Primality proof for n = 68681292269:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=24217663.html>24217663 is prime.</a>
<br>b^((n-1)/24217663)-1 mod n = 67551786400, which is a unit, inverse 3312474643.
<p>(24217663) divides n-1.
<p>(24217663)^2 > n.
<p>n is prime by Pocklington's theorem.