Incremental Sieve of Eratosthenes

sieve.py

'''
Python implementation of Haskell's

sieve xs = sieve' xs Map.empty
  where
    sieve' []     table = []
    sieve' (x:xs) table =
        case Map.lookup x table of
            Nothing     -> x : sieve' xs (Map.insert (x*x) [x] table)
            Just facts  -> sieve' xs (foldl reinsert (Map.delete x table) facts)
          where
            reinsert table prime = Map.insertWith (++) (x+prime) [prime] table

Found in "The Genuine Sieve of Eratosthenes"
'''

def sieve(inflist):
  composites = {}
  while True:
    x = inflist.next()
    if x not in composites:
      yield x
      composites[x*x] = [x]
    else:
      for prime in composites[x]:
        composites.setdefault(x + prime, []).append(prime)
      del composites[x]

def gennums(start):
  n = start
  while True:
    yield n
    n += 1

primes = sieve(gennums(2))
for i in xrange(20): # first 20 primes
  print primes.next(),

# test:
primes = sieve(gennums(2))
for prime in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]:
  assert prime == primes.next()

Great!