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.