[3.11] Improve speed. Reduce auxiliary memory to 16.6% of the main ar…

…ray. (GH-98294) (GH-98303)

Doc/library/itertools.rst

@@ -822,12 +822,13 @@ which incur interpreter overhead.
  def sieve(n):
  "Primes less than n"
  # sieve(30) --> 2 3 5 7 11 13 17 19 23 29
- data = bytearray([1]) * n
- data[:2] = 0, 0
+ data = bytearray((0, 1)) * (n // 2)
+ data[:3] = 0, 0, 0
  limit = math.isqrt(n) + 1
  for p in compress(range(limit), data):
- data[p*p : n : p] = bytearray(len(range(p*p, n, p)))
- return iter_index(data, 1)
+ 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([])
 
  def flatten(list_of_lists):
  "Flatten one level of nesting"