Primality proof for n = 4233394996199:

Take b = 2.

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

7224223543 is prime.
b^((n-1)/7224223543)-1 mod n = 3274022858764, which is a unit, inverse 3679717000035.

(7224223543) divides n-1.

(7224223543)^2 > n.

n is prime by Pocklington's theorem.