Primality proof for n = 82163:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=41081.html>41081 is prime.</a>
<br>b^((n-1)/41081)-1 mod n = 3, which is a unit, inverse 27388.
<p>(41081) divides n-1.
<p>(41081)^2 > n.
<p>n is prime by Pocklington's theorem.