कोडिंग कार्यप्रवाह · सीमित अभाज्य संख्या छलनी

from math import isqrt

def primes_through(limit):
    if type(limit) is not int or not 0 <= limit <= 1000000:
        raise ValueError("limit.range")
    sieve = bytearray([1]) * (limit + 1)
    sieve[0] = 0
    if limit >= 1:
        sieve[1] = 0
    for p in range(2, isqrt(limit) + 1):
        if sieve[p]:
            for multiple in range(p * p, limit + 1, p):
                sieve[multiple] = 0
    return [i for i, prime in enumerate(sieve) if prime]