Primality proof for n = 9816177919:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=514313.html>514313 is prime.</a>
<br>b^((n-1)/514313)-1 mod n = 4147490218, which is a unit, inverse 4389308354.
<p>(514313) divides n-1.
<p>(514313)^2 > n.
<p>n is prime by Pocklington's theorem.