PROJECT EULER #3

Link to Project Euler problem 3

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

The first of the prime questions. I use the "Sieve of Eratostosthenes" to generate primes.

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
   class Program
   {
       static void Main(string[] args)
       {
           //Problem 3
           List<int> primes = new List<int> {2, 3};
           long largeNumber = 600851475143;
           int largestFactor = 0;
           DateTime start = DateTime.Now;
           for (int i = 5; i < Math.Sqrt(largeNumber); i += 2)
           {
               if (i % 3 != 0)
               {
                   primes.Add(i);
                   foreach (int j in primes)
                   {
                       if (i % j == 0 && i != j)
                       {
                           primes.Remove(i);
                           break;
                       }
                   }
               }
           }
           foreach(int k in primes)
           {
               if (largeNumber % k == 0)
                   largestFactor = k;
           }
           TimeSpan time = DateTime.Now - start;
           Console.WriteLine("{0}\nThis took {1}", largestFactor,time);
           Console.ReadKey();
       }
   }
}