#include<stdio.h>
main()
{
    long long unsigned x,y,b,z,e,r,c;
    scanf("%llu",&x);
    if(x<2)return 0;
    scanf("%llu",&y);
    if(y<x)return 0;
    if(x==2)printf("|2");
    if(x%2==0)x+=1;
    if(y%2==0)y-=1;
    for(b=x;b<=y;b+=2)
    {
        z=b;e=0;
        for(c=2;c*c<=z;c++)
        {
            if(z%c==0)e++;
            if(e>0)z=3;
        }
        if(e==0)
        {
            printf("|%llu",z);
            r+=1;
        }
    }
    printf("|\n%llu outputs...\n",r);
    scanf("%llu",&r);
}    

这取决于您的应用程序。这里有一些注意事项:

你需要的仅仅是一些数字是否是质数的信息，你需要所有的质数达到一定的限度，还是你需要(潜在的)所有的质数? 你要处理的数字有多大?

米勒-拉宾和模拟测试只比筛选超过一定规模的数字(我相信大约在几百万左右)的速度快。在这以下，使用试除法(如果你只有几个数字)或筛子会更快。

#include <iostream>

using namespace std;

int set [1000000];

int main (){

    for (int i=0; i<1000000; i++){
        set [i] = 0;
    }
    int set_size= 1000;
    set [set_size];
    set [0] = 2;
    set [1] = 3;
    int Ps = 0;
    int last = 2;

    cout << 2 << " " << 3 << " ";

    for (int n=1; n<10000; n++){
        int t = 0;
        Ps = (n%2)+1+(3*n);
        for (int i=0; i==i; i++){
            if (set [i] == 0) break;
            if (Ps%set[i]==0){
                t=1;
                break;
            }
        }
        if (t==0){
            cout << Ps << " ";
            set [last] = Ps;
            last++;
        }
    }
    //cout << last << endl;


    cout << endl;

    system ("pause");
    return 0;
}

这是找到从1到n的所有质数的最快算法(在我的电脑上，它只花了0.004秒就找到了从1到1000000的所有质数)。

#include <iostream>
#include <fstream>

using namespace std;

double FindPrime(bool* array, int size){
clock_t start;
double runtime;
for (int i = 2; i < size; i++)
    array[i] = true;
start = clock();
for (int i = 2; i <= size; i++)
    if (array[i])
        for (int j = 2 * i; j < size; j += i)
            array[j] = false;
runtime = (double)(clock() - start) / CLOCKS_PER_SEC;
return runtime;
}


int main() {
ofstream fout("prime.txt");
int n = 0;
cout << "Enter the upper limit of prime numbers searching algorithm:";
cin >> n;
bool* array = new bool[n + 1];
double duration = FindPrime(array, n + 1);
printf("\n%f seconds.\n", duration);
for (int i = 2; i <= n; i++)
    if (array[i])
        fout << i << endl;
fout.close();

return 0;
}

Rabin-Miller是一个标准的概率质数检验。(你运行K次，输入数字要么肯定是合数，要么可能是素数，误差概率为4-K。(经过几百次迭代，它几乎肯定会告诉你真相)

拉宾·米勒有一个非概率(确定性)的变体。

The Great Internet Mersenne Prime Search (GIMPS) which has found the world's record for largest proven prime (274,207,281 - 1 as of June 2017), uses several algorithms, but these are primes in special forms. However the GIMPS page above does include some general deterministic primality tests. They appear to indicate that which algorithm is "fastest" depends upon the size of the number to be tested. If your number fits in 64 bits then you probably shouldn't use a method intended to work on primes of several million digits.

I know it's somewhat later, but this could be useful to people arriving here from searches. Anyway, here's some JavaScript that relies on the fact that only prime factors need to be tested, so the earlier primes generated by the code are re-used as test factors for later ones. Of course, all even and mod 5 values are filtered out first. The result will be in the array P, and this code can crunch 10 million primes in under 1.5 seconds on an i7 PC (or 100 million in about 20). Rewritten in C it should be very fast.

var P = [1, 2], j, k, l = 3

for (k = 3 ; k < 10000000 ; k += 2)
{
  loop: if (++l < 5)
  {
    for (j = 2 ; P[j] <= Math.sqrt(k) ; ++j)
      if (k % P[j] == 0) break loop

    P[P.length] = k
  }
  else l = 0
}