Primality proof for n = 688147:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=114691.html>114691 is prime.</a>
<br>b^((n-1)/114691)-1 mod n = 63, which is a unit, inverse 349535.
<p>(114691) divides n-1.
<p>(114691)^2 > n.
<p>n is prime by Pocklington's theorem.