from lib_prime import is_prime


def euler_046():
    n_max = 10000
    twice_squares = [2 * n * n for n in range(1, n_max + 1)]

    def test_conjecture(n):
        for ts in twice_squares:
            if ts > n:
                return False
            if is_prime(n - ts):
                return True

    for n in range(3, n_max + 1, 2):
        if not is_prime(n) and test_conjecture(n) is False:
            return n


if __name__ == "__main__":
    print("e046.py: " + str(euler_046()))
    assert(euler_046() == 5777)