Sieve of Eratosthenes algorithm

sieve_of_eratosthenes.py

def sieve_of_eratosthenes(n: int) -> list[int]:
    """
    Generate all prime numbers up to n using the Sieve of Eratosthenes algorithm.

    Args:
        n (int): Upper bound for generating prime numbers

    Returns:
        list[int]: List of all prime numbers up to n

    Raises:
        ValueError: If n is negative
    """
    if n < 0:
        raise ValueError("Input must be non-negative")
    if n < 2:
        return []

    sieve = [True] * (n + 1)
    sieve[0] = sieve[1] = False

    for i in range(2, int(n**0.5) + 1):
        if sieve[i]:
            for j in range(i * i, n + 1, i):
                sieve[j] = False

    return [i for i in range(n + 1) if sieve[i]]


if __name__ == "__main__":
    n = int(input("Enter a number: "))
    try:
        print(sieve_of_eratosthenes(n))
    except ValueError as e:
        print(f"Error: {e}")