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Find Prime Numbers in C# Using the Sieve of Eratosthenes

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4.80/5 (5 votes)
3 Oct 2011CPOL 63.9K   8   7
This tip illustrates a simple C# console program that uses the Sieve of Eratosthenes algorithm to quickly find prime numbers.
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.
                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
                    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++)

                    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) 
                            // don't bother removing an item that 
                            // is not even in the list
                            if (!primeCandidates.Contains(multiple * prime)) 

                            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


                    // write a line to the output file for 
                    // each list of prime
                    // candidates generated

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

                Console.WriteLine("DONE computing primes");
            catch (Exception ex)


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Written By
Team Leader
United States United States
Brian C. Hart, Ph.D., is a strategic engagement leader on a mission to leverage space technology to protect U.S. interests and assets against adversaries. Throughout Dr. Hart's career, he has enjoyed: Working closely with business executives to provide strategic direction and leadership, translating customer and competitive intelligence into compelling capture strategies and solutions, and mentoring teams to enhance individual and company capabilities while fostering an engaging and accountable environment, being involved in STEAM initiatives and education to develop greater awareness in the community, and serving the armed forces with the U.S. Navy and U.S. Army National Guard. He is excited to begin developing his career in Jacobs's Critical Mission Systems business unit, supporting NORAD and the U.S. Space Force.

Comments and Discussions

GeneralMy vote of 5 Pin
long_cloud31-Mar-13 5:56
long_cloud31-Mar-13 5:56 
GeneralAnother alternative. Pin
Bill Anderson28-Dec-12 13:27
Bill Anderson28-Dec-12 13:27 
Generalvery nice .. Pin
Denno.Secqtinstien18-Nov-11 0:31
Denno.Secqtinstien18-Nov-11 0:31 
GeneralReason for my vote of 5 Loved it... Pin
GPUToaster™13-Sep-11 0:33
GPUToaster™13-Sep-11 0:33 
GeneralReason for my vote of 5 Nice concept... Pin
Pravin Patil, Mumbai12-Sep-11 9:21
Pravin Patil, Mumbai12-Sep-11 9:21 
GeneralEdit: Added wiki link to the sieve definition for those who ... Pin
DaveAuld11-Sep-11 11:23
professionalDaveAuld11-Sep-11 11:23 
GeneralRe: Edit: Fixed the link Pin
Reiss12-Sep-11 1:27
professionalReiss12-Sep-11 1:27 

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