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.