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.