Take b = 3.

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

29 is prime.

b^((n-1)/29)-1 mod n = 880, which is a unit, inverse 1193.

11 is prime.

b^((n-1)/11)-1 mod n = 1023, which is a unit, inverse 340.

(11 * 29) divides n-1.

(11 * 29)^2 > n.

n is prime by Pocklington's theorem.