Primality proof for n = 407723:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=29123.html>29123 is prime.</a>
<br>b^((n-1)/29123)-1 mod n = 16383, which is a unit, inverse 2862.
<p>(29123) divides n-1.
<p>(29123)^2 > n.
<p>n is prime by Pocklington's theorem.