Sunday, March 29, 2015

Sieve Algorithm of finding prime number

To find all the prime numbers less than or equal to a given integer n by Sieve Eratosthenes' method:

1.    Create a list of consecutive integers from 2 to n: (2, 3, 4, ..., n).
2.    Initially, let p equal 2, the first prime number.
3.    Starting from p, count up in increments of p and mark each of these numbers greater than p itself in the list.
      These numbers will be 2p, 3p, 4p, etc.; note that some of them may have already been marked.
4.    Find the first number greater than p in the list that is not marked.
      If there was no such number, stop. Otherwise, let p now equal this number (which is the next prime), and repeat from step 3.