Primality proof for n = 14944121:
Take b = 2.
b^(n-1) mod n = 1.
7949 is prime. b^((n-1)/7949)-1 mod n = 11365993, which is a unit, inverse 12004624.
(7949) divides n-1.
(7949)^2 > n.
n is prime by Pocklington's theorem.