sieve of Eratosthenes

The sieve of EratosthenesMathworldPlanetmathPlanetmath is a simple algorithm for generating a list of the prime numbersMathworldPlanetmath between 1 and some integer N2.

Let p=2, which is of course known to be prime. Mark all positive multiplesMathworldPlanetmath of p (e.g. 2,4,6,8), up until N, as composite. Now let p be the smallest number not marked as composite (in this case, 3); it must be the next prime. Again, mark all positive multiples of p as composite. Continue this process while pN. When done, all numbers less than N that have not been marked as composite are prime.

For many years, the sieve of Eratosthenes was the fastest known algorithm for listing primes. Today, there are faster methods, such as a quadratic sieveMathworldPlanetmath.

Title sieve of Eratosthenes
Canonical name SieveOfEratosthenes
Date of creation 2013-03-22 12:39:34
Last modified on 2013-03-22 12:39:34
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Definition
Classification msc 11A41
Related topic BrunsPureSieve