Primality proof for n = 44706919:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=9349.html>9349 is prime.</a>
<br>b^((n-1)/9349)-1 mod n = 24793508, which is a unit, inverse 35850462.
<p>(9349) divides n-1.
<p>(9349)^2 > n.
<p>n is prime by Pocklington's theorem.