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.