from lib_prime import primes
from typing import Optional, Tuple


def s(n):
    ps = primes(n)

    sum = 0
    for p1_index in range(len(ps)):
        p1 = ps[p1_index]
        for p2_index in range(p1_index + 1, len(ps)):
            p2 = ps[p2_index]
            if p1 * p2 > n:
                break
            largest: Optional[Tuple[int, int, int]] = None
            p1e = 1
            while p1**p1e * p2 <= n:
                p2e = 1
                m = p1**p1e * p2**p2e
                while m <= n:
                    if largest is None or m > largest[2]:
                        largest = (p1, p2, m)
                    p2e += 1
                    m = p1**p1e * p2**p2e
                p1e += 1
            assert largest is not None
            sum += largest[2]
    return sum


def euler_347():
    assert s(100) == 2262
    return s(10_000_000)


if __name__ == "__main__":
    solution = euler_347()
    print("e347.py: " + str(solution))
    assert solution == 11109800204052