Primality proof for n = 135382853293:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=275168401.html>275168401 is prime.</a>
<br>b^((n-1)/275168401)-1 mod n = 83541084863, which is a unit, inverse 117645950070.
<p>(275168401) divides n-1.
<p>(275168401)^2 > n.
<p>n is prime by Pocklington's theorem.