Take b = 2.

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

108654662777 is prime. b^((n-1)/108654662777)-1 mod n = 255, which is a unit, inverse 739703900318.

(108654662777) divides n-1.

(108654662777)^2 > n.

n is prime by Pocklington's theorem.