Primality proof for n = 16879:
Take b = 2.
b^(n-1) mod n = 1.
97 is prime.
b^((n-1)/97)-1 mod n = 7200, which is a unit, inverse 13318.
29 is prime.
b^((n-1)/29)-1 mod n = 5093, which is a unit, inverse 5876.
(29 * 97) divides n-1.
(29 * 97)^2 > n.
n is prime by Pocklington's theorem.