Primality proof for n = 16903:

Take b = 2.

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

313 is prime.
b^((n-1)/313)-1 mod n = 12266, which is a unit, inverse 1418.

(313) divides n-1.

(313)^2 > n.

n is prime by Pocklington's theorem.