Primality proof for n = 499067:

Take b = 2.

b^(n-1) mod n = 1.

249533 is prime.
b^((n-1)/249533)-1 mod n = 3, which is a unit, inverse 166356.

(249533) divides n-1.

(249533)^2 > n.

n is prime by Pocklington's theorem.