Primality proof for n = 27678676889:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=119087.html>119087 is prime.</a>
<br>b^((n-1)/119087)-1 mod n = 11069242734, which is a unit, inverse 20394477560.
<p><a href=1709.html>1709 is prime.</a>
<br>b^((n-1)/1709)-1 mod n = 14370813982, which is a unit, inverse 12694812043.
<p>(1709 * 119087) divides n-1.
<p>(1709 * 119087)^2 > n.
<p>n is prime by Pocklington's theorem.