A module for lazily generating prime numbers with python generators and the Sieve of Eratosthenes.

primes.py

from itertools import takewhile, chain, count, islice
from collections import deque

knownPrimes = [2] # Numbers are tested by counting upwards from here. This also acts as a cache.

def storeAndReturn(p):
    knownPrimes.append(p)
    return p

def isNotDivisibleByKnownPrimes(n):
    root_n = n**0.5 # Square root of n
    return all((n % p) != 0 for p in takewhile(lambda p: p <= root_n, knownPrimes)) # Test for divisibility by known primes <= sqrt(n)

def primeFilter(sequence): return (storeAndReturn(i) for i in sequence if isNotDivisibleByKnownPrimes(i))

def allPrimes(): return chain(knownPrimes, primeFilter(count(knownPrimes[-1] + 1)))

def primesUpTo(limit): return takewhile(lambda p: p < limit, allPrimes())

def firstNPrimes(n): return islice(allPrimes(), None, n, None)

def nthPrime(n): return deque(firstNPrimes(n), maxlen=1).pop() # deque construction is apparently the
# fastest way to consume an iterator (partly because it's raw C)

if __name__ == '__main__': # Module Test
    print "Primes below 20:"
    print '\n'.join(map(str, primesUpTo(20)))
    
    print "First 10 primes:"
    print '\n'.join(map(str, firstNPrimes(10)))
    
    print "10,000th prime:"
    print nthPrime(10000)