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.