Primality proof for n = 155317:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=43.html>43 is prime.</a>
<br>b^((n-1)/43)-1 mod n = 23631, which is a unit, inverse 148074.
<p>(43^2) divides n-1.
<p>(43^2)^2 > n.
<p>n is prime by Pocklington's theorem.