Primality proof for n = 281276467:
Take b = 2.
b^(n-1) mod n = 1.
46879411 is prime. b^((n-1)/46879411)-1 mod n = 63, which is a unit, inverse 102688234.
(46879411) divides n-1.
(46879411)^2 > n.
n is prime by Pocklington's theorem.