Primality proof for n = 500723:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=250361.html>250361 is prime.</a>
<br>b^((n-1)/250361)-1 mod n = 3, which is a unit, inverse 166908.
<p>(250361) divides n-1.
<p>(250361)^2 > n.
<p>n is prime by Pocklington's theorem.