Lazier sieve

Doc/library/itertools.rst

@@ -1030,13 +1030,16 @@ The following recipes have a more mathematical flavor:
  def sieve(n):
  "Primes less than n."
  # sieve(30) --> 2 3 5 7 11 13 17 19 23 29
+ if n > 2:
+ yield 2
+ start = 3
  data = bytearray((0, 1)) * (n // 2)
- data[:3] = 0, 0, 0
  limit = math.isqrt(n) + 1
- for p in compress(range(limit), data):
+ for p in iter_index(data, 1, start, limit):
+ yield from iter_index(data, 1, start, p*p)
  data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
- data[2] = 1
- return iter_index(data, 1) if n > 2 else iter([])
+  start = p*p
+ yield from iter_index(data, 1, start)
 
  def factor(n):
  "Prime factors of n."