Question

Possible Duplicate:
Prime Number Formula

I am trying to write some code in c# that will give me the nth prime number but once my code gets past 121 as a prime number it starts giving me incorrect numbers back.

Now this could be that i have based my code off the wrong algorithm but i wanted to ask here and see if there is something i have done wrong.

the code ask for nth prime 10001 – output: 43751 (which i know is wrong)

Any where here is my code.

int[] p;
int x = 0;
p = new int[10002];
for (int i = 0; i < 1000000; i++)
if (i % 2 != 0)
{
    if (i % 3 != 0)
    {
        if (i % 5 != 0)
        {
            if (i % 7 != 0)
            {
                p[x] = i;
                x++;
                if (x == 10001)
                {
                    Console.WriteLine("{0}", i);
                    break;
                }
            }
        }
    }
}

Answer 1

That’s not how the Sieve of Eratosthenes works, you should read this section from the Wikipedia article :

• Create a list of consecutive integers from 2 to n: (2, 3, 4, …, n).
• Initially, let p equal 2, the first prime number.
• Starting from p, count up in increments of p and mark each of these numbers greater than p itself in the list. These numbers will be 2p, 3p, 4p, etc.; note that some of them may have already been marked.
• Find the first number greater than p in the list that is not marked; let p now equal this number (which is the next prime).
• If there were no more unmarked numbers in the list, stop. Otherwise, repeat from step 3.

So basically what you think is the limit (121, from your comments) is just an example they used in that animated .gif.

here’s a C# implementation of this method :

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

namespace sieve
{
    class Program
    {
        static void Main(string[] args)
        {
            int maxprime = int.Parse(args[0]);
            ArrayList primelist = sieve(maxprime);

            foreach (int prime in primelist)
                Console.WriteLine(prime);

            Console.WriteLine("Count = " + primelist.Count);
            Console.ReadLine();
        }

        static ArrayList sieve(int arg_max_prime)
        {
            BitArray al = new BitArray(arg_max_prime, true);

            int lastprime = 1;
            int lastprimeSquare = 1;

            while (lastprimeSquare <= arg_max_prime)
            {
                lastprime++;

                while (!(bool)al[lastprime])
                    lastprime++;

                lastprimeSquare = lastprime * lastprime;

                for (int i = lastprimeSquare; i < arg_max_prime; i += lastprime)
                    if (i > 0)
                        al[i] = false;
            }

            ArrayList sieve_2_return = new ArrayList();

            for (int i = 2; i < arg_max_prime; i++)
                if (al[i])
                    sieve_2_return.Add(i);

            return sieve_2_return;
        }
    }
}

Credits go to Rosetta Code