Primality proof for n = 23189:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 20539, which is a unit, inverse 19330.
<p><a href=17.html>17 is prime.</a>
<br>b^((n-1)/17)-1 mod n = 6134, which is a unit, inverse 12154.
<p>(17 * 31) divides n-1.
<p>(17 * 31)^2 > n.
<p>n is prime by Pocklington's theorem.