Primality proof for n = 453119:
Take b = 2.
b^(n-1) mod n = 1.
13327 is prime. b^((n-1)/13327)-1 mod n = 315417, which is a unit, inverse 92712.
(13327) divides n-1.
(13327)^2 > n.
n is prime by Pocklington's theorem.