Take b = 2.

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

3037491448319 is prime.
b^((n-1)/3037491448319)-1 mod n = 1452898121960331870, which is a unit, inverse 1906564763848279624.

(3037491448319) divides n-1.

(3037491448319)^2 > n.

n is prime by Pocklington's theorem.