Eratosthenes prime sieve using iterators

eratosthenes_iter.py

from __future__ import annotations
from collections import deque
from itertools import count, cycle, islice
from typing import Final, Iterator
from time import perf_counter

def sieve() -> Iterator[int]:
    """
    A slightly improved Eratosthenes prime sieve, implemented using iterators.
    Cycles start on squares of primes because adding them earlier is unnecessary.
    """
    yield 2
    yield 3
    cycles: list[Iterator[int]] = []
    schedule_cycles = deque([(9, 3)])
    for n in count(5, 2):
        if n == schedule_cycles[0][0]:
            cycles.append(cycle(range(schedule_cycles[0][1])))
            schedule_cycles.popleft()
        is_prime = True
        for c in cycles:
            if next(c) == 0:
                is_prime = False
        if is_prime:
            yield n
            schedule_cycles.append((n * n, n))

def main() -> None:
    COUNT: Final = 100_000
    t1 = perf_counter()
    primes = list(islice(sieve(), COUNT))
    t2 = perf_counter()
    print(f'Computed {COUNT:_} primes in {t2 - t1 :.5f} sec.\nFirst 50:')
    print(primes[:50])
    print(f'Last 10:\n{primes[-10:]}\nTesting first 5000 numbers for primality...')
    all_prime = True
    for n, pn in enumerate(primes):
        if n == 5000:
            break
        if not all(pn % p for p in primes[:n]):
            all_prime = False
            print(f'ERROR! A composite number {pn} is a multiple of an earlier listed number!')
            break
    if all_prime:
        print('No number is a multiple of an earlier one! As intended.')

if __name__ == '__main__':
    main()