from lib_prime import primes
from functools import lru_cache


@lru_cache
def next_prime(n):
    if n == 1:
        return 2
    ps = primes(105)
    assert n < ps[-1]
    for i, p in enumerate(ps):
        if p == n and i + 1 < len(ps):
            return ps[i + 1]
    assert False


def count(current_product, max_product, current_prime, max_prime):
    if current_product > max_product:
        return 0
    r = 1

    if current_prime > 1:
        r += count(current_product * current_prime, max_product, current_prime, max_prime)

    while (current_prime := next_prime(current_prime)) <= max_prime:
        r += count(current_product * current_prime, max_product, current_prime, max_prime)
    return r


def euler_204():
    assert count(1, 10**8, 1, 5) == 1105
    return count(1, 10**9, 1, 100)


if __name__ == "__main__":
    solution = euler_204()
    print("e204.py: " + str(solution))
    assert(solution == 2944730)