Primality proof for n = 409477:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=34123.html>34123 is prime.</a>
<br>b^((n-1)/34123)-1 mod n = 4095, which is a unit, inverse 391678.
<p>(34123) divides n-1.
<p>(34123)^2 > n.
<p>n is prime by Pocklington's theorem.