30-seconds-of-code/snippets/fermat_test.md

fermat_test

Checks if the number is prime or not. Returns True if passed number is prime, and False if not.

The function uses Fermat's theorem. First, it picks the number A in range 1..(n-1), then it checks if A to the power of n-1 modulo n equals 1. If not, the number is not prime, else it's pseudoprime with probability 1/2. Applying this test k times we have probability 1/(2^k). For example, if the number passes the test 10 times, we have probability 0.00098.

from random import randint


def fermat_test(n, k=100):
    if n <= 1:
        return False
    for i in range(k):
        a = randint(1, n - 1)
        if pow(a, n - 1, n) != 1:
            return False
    return True

fermat_test(0)  # False
fermat_test(1)  # False
fermat_test(561)  # False
fermat_test(41041)  # False
fermat_test(17)  # True
fermat_test(162259276829213363391578010288127)  # True
fermat_test(-1)  # False