Primality proof for n = 492167257:
Take b = 2.
b^(n-1) mod n = 1.
7649 is prime.
b^((n-1)/7649)-1 mod n = 336649638, which is a unit, inverse 354522845.
383 is prime.
b^((n-1)/383)-1 mod n = 168613394, which is a unit, inverse 184765166.
(383 * 7649) divides n-1.
(383 * 7649)^2 > n.
n is prime by Pocklington's theorem.