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.