Take b = 2.

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

280518779831 is prime.
b^((n-1)/280518779831)-1 mod n = 260973156773322066, which is a unit, inverse 3408500999431271982.

(280518779831) divides n-1.

(280518779831)^2 > n.

n is prime by Pocklington's theorem.