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

Here is a very fast generator with reduced memory usage.

def pgen(maxnum): # Sieve of Eratosthenes generator
    yield 2
    np_f = {}
    for q in xrange(3, maxnum + 1, 2):
        f = np_f.pop(q, None)
        if f:
            while f != np_f.setdefault(q+f, f):
                q += f
        else:
            yield q
            np = q*q
            if np < maxnum:  # does not add to dict beyond maxnum
                np_f[np] = q+q

def is_prime(n):
    return n in pgen(n)

>>> is_prime(541)
True
>>> is_prime(539)
False
>>> 83 in pgen(100)
True
>>> list(pgen(100)) # List prime numbers less than or equal to 100
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97]