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.