Take b = 2.

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

29 is prime.

b^((n-1)/29)-1 mod n = 4988, which is a unit, inverse 6838.

13 is prime.

b^((n-1)/13)-1 mod n = 1960, which is a unit, inverse 227.

(13 * 29) divides n-1.

(13 * 29)^2 > n.

n is prime by Pocklington's theorem.