Primality proof for n = 249533:

Take b = 2.

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

62383 is prime.
b^((n-1)/62383)-1 mod n = 15, which is a unit, inverse 216262.

(62383) divides n-1.

(62383)^2 > n.

n is prime by Pocklington's theorem.