Primality proof for n = 8963:
Take b = 2.
b^(n-1) mod n = 1.
4481 is prime. b^((n-1)/4481)-1 mod n = 3, which is a unit, inverse 2988.
(4481) divides n-1.
(4481)^2 > n.
n is prime by Pocklington's theorem.