Primality proof for n = 12110864880705284755213021:

Take b = 2.

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

359799907329331097897 is prime.
b^((n-1)/359799907329331097897)-1 mod n = 4640103115232297512110359, which is a unit, inverse 1000779572490977432260193.

(359799907329331097897) divides n-1.

(359799907329331097897)^2 > n.

n is prime by Pocklington's theorem.