Primality proof for n = 6193811023329968617:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=45467703727.html>45467703727 is prime.</a>
<br>b^((n-1)/45467703727)-1 mod n = 2795102667851351273, which is a unit, inverse 3057181491676025995.
<p>(45467703727) divides n-1.
<p>(45467703727)^2 > n.
<p>n is prime by Pocklington's theorem.