Primality proof for n = 13903:

Take b = 2.

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

331 is prime.
b^((n-1)/331)-1 mod n = 6156, which is a unit, inverse 10093.

(331) divides n-1.

(331)^2 > n.

n is prime by Pocklington's theorem.