Primality proof for n = 18287:

Take b = 2.

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

223 is prime.
b^((n-1)/223)-1 mod n = 13053, which is a unit, inverse 11715.

(223) divides n-1.

(223)^2 > n.

n is prime by Pocklington's theorem.