Primality proof for n = 9463:
Take b = 2.
b^(n-1) mod n = 1.
83 is prime.
b^((n-1)/83)-1 mod n = 6022, which is a unit, inverse 11.
19 is prime.
b^((n-1)/19)-1 mod n = 6271, which is a unit, inverse 9128.
(19 * 83) divides n-1.
(19 * 83)^2 > n.
n is prime by Pocklington's theorem.