Primality proof for n = 108140989558681:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=23609.html>23609 is prime.</a>
<br>b^((n-1)/23609)-1 mod n = 27458299228746, which is a unit, inverse 10679667100567.
<p><a href=1433.html>1433 is prime.</a>
<br>b^((n-1)/1433)-1 mod n = 13658565625703, which is a unit, inverse 104633227636071.
<p>(1433 * 23609) divides n-1.
<p>(1433 * 23609)^2 > n.
<p>n is prime by Pocklington's theorem.