Primality proof for n = 109829:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=27457.html>27457 is prime.</a>
<br>b^((n-1)/27457)-1 mod n = 15, which is a unit, inverse 7322.
<p>(27457) divides n-1.
<p>(27457)^2 > n.
<p>n is prime by Pocklington's theorem.