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.