素数チェッカー

def is_prime(n: int) -> bool:
    """Check if n is a prime number."""
    if n < 2:
        return False
    if n == 2:
        return True
    if n % 2 == 0:
        return False
    for i in range(3, int(n**0.5) + 1, 2):
        if n % i == 0:
            return False
    return True

def primes_up_to(limit: int) -> list[int]:
    """Sieve of Eratosthenes: find all primes up to limit."""
    if limit < 2:
        return []
    sieve = [True] * (limit + 1)
    sieve[0] = sieve[1] = False
    for i in range(2, int(limit**0.5) + 1):
        if sieve[i]:
            for j in range(i*i, limit + 1, i):
                sieve[j] = False
    return [i for i, v in enumerate(sieve) if v]

print(is_prime(17))         # True
print(is_prime(18))         # False
print(primes_up_to(50))     # [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]