Primality proof for n = 163131120638915058577002756917:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=760192948315673.html>760192948315673 is prime.</a>
<br>b^((n-1)/760192948315673)-1 mod n = 145847107365479093624900908603, which is a unit, inverse 145881772526240962556179613612.
<p>(760192948315673) divides n-1.
<p>(760192948315673)^2 > n.
<p>n is prime by Pocklington's theorem.