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.