Primality proof for n = 1418023:
Take b = 2.
b^(n-1) mod n = 1.
78779 is prime. b^((n-1)/78779)-1 mod n = 262143, which is a unit, inverse 269510.
(78779) divides n-1.
(78779)^2 > n.
n is prime by Pocklington's theorem.