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.