Take b = 2.

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

47 is prime.

b^((n-1)/47)-1 mod n = 1087, which is a unit, inverse 1504.

17 is prime.

b^((n-1)/17)-1 mod n = 13134, which is a unit, inverse 3061.

(17 * 47) divides n-1.

(17 * 47)^2 > n.

n is prime by Pocklington's theorem.