Take b = 2.

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

31 is prime.

b^((n-1)/31)-1 mod n = 17224, which is a unit, inverse 14084.

13 is prime.

b^((n-1)/13)-1 mod n = 14080, which is a unit, inverse 923.

(13 * 31) divides n-1.

(13 * 31)^2 > n.

n is prime by Pocklington's theorem.