Primality proof for n = 84178317913:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3415219.html>3415219 is prime.</a>
<br>b^((n-1)/3415219)-1 mod n = 45664754278, which is a unit, inverse 59930863590.
<p>(3415219) divides n-1.
<p>(3415219)^2 > n.
<p>n is prime by Pocklington's theorem.