Primality proof for n = 285457:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=313.html>313 is prime.</a>
<br>b^((n-1)/313)-1 mod n = 37537, which is a unit, inverse 170170.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 141744, which is a unit, inverse 11888.
<p>(19 * 313) divides n-1.
<p>(19 * 313)^2 > n.
<p>n is prime by Pocklington's theorem.