Primality proof for n = 10434257:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=13309.html>13309 is prime.</a>
<br>b^((n-1)/13309)-1 mod n = 8271012, which is a unit, inverse 4898857.
<p>(13309) divides n-1.
<p>(13309)^2 > n.
<p>n is prime by Pocklington's theorem.