- 7th Apr 2023
- 20:07 pm

**C# Homework Question** - C# Logical Puzzles, Games, and Algorithms: Sieve Eratosthenes

**C# Homework Solution**

Here is an example implementation of the Sieve of Eratosthenes algorithm in C#:

using System;

class Program {

static void Main() {

int limit = 100;

bool[] primes = new bool[limit+1];

for (int i = 2; i <= limit; i++) {

primes[i] = true;

}

for (int i = 2; i <= Math.Sqrt(limit); i++) {

if (primes[i]) {

for (int j = i*i; j <= limit; j += i) {

primes[j] = false;

}

}

}

Console.Write("Prime numbers between 2 and {0}: ", limit);

for (int i = 2; i <= limit; i++) {

if (primes[i]) {

Console.Write("{0} ", i);

}

}

}

}

This program initializes an array of boolean values, where primes[i] is initially true for all i between 2 and limit inclusive. It then loops over all integers i between 2 and the square root of limit, checking if primes[i] is true. If it is, it marks all multiples of i as composite by setting primes[j] to false for all j equal to i*i, i*i+i, i*i+2i, and so on, up to limit. Finally, it outputs all values of i between 2 and limit for which primes[i] is true, which represent the prime numbers.