Primality proof for n = 463692400718849804323:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=214692087848261.html>214692087848261 is prime.</a>
<br>b^((n-1)/214692087848261)-1 mod n = 100838370301940303199, which is a unit, inverse 27417911611131244732.
<p>(214692087848261) divides n-1.
<p>(214692087848261)^2 > n.
<p>n is prime by Pocklington's theorem.