Primality proof for n = 288135026414491:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=27678676889.html>27678676889 is prime.</a>
<br>b^((n-1)/27678676889)-1 mod n = 52597996143790, which is a unit, inverse 48789247497112.
<p>(27678676889) divides n-1.
<p>(27678676889)^2 > n.
<p>n is prime by Pocklington's theorem.