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.