Primality proof for n = 288773:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=6563.html>6563 is prime.</a>
<br>b^((n-1)/6563)-1 mod n = 27424, which is a unit, inverse 233375.
<p>(6563) divides n-1.
<p>(6563)^2 > n.
<p>n is prime by Pocklington's theorem.