Primality proof for n = 3415417404097:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=78364019.html>78364019 is prime.</a>
<br>b^((n-1)/78364019)-1 mod n = 656864911062, which is a unit, inverse 859845615215.
<p>(78364019) divides n-1.
<p>(78364019)^2 > n.
<p>n is prime by Pocklington's theorem.