Take b = 2.

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

79 is prime.

b^((n-1)/79)-1 mod n = 296958, which is a unit, inverse 92621.

23 is prime.

b^((n-1)/23)-1 mod n = 10691, which is a unit, inverse 335538.

(23 * 79) divides n-1.

(23 * 79)^2 > n.

n is prime by Pocklington's theorem.