Primality proof for n = 14072969:

Take b = 2.

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

1487 is prime.
b^((n-1)/1487)-1 mod n = 4493176, which is a unit, inverse 3493289.

13 is prime.
b^((n-1)/13)-1 mod n = 5189481, which is a unit, inverse 10174223.

(13^2 * 1487) divides n-1.

(13^2 * 1487)^2 > n.

n is prime by Pocklington's theorem.