Primality proof for n = 72371792138339:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=27213313.html>27213313 is prime.</a>
<br>b^((n-1)/27213313)-1 mod n = 4466101998437, which is a unit, inverse 66153038314064.
<p>(27213313) divides n-1.
<p>(27213313)^2 > n.
<p>n is prime by Pocklington's theorem.