Primality proof for n = 117411509:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=163.html>163 is prime.</a>
<br>b^((n-1)/163)-1 mod n = 39742528, which is a unit, inverse 102025030.
<p><a href=157.html>157 is prime.</a>
<br>b^((n-1)/157)-1 mod n = 23857135, which is a unit, inverse 20957351.
<p>(157 * 163) divides n-1.
<p>(157 * 163)^2 > n.
<p>n is prime by Pocklington's theorem.