Take b = 2.

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

31 is prime.

b^((n-1)/31)-1 mod n = 488, which is a unit, inverse 810.

23 is prime.

b^((n-1)/23)-1 mod n = 964, which is a unit, inverse 1014.

(23 * 31) divides n-1.

(23 * 31)^2 > n.

n is prime by Pocklington's theorem.