Primality proof for n = 110947:

Take b = 2.

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

41 is prime.
b^((n-1)/41)-1 mod n = 50456, which is a unit, inverse 67121.

(41^2) divides n-1.

(41^2)^2 > n.

n is prime by Pocklington's theorem.