Function solution

project_euler/problem_187/sol1.py:117–139

Returns the number of composite integers below max_number have precisely two, not necessarily distinct, prime factors. >>> solution(30) 10

(max_number: int = 10**8)

def solution(max_number: int = 10**8) -> int:
    """
    Returns the number of composite integers below max_number have precisely two,
    not necessarily distinct, prime factors.

    >>> solution(30)
    10
    """

    prime_numbers = calculate_prime_numbers(max_number // 2)

    semiprimes_count = 0
    right = len(prime_numbers) - 1
    for left in range(len(prime_numbers)):
        if left > right:
            break
        for r in range(right, left - 2, -1):
            if prime_numbers[left] * prime_numbers[r] < max_number:
                break
        right = r
        semiprimes_count += right - left + 1

    return semiprimes_count


def benchmark() -> None: