Primality proof for n = 34367:
Take b = 2.
b^(n-1) mod n = 1.
17183 is prime. b^((n-1)/17183)-1 mod n = 3, which is a unit, inverse 11456.
(17183) divides n-1.
(17183)^2 > n.
n is prime by Pocklington's theorem.