Primality proof for n = 140731847223860698993672433903061203299016858671554230293:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=21561596637519154364530566979.html>21561596637519154364530566979 is prime.</a>
<br>b^((n-1)/21561596637519154364530566979)-1 mod n = 93838646185460646404182154013221873569480931329864712019, which is a unit, inverse 89185208156111169819064954848987757484831368627523891035.
<p>(21561596637519154364530566979) divides n-1.
<p>(21561596637519154364530566979)^2 > n.
<p>n is prime by Pocklington's theorem.