Take b = 2.

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

23 is prime.

b^((n-1)/23)-1 mod n = 497, which is a unit, inverse 276.

13 is prime.

b^((n-1)/13)-1 mod n = 18, which is a unit, inverse 233.

(13 * 23) divides n-1.

(13 * 23)^2 > n.

n is prime by Pocklington's theorem.