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.