Primality proof for n = 289249:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=131.html>131 is prime.</a>
<br>b^((n-1)/131)-1 mod n = 230861, which is a unit, inverse 30204.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 200722, which is a unit, inverse 243261.
<p>(23 * 131) divides n-1.
<p>(23 * 131)^2 > n.
<p>n is prime by Pocklington's theorem.