Primality proof for n = 19319:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=743.html>743 is prime.</a>
<br>b^((n-1)/743)-1 mod n = 13976, which is a unit, inverse 3717.
<p>(743) divides n-1.
<p>(743)^2 > n.
<p>n is prime by Pocklington's theorem.