Primality proof for n = 7817573:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=151.html>151 is prime.</a>
<br>b^((n-1)/151)-1 mod n = 6326917, which is a unit, inverse 6002329.
<p><a href=43.html>43 is prime.</a>
<br>b^((n-1)/43)-1 mod n = 5487877, which is a unit, inverse 3904696.
<p>(43^2 * 151) divides n-1.
<p>(43^2 * 151)^2 > n.
<p>n is prime by Pocklington's theorem.