def allnumbers(i=1):
  while True:
    yield i
    i += 1

def fastforward(it, till, it_head=None):
  n = next(it) if it_head is None else it_head
  while n < till:
    n = next(it)
  return n

def multiples(n):
  for m in allnumbers():
    yield n * m

def exclude(xs, ys):
  y = None
  for x in xs:
    y = fastforward(ys, x, it_head=y)
    if x is not y:
      yield x

def sieve(s=allnumbers(i=2)):
  while True:
    s1 = next(s)
    yield s1
    s = exclude(s, multiples(s1)