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.