Primality proof for n = 161567415114024992333870349255799:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=147147008300569209775838205151.html>147147008300569209775838205151 is prime.</a>
<br>b^((n-1)/147147008300569209775838205151)-1 mod n = 90624283463138356983451427280174, which is a unit, inverse 19226912688727871432431575015003.
<p>(147147008300569209775838205151) divides n-1.
<p>(147147008300569209775838205151)^2 > n.
<p>n is prime by Pocklington's theorem.