Take b = 2.

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

113 is prime.

b^((n-1)/113)-1 mod n = 4082, which is a unit, inverse 17785.

5 is prime.

b^((n-1)/5)-1 mod n = 16686, which is a unit, inverse 11344.

(5 * 113) divides n-1.

(5 * 113)^2 > n.

n is prime by Pocklington's theorem.