Find Prime Numbers in C# Using the Sieve of Eratosthenes

Ever been tasked to come up with lists of prime numbers and you want to use the Sieve of Eratosthenes[^] to do so, but aren't quite sure how to code it up in C#? If so, then this simple console program written with .NET should do the trick:

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

namespace PrimeFinder
{
    class Program
    {
        static void Main(string[] args)
        {
            // this method encodes the Sieve of Eratosthenes
            // with some intelligent shortcuts, such as excluding
            // all even numbers greater than 2 etc.
            try
            {
                List<string> outputLines = new List<string>();

                // read in the numbers specified in the argument
                string[] numbersList = File.ReadAllLines(args[0]);
                foreach(string number in numbersList) {
                    int N = Int32.Parse(number);
                    List<int> primeCandidates = new List<int>(N);
                    if (N==2)
                    {
                        outputLines.Add("2\r\n");  // trivial case
                        continue;
                    }
                    if (N==1)
                    {
                        throw new InvalidArgumentException("The number one is trivially prime.");
                    }

                    // initialize primeCandidates with 2 
                    // and the list of all odd numbers
                    // less than N -- because all even numbers 
                    // save 2 are nonprime by definition
                    primeCandidates.Add(2); // the number 2 is always prime
                    for (int i = 2; i <= (N+1)/2; i++)
                        primeCandidates.Add(2*i-1);

                    for(int j = 0;j < primeCandidates.Count;++j) {
                        // initialize first prime
                        int prime = primeCandidates[j];

                        // use for loop to go through the multiples of the prime
                        for( int multiple = 2;multiple*prime <= N;++multiple) {
                            if (prime == 2) break; // duh, 2 is a prime

                            // skip all even multiples of 2
                            if ((multiple * prime) % 2 == 0) 
                               continue;                              
 
                            // don't bother removing an item that 
                            // is not even in the list
                            if (!primeCandidates.Contains(multiple * prime)) 
                               continue;  

                            primeCandidates.Remove(multiple * prime);
                        }
                    }

                    // put together a string representing 
                    // current output line of primes
                    string currentOutputLine = string.Empty;
                    foreach (int value in primeCandidates)
                        currentOutputLine += value.ToString() + ',';
                    currentOutputLine = 
                       currentOutputLine.Remove(currentOutputLine.Length - 1);
                    currentOutputLine += "\r\n"; // Windows CRLF encoding

                    Console.Write(currentOutputLine);

                    // write a line to the output file for 
                    // each list of prime
                    // candidates generated
                    outputLines.Add(currentOutputLine);
                }

                File.WriteAllLines(args[1], outputLines);

                Console.WriteLine("DONE computing primes");
                Console.ReadKey();
            }
            catch (Exception ex)
            {
                Console.WriteLine(ex.Message);
                Console.ReadKey();
            }
        }
    }
}