Take b = 2.

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

257 is prime.

b^((n-1)/257)-1 mod n = 527100, which is a unit, inverse 887021.

5 is prime.

b^((n-1)/5)-1 mod n = 431708, which is a unit, inverse 782333.

(5^2 * 257) divides n-1.

(5^2 * 257)^2 > n.

n is prime by Pocklington's theorem.