Primality proof for n = 4348819:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=241601.html>241601 is prime.</a>
<br>b^((n-1)/241601)-1 mod n = 262143, which is a unit, inverse 517476.
<p>(241601) divides n-1.
<p>(241601)^2 > n.
<p>n is prime by Pocklington's theorem.