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

title, tags

title	tags
fermat_test	math

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