Take b = 2.

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

43 is prime.

b^((n-1)/43)-1 mod n = 27519, which is a unit, inverse 15419.

17 is prime.

b^((n-1)/17)-1 mod n = 24291, which is a unit, inverse 22060.

(17 * 43) divides n-1.

(17 * 43)^2 > n.

n is prime by Pocklington's theorem.