Fermat's primality test

Asked Apr 21 '21 at 08:57

Active Apr 21 '21 at 08:57

Viewed 71 times

From my understanding, the fermat's primality test should fail for all carmichael numbers. This seems to identify prime numbers fine, but all the carmichael numbers that I tested returned 'composite' for high k values, which is unexpected.

Can anyone see what mistake I made?

def mod_exp(x, y, N):
    if y == 0:
        return 1
    z = mod_exp(x, y//2, N)
    if y % 2 == 0:
        return z*z % N
    else:
        return x * z*z % N

def fermat(N,k):
    isPrime = 'prime'
    for i in range(k):
        a = random.randint(1, N - 1)
        if mod_exp(a, N - 1, N) != 1:
            isPrime = 'composite'
    return isPrime

asked Apr 21 '21 at 08:57

Alex Kang

In the mathematics analyzing carmichael numbers and the fermat primality test it is assumed that gcd(a, N) = 1. Your code doesn't ensure that. Of course, if 1 1 then for sure N is composite. There is a slightly different formulation of the fermat test that eliminates the requirement that gcd(a, N) = 1: test instead that a\*\*N == a mod N. – President James K. Polk Apr 21 '21 at 13:16

Fermat's primality test

0 Answers0