Primality proof for n = 3044861653679985063343:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=137849.html>137849 is prime.</a>
<br>b^((n-1)/137849)-1 mod n = 2698095051855333426110, which is a unit, inverse 1377102493580837955588.
<p><a href=132667.html>132667 is prime.</a>
<br>b^((n-1)/132667)-1 mod n = 1024945230919412454122, which is a unit, inverse 2641809638318597396287.
<p><a href=82163.html>82163 is prime.</a>
<br>b^((n-1)/82163)-1 mod n = 150916308174585819653, which is a unit, inverse 2254829869378658001638.
<p>(82163 * 132667 * 137849) divides n-1.
<p>(82163 * 132667 * 137849)^2 > n.
<p>n is prime by Pocklington's theorem.