Primality proof for n = 19211:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=113.html>113 is prime.</a>
<br>b^((n-1)/113)-1 mod n = 4082, which is a unit, inverse 17785.
<p><a href=5.html>5 is prime.</a>
<br>b^((n-1)/5)-1 mod n = 16686, which is a unit, inverse 11344.
<p>(5 * 113) divides n-1.
<p>(5 * 113)^2 > n.
<p>n is prime by Pocklington's theorem.