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# Sieve of Eratosthenes
# Code by David Eppstein, UC Irvine, 28 Feb 2002
# http://code.activestate.com/recipes/117119/

def gen_primes():
    """ Generate an infinite sequence of prime numbers.
    """
    # Maps composites to primes witnessing their compositeness.
    # This is memory efficient, as the sieve is not "run forward"
    # indefinitely, but only as long as required by the current
    # number being tested.
    #
    D = {}
    
    # The running integer that's checked for primeness
    q = 2
    
    while True:
        if q not in D:
            # q is a new prime.
            # Yield it and mark its first multiple that isn't
            # already marked in previous iterations
            # 
            yield q
            D[q * q] = [q]
        else:
            # q is composite. D[q] is the list of primes that
            # divide it. Since we've reached q, we no longer
            # need it in the map, but we'll mark the next 
            # multiples of its witnesses to prepare for larger
            # numbers
            # 
            for p in D[q]:
                D.setdefault(p + q, []).append(p)
            del D[q]
        
        q += 1

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for x in range(0,20):
		gen_primes()

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for x in gen_primes():
    print(x)

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from collections import defaultdict
def generate_primes():
    """ Generate an infinite sequence of prime numbers.
    """
    # Maps composites to primes witnessing their compositeness.
    # This is memory efficient, as the sieve is not "run forward"
    # indefinitely, but only as long as required by the current
    # number being tested.
    yield 2
    
    sieve = defaultdict(list)
    number = 3
    while True:
        if number not in sieve:
            # number is a new prime.
            # Yield it and mark its first multiple that isn't
            # already marked in previous iterations
            yield number
            sieve[number * number] = [number]
        else:
            # number is composite. sieve[number] is the list of primes that
            # divide it. Since we've reached number, we no longer
            # need it in the map, but we'll mark the next 
            # multiples of its witnesses to prepare for larger
            # numbers
            for p in sieve.pop(number):
                sieve[number + 2*p].append(p)
        number += 2