from math import gcd
from lib_prime import is_prime_rabin_miller


def r_modulo_closed_form(n, m):
    assert n > 0 and m > 0
    return ((pow(10, n, 9 * m) - 1) // 9) % m


def a_special(n):
    k = n - 1
    if r_modulo_closed_form(k, n) == 0:
        return k
    return None


def euler_130():
    c, r = 0, 0
    for n in range(2, 10**9):
        if gcd(n, 10) == 1 and not is_prime_rabin_miller(n):
            if a_special(n) is not None:
                r += n
                c += 1
            if c == 25:
                break
    return r


if __name__ == "__main__":
    solution = euler_130()
    print("e130.py: " + str(solution))
    assert(solution == 149253)