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.