Take b = 2.

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

257 is prime.

b^((n-1)/257)-1 mod n = 748577, which is a unit, inverse 339656.

37 is prime.

b^((n-1)/37)-1 mod n = 966520, which is a unit, inverse 486638.

(37 * 257) divides n-1.

(37 * 257)^2 > n.

n is prime by Pocklington's theorem.