# Sieve of Eratosthenes
# David Eppstein, UC Irvine, 28 Feb 2002
from __future__ import generators
def eratosthenes():
'''Yields the sequence of prime numbers via the Sieve of Eratosthenes.'''
D = {} # map composite integers to primes witnessing their compositeness
q = 2 # first integer to test for primality
while 1:
if q not in D:
yield q # not marked composite, must be prime
D[q*q] = [q] # first multiple of q not already marked
else:
for p in D[q]: # move each witness to its next multiple
D.setdefault(p+q,[]).append(p)
del D[q] # no longer need D[q], free memory
q += 1