python prime numbers Sieve of Eratosthenes

Question

Hi can anyone tell me how to implement Sieve of Eratosthenes within this code to make it fast? Help will be really appreciated if you can complete it with sieve. I am really

Answer 1

Both the original poster and the other solution posted here make the same mistake; if you use the modulo operator, or division in any form, your algorithm is trial division, not the Sieve of Eratosthenes, and will be far slower, O(n^2) instead of O(n log log n). Here is a simple Sieve of Eratosthenes in Python:

def primes(n): # sieve of eratosthenes
    ps, sieve = [], [True] * (n + 1)
    for p in range(2, n + 1):
        if sieve[p]:
           ps.append(p)
           for i in range(p * p, n + 1, p):
               sieve[i] = False
    return ps

That should find all the primes less than a million in less than a second. If you're interested in programming with prime numbers, I modestly recommend this essay at my blog.