Take b = 3.

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

17 is prime. b^((n-1)/17)-1 mod n = 511, which is a unit, inverse 232.

2 is prime. b^((n-1)/2)-1 mod n = 917, which is a unit, inverse 459.

(2 * 17) divides n-1.

(2 * 17)^2 > n.

n is prime by Pocklington's theorem.