Primality proof for n = 19953467139239:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=85831.html>85831 is prime.</a>
<br>b^((n-1)/85831)-1 mod n = 4476454517442, which is a unit, inverse 8460635604093.
<p><a href=2549.html>2549 is prime.</a>
<br>b^((n-1)/2549)-1 mod n = 12746029004369, which is a unit, inverse 9531362705223.
<p>(2549 * 85831) divides n-1.
<p>(2549 * 85831)^2 > n.
<p>n is prime by Pocklington's theorem.