Primality proof for n = 9743:
Take b = 2.
b^(n-1) mod n = 1.
4871 is prime. b^((n-1)/4871)-1 mod n = 3, which is a unit, inverse 3248.
(4871) divides n-1.
(4871)^2 > n.
n is prime by Pocklington's theorem.