Primality proof for n = 14633:

Take b = 2.

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

59 is prime.
b^((n-1)/59)-1 mod n = 2174, which is a unit, inverse 12782.

31 is prime.
b^((n-1)/31)-1 mod n = 4627, which is a unit, inverse 12979.

(31 * 59) divides n-1.

(31 * 59)^2 > n.

n is prime by Pocklington's theorem.