Take b = 2.

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

9816177919 is prime. b^((n-1)/9816177919)-1 mod n = 15, which is a unit, inverse 18323532116.

(9816177919) divides n-1.

(9816177919)^2 > n.

n is prime by Pocklington's theorem.