寻找素数的程序

问题描述

我想找到 0 和 long 变量之间的质数，但我无法得到任何输出.

I want to find the prime number between 0 and a long variable but I am not able to get any output.

程序是

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication16
{
    class Program
    {
        void prime_num(long num)
        {
            bool isPrime = true;
            for (int i = 0; i <= num; i++)
            {
                for (int j = 2; j <= num; j++)
                {
                    if (i != j && i % j == 0)
                    {
                        isPrime = false;
                        break;
                    }
                }
                if (isPrime)
                {
                    Console.WriteLine ( "Prime:" + i );
                }
                isPrime = true;
            }
        }

        static void Main(string[] args)
        {
            Program p = new Program();
            p.prime_num (999999999999999L);
            Console.ReadLine();
        }
    }
}

谁能帮我找出程序中可能存在的错误?

Can any one help me out and find what is the possible error in the program?

推荐答案

您可以像这样在一行(长)行中使用近乎最优 的试验分割筛来更快地完成此操作:

You can do this faster using a nearly optimal trial division sieve in one (long) line like this:

Enumerable.Range(0, Math.Floor(2.52*Math.Sqrt(num)/Math.Log(num))).Aggregate(
    Enumerable.Range(2, num-1).ToList(),
    (result, index) => {
        var bp = result[index]; var sqr = bp * bp;
        result.RemoveAll(i => i >= sqr && i % bp == 0);
        return result;
    }
);

这里使用的素数数量的近似公式是π(x)＜1.26 x/ln(x).我们只需要通过不大于x = sqrt(num)的素数进行测试.

The approximation formula for number of primes used here is π(x) < 1.26 x / ln(x). We only need to test by primes not greater than x = sqrt(num).

请注意，埃拉托色尼筛分的运行时间复杂度比试除法(应该运行如果正确实现，对于更大的 num 值，速度会更快).

Note that the sieve of Eratosthenes has much better run time complexity than trial division (should run much faster for bigger num values, when properly implemented).

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