Primality proof for n = 14878771:

Take b = 2.

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

495959 is prime.
b^((n-1)/495959)-1 mod n = 2470311, which is a unit, inverse 7007573.

(495959) divides n-1.

(495959)^2 > n.

n is prime by Pocklington's theorem.