Primality proof for n = 983685833987:

Take b = 2.

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

8336320627 is prime.
b^((n-1)/8336320627)-1 mod n = 950236973967, which is a unit, inverse 137188557913.

(8336320627) divides n-1.

(8336320627)^2 > n.

n is prime by Pocklington's theorem.