Primality proof for n = 9080963:
Take b = 2.
b^(n-1) mod n = 1.
412771 is prime. b^((n-1)/412771)-1 mod n = 4194303, which is a unit, inverse 4267675.
(412771) divides n-1.
(412771)^2 > n.
n is prime by Pocklington's theorem.