Sieve of Eratosthenes

sieve.py

def sieve(MAX):
    # list of primes
    primes = []
    # list of all numbers, non-primes will be slowly zeroed out
    nums = []
    # start with first prime
    prime = 2
    # populate list from 0 to MAX
    nums = [i for i in range(MAX+1)]
    # zero out 1, non-prime 
    nums[1] = 0
    
    # start sieving
    while prime <= MAX:
        # continue loop, if this number has already been zeroed out
        if nums[prime] == 0:
           prime += 1
           continue

        # not zeroed out, so a prime!
        # So append to primes list
        primes.append(prime)
        # pmult is multiple of prime
        pmult = prime
        while (pmult + prime) <= MAX:
            # inc pmult by current prime
            pmult += prime
            # zero out multiple of current prime
            nums[pmult] = 0
 
        prime += 1 

    return primes

# Project Euler problem 10
p = []
m = 1999999
p = sieve(m)
print "number of primes less than", m, ":", len(p)
print sum(p)