Fastest way to calculate primes in C#?

Question

I actually have an answer to my question but it is not parallelized so I am interested in ways to improve the algorithm. Anyway it might be useful as-is for some people.

int Until = 20000000;
BitArray PrimeBits = new BitArray(Until, true);

/*
 * Sieve of Eratosthenes
 * PrimeBits is a simple BitArray where all bit is an integer
 * and we mark composite numbers as false
 */

PrimeBits.Set(0, false); // You don't actually need this, just
PrimeBits.Set(1, false); // remindig you that 2 is the smallest prime

for (int P = 2; P < (int)Math.Sqrt(Until) + 1; P++)
    if (PrimeBits.Get(P))
        // These are going to be the multiples of P if it is a prime
        for (int PMultiply = P * 2; PMultiply < Until; PMultiply += P)
            PrimeBits.Set(PMultiply, false);

// We use this to store the actual prime numbers
List<int> Primes = new List<int>();

for (int i = 2; i < Until; i++)
    if (PrimeBits.Get(i))
        Primes.Add(i);

Maybe I could use multiple BitArrays and BitArray.And() them together?

Answer 1

You might save some time by cross-referencing your bit array with a doubly-linked list, so you can more quickly advance to the next prime.

Also, in eliminating later composites once you hit a new prime p for the first time - the first composite multiple of p remaining will be p*p, since everything before that has already been eliminated. In fact, you only need to multiply p by all the remaining potential primes that are left after it in the list, stopping as soon as your product is out of range (larger than Until).

There are also some good probabilistic algorithms out there, such as the Miller-Rabin test. The wikipedia page is a good introduction.