Primality proof for n = 473471:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=419.html>419 is prime.</a>
<br>b^((n-1)/419)-1 mod n = 462977, which is a unit, inverse 360540.
<p><a href=113.html>113 is prime.</a>
<br>b^((n-1)/113)-1 mod n = 331310, which is a unit, inverse 391197.
<p>(113 * 419) divides n-1.
<p>(113 * 419)^2 > n.
<p>n is prime by Pocklington's theorem.