from lib_prime import primes


def is_cube(n):
    if n == 0:
        return False
    return round(n ** (1/3)) ** 3 == n


def euler_131():
    r = 0
    ps = primes(10**6)
    minm = 1
    for p in ps:
        for m in range(minm, minm + 20):
            n = m * m * m
            x = n * n * n + n * n * p
            if is_cube(x):
                # print(p, n)
                r += 1
                minm = m
                break
    return r


if __name__ == "__main__":
    solution = euler_131()
    print("e131.py: " + str(solution))
    assert(solution == 173)