Primality proof for n = 34282281433:

Take b = 2.

b^(n-1) mod n = 1.

204061199 is prime.
b^((n-1)/204061199)-1 mod n = 29889646154, which is a unit, inverse 5692688330.

(204061199) divides n-1.

(204061199)^2 > n.

n is prime by Pocklington's theorem.