Primality proof for n = 280740833:
Take b = 2.
b^(n-1) mod n = 1.
8773151 is prime. b^((n-1)/8773151)-1 mod n = 83854800, which is a unit, inverse 272740271.
(8773151) divides n-1.
(8773151)^2 > n.
n is prime by Pocklington's theorem.