Take b = 2.
b^(n-1) mod n = 1.
115347420731 is prime. b^((n-1)/115347420731)-1 mod n = 9361982794440, which is a unit, inverse 26704078487.
(115347420731) divides n-1.
(115347420731)^2 > n.
n is prime by Pocklington's theorem.