Primality proof for n = 14717:

Take b = 2.

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

283 is prime.
b^((n-1)/283)-1 mod n = 3542, which is a unit, inverse 7774.

(283) divides n-1.

(283)^2 > n.

n is prime by Pocklington's theorem.