Primality proof for n = 172307:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=853.html>853 is prime.</a>
<br>b^((n-1)/853)-1 mod n = 47346, which is a unit, inverse 48654.
<p>(853) divides n-1.
<p>(853)^2 > n.
<p>n is prime by Pocklington's theorem.