Take b = 2.

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

29 is prime.

b^((n-1)/29)-1 mod n = 135191, which is a unit, inverse 126977.

23 is prime.

b^((n-1)/23)-1 mod n = 130366, which is a unit, inverse 13687.

(23 * 29) divides n-1.

(23 * 29)^2 > n.

n is prime by Pocklington's theorem.