Primality proof for n = 592299861982871449195634528262215319398393153:

Take b = 2.

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

4868010057124911294296551654477037 is prime.
b^((n-1)/4868010057124911294296551654477037)-1 mod n = 580710220979877823123741188012495558481016532, which is a unit, inverse 453212339599639552652966493173062806921142108.

(4868010057124911294296551654477037) divides n-1.

(4868010057124911294296551654477037)^2 > n.

n is prime by Pocklington's theorem.