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.