Primality proof for n = 832327:

Take b = 2.

b^(n-1) mod n = 1.

12611 is prime.
b^((n-1)/12611)-1 mod n = 552246, which is a unit, inverse 390403.

(12611) divides n-1.

(12611)^2 > n.

n is prime by Pocklington's theorem.