Primality proof for n = 9547:
Take b = 2.
b^(n-1) mod n = 1.
43 is prime.
b^((n-1)/43)-1 mod n = 1467, which is a unit, inverse 7471.
37 is prime.
b^((n-1)/37)-1 mod n = 3056, which is a unit, inverse 1990.
(37 * 43) divides n-1.
(37 * 43)^2 > n.
n is prime by Pocklington's theorem.