Primality proof for n = 13463:

Take b = 2.

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

127 is prime.
b^((n-1)/127)-1 mod n = 6369, which is a unit, inverse 1467.

(127) divides n-1.

(127)^2 > n.

n is prime by Pocklington's theorem.