Primality proof for n = 108881:
Take b = 2.
b^(n-1) mod n = 1.
1361 is prime. b^((n-1)/1361)-1 mod n = 48855, which is a unit, inverse 73588.
(1361) divides n-1.
(1361)^2 > n.
n is prime by Pocklington's theorem.