Primality proof for n = 9473:
Take b = 3.
b^(n-1) mod n = 1.
37 is prime.
b^((n-1)/37)-1 mod n = 1299, which is a unit, inverse 5958.
2 is prime.
b^((n-1)/2)-1 mod n = 9471, which is a unit, inverse 4736.
(2^8 * 37) divides n-1.
(2^8 * 37)^2 > n.
n is prime by Pocklington's theorem.