Take b = 2.

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

5 is prime. b^((n-1)/5)-1 mod n = 8, which is a unit, inverse 23.

3 is prime. b^((n-1)/3)-1 mod n = 46, which is a unit, inverse 4.

(3 * 5) divides n-1.

(3 * 5)^2 > n.

n is prime by Pocklington's theorem.