Take b = 2.

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

97 is prime.

b^((n-1)/97)-1 mod n = 10523, which is a unit, inverse 7749.

13 is prime.

b^((n-1)/13)-1 mod n = 5484, which is a unit, inverse 7453.

(13 * 97) divides n-1.

(13 * 97)^2 > n.

n is prime by Pocklington's theorem.