Primality proof for n = 6827:
Take b = 2.
b^(n-1) mod n = 1.
3413 is prime. b^((n-1)/3413)-1 mod n = 3, which is a unit, inverse 2276.
(3413) divides n-1.
(3413)^2 > n.
n is prime by Pocklington's theorem.