Take b = 2.

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

23 is prime.

b^((n-1)/23)-1 mod n = 61693, which is a unit, inverse 1651.

17 is prime.

b^((n-1)/17)-1 mod n = 75227, which is a unit, inverse 52367.

(17 * 23) divides n-1.

(17 * 23)^2 > n.

n is prime by Pocklington's theorem.