Primality proof for n = 457:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 214, which is a unit, inverse 126.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 322, which is a unit, inverse 44.
<p>(3 * 19) divides n-1.
<p>(3 * 19)^2 > n.
<p>n is prime by Pocklington's theorem.