Primality proof for n = 10485409823782909:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=11636921.html>11636921 is prime.</a>
<br>b^((n-1)/11636921)-1 mod n = 5405584624689910, which is a unit, inverse 7910347825997103.
<p><a href=55579.html>55579 is prime.</a>
<br>b^((n-1)/55579)-1 mod n = 5677608841230753, which is a unit, inverse 2829817572263935.
<p>(55579 * 11636921) divides n-1.
<p>(55579 * 11636921)^2 > n.
<p>n is prime by Pocklington's theorem.