Primality proof for n = 9466553:
Take b = 2.
b^(n-1) mod n = 1.
1481 is prime.
b^((n-1)/1481)-1 mod n = 7272989, which is a unit, inverse 8533472.
17 is prime.
b^((n-1)/17)-1 mod n = 5646427, which is a unit, inverse 7186599.
(17 * 1481) divides n-1.
(17 * 1481)^2 > n.
n is prime by Pocklington's theorem.