Primality proof for n = 7240555601:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=15173.html>15173 is prime.</a>
<br>b^((n-1)/15173)-1 mod n = 4761324069, which is a unit, inverse 3376787645.
<p><a href=1193.html>1193 is prime.</a>
<br>b^((n-1)/1193)-1 mod n = 5989585659, which is a unit, inverse 4568713278.
<p>(1193 * 15173) divides n-1.
<p>(1193 * 15173)^2 > n.
<p>n is prime by Pocklington's theorem.