Find Prime Numbers in C# Using the Sieve of Eratosthenes

This solution uses half the space by simply ignoring all even numbers. It will require a little index calculation. Also, primes are generated one by one instead of returning a list.

Another optimization can be made by starting the crossing out of multiples of a prime p at p². Any smaller number will already have been crossed out. For the same reason, we can stop looking for non-primes at Sqrt(bound). (Any number greater than that will have been crossed out as a multiple of a smaller number.)

public static IEnumerable<int> Primes(int bound)
{
    if (bound < 2) yield break;
    //The first prime number is 2
    yield return 2;

    //Create a sieve of 'half size' starting at 3
    BitArray notPrime = new BitArray((bound - 1) >> 1);
    int limit = ((int)(Math.Sqrt(bound)) - 1) >> 1;
    for (int i = 0; i < limit; i++) {
        if (notPrime[i]) continue;
        //The first number not crossed out is prime
        int prime = 2 * i + 3;
        yield return prime;
        //cross out all multiples of this prime, starting at the prime squared
        for (int j = (prime * prime - 2) >> 1; j < notPrime.Count; j += prime) {
            notPrime[j] = true;
        }
    }
    //The remaining numbers not crossed out are also prime
    for (int i = limit; i < notPrime.Count; i++) {
        if (!notPrime[i]) yield return 2 * i + 3;
    }
}