Primality proof for n = 127727:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=63863.html>63863 is prime.</a>
<br>b^((n-1)/63863)-1 mod n = 3, which is a unit, inverse 42576.
<p>(63863) divides n-1.
<p>(63863)^2 > n.
<p>n is prime by Pocklington's theorem.