Primality proof for n = 14851:
Take b = 2.
b^(n-1) mod n = 1.
11 is prime.
b^((n-1)/11)-1 mod n = 10518, which is a unit, inverse 14426.
5 is prime.
b^((n-1)/5)-1 mod n = 7926, which is a unit, inverse 9599.
(5^2 * 11) divides n-1.
(5^2 * 11)^2 > n.
n is prime by Pocklington's theorem.