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.