Take b = 2.

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

89 is prime.

b^((n-1)/89)-1 mod n = 24661, which is a unit, inverse 9471.

23 is prime.

b^((n-1)/23)-1 mod n = 82399, which is a unit, inverse 26297.

(23 * 89) divides n-1.

(23 * 89)^2 > n.

n is prime by Pocklington's theorem.