Primality proof for n = 693989:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=173497.html>173497 is prime.</a>
<br>b^((n-1)/173497)-1 mod n = 15, which is a unit, inverse 46266.
<p>(173497) divides n-1.
<p>(173497)^2 > n.
<p>n is prime by Pocklington's theorem.