Primality proof for n = 105943:
Take b = 2.
b^(n-1) mod n = 1.
17657 is prime. b^((n-1)/17657)-1 mod n = 63, which is a unit, inverse 18498.
(17657) divides n-1.
(17657)^2 > n.
n is prime by Pocklington's theorem.