Primality proof for n = 11198022081713:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=16183.html>16183 is prime.</a>
<br>b^((n-1)/16183)-1 mod n = 8623673830514, which is a unit, inverse 7904725718434.
<p><a href=641.html>641 is prime.</a>
<br>b^((n-1)/641)-1 mod n = 426767406451, which is a unit, inverse 1055198904181.
<p>(641 * 16183) divides n-1.
<p>(641 * 16183)^2 > n.
<p>n is prime by Pocklington's theorem.