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

Fastest implementation I could think of

def sieve(maxNum):
    yield 2
    D, q = {}, 3
    while q <= maxNum:
        p = D.pop(q, 0)
        if p:
            x = q + p
            while x in D: x += p
            D[x] = p
        else:
            yield q
            D[q*q] = 2*q
        q += 2
    raise StopIteration

Source: http://code.activestate.com/recipes/117119-sieve-of-eratosthenes/#c4

Replace this part

import math
def is_prime(n):
    if n == 2:
        return True
    if n%2 == 0 or n <= 1:
        return False
    sqr = int(math.sqrt(n)) + 1
    for divisor in range(3, sqr, 2):
        if n%divisor == 0:
            return False
    return True

with

primes = [prime for prime in sieve(10000000)]
def is_prime(n):
    return n in primes

Instead of 10000000 you can put whatever the maximum number till which you need prime numbers.