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# Find Prime Numbers in C# Using the Sieve of Eratosthenes

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20 Sep 2011CPOL 14.1K   1
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...

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.)

C#
```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;
}
}```

Written By
Software Developer (Junior)
Netherlands
Software developer with a bachelor degree and a few years experience (studied computer science at a university as well, but didn't finish). Really love C#, but work usually involves Java. Some experience with VB and C as well.

When hobbying I almost exclusively use C# and AutoHotkey. In a previous life I did some Haskell and Modula-3 and similar stuff. I enjoy games and solving puzzles like on http://projecteuler.net/ (I think I'm stuck at level 4, though)