Primality proof for n = 8118493917152534667909188789691403:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1157184950641651.html>1157184950641651 is prime.</a>
<br>b^((n-1)/1157184950641651)-1 mod n = 2528841039191114321908198064092886, which is a unit, inverse 5436661002290877855499620786200950.
<p><a href=21325306200707.html>21325306200707 is prime.</a>
<br>b^((n-1)/21325306200707)-1 mod n = 669304182202262331886779156274870, which is a unit, inverse 6838479453119295896735942967752210.
<p>(21325306200707 * 1157184950641651) divides n-1.
<p>(21325306200707 * 1157184950641651)^2 > n.
<p>n is prime by Pocklington's theorem.