Primality proof for n = 8839:

Take b = 2.

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

491 is prime.
b^((n-1)/491)-1 mod n = 5812, which is a unit, inverse 2228.

(491) divides n-1.

(491)^2 > n.

n is prime by Pocklington's theorem.