Primality proof for n = 127:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 3, which is a unit, inverse 85.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 106, which is a unit, inverse 6.
<p>(3^2 * 7) divides n-1.
<p>(3^2 * 7)^2 > n.
<p>n is prime by Pocklington's theorem.