Primality proof for n = 14741:
Take b = 2.
b^(n-1) mod n = 1.
67 is prime.
b^((n-1)/67)-1 mod n = 11248, which is a unit, inverse 12019.
11 is prime.
b^((n-1)/11)-1 mod n = 2613, which is a unit, inverse 5286.
(11 * 67) divides n-1.
(11 * 67)^2 > n.
n is prime by Pocklington's theorem.