Primality proof for n = 4098533:
Take b = 2.
b^(n-1) mod n = 1.
1024633 is prime. b^((n-1)/1024633)-1 mod n = 15, which is a unit, inverse 3552062.
(1024633) divides n-1.
(1024633)^2 > n.
n is prime by Pocklington's theorem.