Primality proof for n = 596242599987116128415063:

Take b = 3.

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

36131535570665139281 is prime.
b^((n-1)/36131535570665139281)-1 mod n = 246463439989986452791527, which is a unit, inverse 465801323734362530676345.

(36131535570665139281) divides n-1.

(36131535570665139281)^2 > n.

n is prime by Pocklington's theorem.