Primality proof for n = 6848045079628454069:

Take b = 2.

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

54897371 is prime.
b^((n-1)/54897371)-1 mod n = 4400235364529464752, which is a unit, inverse 5578272510406967279.

13043 is prime.
b^((n-1)/13043)-1 mod n = 300628652347401897, which is a unit, inverse 4396050372818733173.

(13043 * 54897371) divides n-1.

(13043 * 54897371)^2 > n.

n is prime by Pocklington's theorem.