Take b = 2.

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

47 is prime.

b^((n-1)/47)-1 mod n = 3451, which is a unit, inverse 33166.

13 is prime.

b^((n-1)/13)-1 mod n = 24206, which is a unit, inverse 5144.

(13 * 47) divides n-1.

(13 * 47)^2 > n.

n is prime by Pocklington's theorem.