Primality proof for n = 8699:

Take b = 2.

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

4349 is prime.
b^((n-1)/4349)-1 mod n = 3, which is a unit, inverse 2900.

(4349) divides n-1.

(4349)^2 > n.

n is prime by Pocklington's theorem.