Primality proof for n = 14741173:

Take b = 2.

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

409477 is prime.
b^((n-1)/409477)-1 mod n = 10869382, which is a unit, inverse 3061083.

(409477) divides n-1.

(409477)^2 > n.

n is prime by Pocklington's theorem.