Primality proof for n = 84457:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 61693, which is a unit, inverse 1651.
<p><a href=17.html>17 is prime.</a>
<br>b^((n-1)/17)-1 mod n = 75227, which is a unit, inverse 52367.
<p>(17 * 23) divides n-1.
<p>(17 * 23)^2 > n.
<p>n is prime by Pocklington's theorem.