Take b = 2.

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

11 is prime.
b^((n-1)/11)-1 mod n = 633, which is a unit, inverse 118.

5 is prime.
b^((n-1)/5)-1 mod n = 246, which is a unit, inverse 352.

(5 * 11) divides n-1.

(5 * 11)^2 > n.

n is prime by Pocklington's theorem.