Take b = 2.

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

13830319 is prime. b^((n-1)/13830319)-1 mod n = 1997627661848, which is a unit, inverse 3839031531301.

(13830319) divides n-1.

(13830319)^2 > n.

n is prime by Pocklington's theorem.