Take b = 2.

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

269 is prime.

b^((n-1)/269)-1 mod n = 9879702, which is a unit, inverse 20740614.

37 is prime.

b^((n-1)/37)-1 mod n = 32266437, which is a unit, inverse 20400376.

(37 * 269) divides n-1.

(37 * 269)^2 > n.

n is prime by Pocklington's theorem.