Primality proof for n = 280518779831:

Take b = 2.

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

3110999 is prime.
b^((n-1)/3110999)-1 mod n = 48843628328, which is a unit, inverse 165788124660.

(3110999) divides n-1.

(3110999)^2 > n.

n is prime by Pocklington's theorem.