Primality proof for n = 255061103803346185973548526989:

Take b = 2.

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

391669282183 is prime.
b^((n-1)/391669282183)-1 mod n = 197690604069135969009134633081, which is a unit, inverse 83843030690213050324461345524.

1075060097 is prime.
b^((n-1)/1075060097)-1 mod n = 247019199996362412111726712205, which is a unit, inverse 12859343024447538925475948031.

(1075060097 * 391669282183) divides n-1.

(1075060097 * 391669282183)^2 > n.

n is prime by Pocklington's theorem.