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.