Primality proof for n = 19813:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=127.html>127 is prime.</a>
<br>b^((n-1)/127)-1 mod n = 70, which is a unit, inverse 6510.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 9354, which is a unit, inverse 10292.
<p>(13 * 127) divides n-1.
<p>(13 * 127)^2 > n.
<p>n is prime by Pocklington's theorem.