Primality proof for n = 9839:

Take b = 2.

b^(n-1) mod n = 1.

4919 is prime.
b^((n-1)/4919)-1 mod n = 3, which is a unit, inverse 3280.

(4919) divides n-1.

(4919)^2 > n.

n is prime by Pocklington's theorem.