{
int m;
while (scanf("%d", &m) != EOF)
{
int cnt = 0;
for (int i = 0; i < m; i++)
{
LL n;
scanf("%lld", &n);
int s = 50;
cnt += miller_rabin(n, s);
}
printf("%d\n", cnt);
}
return 0;
}