Take b = 2.

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

83 is prime.

b^((n-1)/83)-1 mod n = 188819, which is a unit, inverse 153022.

13 is prime.

b^((n-1)/13)-1 mod n = 247179, which is a unit, inverse 193667.

(13 * 83) divides n-1.

(13 * 83)^2 > n.

n is prime by Pocklington's theorem.