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.