Primality proof for n = 6848045079628454069:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=54897371.html>54897371 is prime.</a>
<br>b^((n-1)/54897371)-1 mod n = 4400235364529464752, which is a unit, inverse 5578272510406967279.
<p><a href=13043.html>13043 is prime.</a>
<br>b^((n-1)/13043)-1 mod n = 300628652347401897, which is a unit, inverse 4396050372818733173.
<p>(13043 * 54897371) divides n-1.
<p>(13043 * 54897371)^2 > n.
<p>n is prime by Pocklington's theorem.