Primality proof for n = 108261709:
Take b = 2.
b^(n-1) mod n = 1.
29387 is prime. b^((n-1)/29387)-1 mod n = 17904350, which is a unit, inverse 13140389.
(29387) divides n-1.
(29387)^2 > n.
n is prime by Pocklington's theorem.