Primality proof for n = 198211423230930754013084525763697:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=3044861653679985063343.html>3044861653679985063343 is prime.</a>
<br>b^((n-1)/3044861653679985063343)-1 mod n = 75003846807402791567026918316103, which is a unit, inverse 169495726156219349589498880139957.
<p>(3044861653679985063343) divides n-1.
<p>(3044861653679985063343)^2 > n.
<p>n is prime by Pocklington's theorem.