Take b = 3.

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

11 is prime.

b^((n-1)/11)-1 mod n = 139, which is a unit, inverse 160.

2 is prime.

b^((n-1)/2)-1 mod n = 351, which is a unit, inverse 176.

(2^5 * 11) divides n-1.

(2^5 * 11)^2 > n.

n is prime by Pocklington's theorem.