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.