Primality proof for n = 497993:

Take b = 2.

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

5659 is prime.
b^((n-1)/5659)-1 mod n = 12151, which is a unit, inverse 450206.

(5659) divides n-1.

(5659)^2 > n.

n is prime by Pocklington's theorem.