Take b = 2.

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

8436937 is prime. b^((n-1)/8436937)-1 mod n = 11971005240044, which is a unit, inverse 13481103733183.

(8436937) divides n-1.

(8436937)^2 > n.

n is prime by Pocklington's theorem.