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.