Take b = 2.

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

11 is prime. b^((n-1)/11)-1 mod n = 157, which is a unit, inverse 174.

7 is prime. b^((n-1)/7)-1 mod n = 117, which is a unit, inverse 186.

(7 * 11) divides n-1.

(7 * 11)^2 > n.

n is prime by Pocklington's theorem.