Two ways of generating an infinite stream of prime numbers via sieve of Eratosthenes

prime_stream.py

import itertools 
 
def take(n, iterable): 
    return list(itertools.islice(iterable, n)) 
 
def enum_integers(start): 
    return itertools.count(start) 
 
def is_not_divisible_by(n, which): 
    return n%which != 0 
 
def recursive_prime_gen(): 
    gen = enum_integers(start=2) 
 
    def yield_sieve(gen): 
        head = next(gen) 
        yield head 
 
        # Filter out multiples of `head` from next generator 
        gen = itertools.ifilter(lambda e: is_not_divisible_by(e, head), gen)

        for v in yield_sieve(gen):
            yield v

    return yield_sieve(gen)

def iterative_prime_gen():
    gen = enum_integers(start=2)

    while True:
        head = next(gen)
        yield head

        # Filter out multiples of `head` from next generator
        gen = itertools.ifilter(lambda e: is_not_divisible_by(e, head), gen)


print "Recursive: ", take(10, recursive_prime_gen())
# Recursive:  [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
# ^ Expected result

print "Iterative: ", take(10, iterative_prime_gen())
# Iterative: [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
# ^ Not really what I expected

# Initially I thought we can't for some reason update the value of `gen`
# in the iterative version, but that is just not true:

def iterative_multiples_of_5_gen():
    gen = enum_integers(start=5)

    while True:
        head = next(gen)
        yield head

        # Filter out multiples of 5 from next generator
        gen = itertools.ifilter(lambda e: not is_not_divisible_by(e, 5), gen)

print "Iterative multiples of 5: ", take(10, iterative_multiples_of_5_gen())
# Iterative multiples of 5:  [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]

# The problem is analogous to:
import sys

funcs = []
for i in xrange(5):
    funcs.append(lambda: sys.stdout.write("Func #{}\n".format(i)))

for func in funcs:
    func()

# Prints:
# Func #4
# Func #4
# Func #4
# Func #4
# Func #4

# Fixing it is as easy as creating a binding upon defining each
# lambda. It can be done by passing `i` as an argument:

funcs = []
for i in xrange(5):
    funcs.append(lambda i=i: sys.stdout.write("Func #{}\n".format(i)))

for func in funcs:
    func()

# Prints
# Func #0
# Func #1
# Func #2
# Func #3
# Func #4

# Let's not try to fix the iterative version with this idea:

def iterative_prime_gen_fixed():
    gen = enum_integers(start=2)

    while True:
        head = next(gen)
        yield head

        # Filter out multiples of `head` from next generator
        gen = itertools.ifilter(lambda e, head=head: is_not_divisible_by(e, head), gen)

print "Iterative with fix: ", take(10, iterative_prime_gen_fixed())
# Iterative whit fix:  [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]