# Copyright (C) 2019, 2020 Hesham T. Banafa

#From: https://stackoverflow.com/questions/17298130/working-with-large-primes-in-python
from random import randrange
def is_prime(n, k=10):
    if n == 2:
        return True
    if not n & 1:
        return False

    def check(a, s, d, n):
        x = pow(a, d, n)
        if x == 1:
            return True
        for i in range(s - 1):
            if x == n - 1:
                return True
            x = pow(x, 2, n)
        return x == n - 1

    s = 0
    d = n - 1

    while d % 2 == 0:
        d >>= 1
        s += 1

    for i in range(k):
        a = randrange(2, n - 1)
        if not check(a, s, d, n):
            return False
    return True