Primality proof for n = 47840521:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=337.html>337 is prime.</a>
<br>b^((n-1)/337)-1 mod n = 28864528, which is a unit, inverse 13386653.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 14072982, which is a unit, inverse 19538637.
<p>(13^2 * 337) divides n-1.
<p>(13^2 * 337)^2 > n.
<p>n is prime by Pocklington's theorem.