Take b = 2.

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

29 is prime.

b^((n-1)/29)-1 mod n = 963, which is a unit, inverse 61.

11 is prime.

b^((n-1)/11)-1 mod n = 134, which is a unit, inverse 1115.

(11 * 29) divides n-1.

(11 * 29)^2 > n.

n is prime by Pocklington's theorem.