Primality proof for n = 16979:

Take b = 2.

b^(n-1) mod n = 1.

653 is prime.
b^((n-1)/653)-1 mod n = 7855, which is a unit, inverse 4509.

(653) divides n-1.

(653)^2 > n.

n is prime by Pocklington's theorem.