Primality proof for n = 110244005101:

Take b = 2.

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

13610371 is prime.
b^((n-1)/13610371)-1 mod n = 90519940136, which is a unit, inverse 61327983725.

(13610371) divides n-1.

(13610371)^2 > n.

n is prime by Pocklington's theorem.