Take b = 2.

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

23 is prime.

b^((n-1)/23)-1 mod n = 1991, which is a unit, inverse 8561.

19 is prime.

b^((n-1)/19)-1 mod n = 7295, which is a unit, inverse 538.

(19 * 23) divides n-1.

(19 * 23)^2 > n.

n is prime by Pocklington's theorem.