Primality proof for n = 10831:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 8821, which is a unit, inverse 6310.
<p>(19^2) divides n-1.
<p>(19^2)^2 > n.
<p>n is prime by Pocklington's theorem.