Primality proof for n = 19757330305831588566944191468367130476339:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=172054593956031949258510691.html>172054593956031949258510691 is prime.</a>
<br>b^((n-1)/172054593956031949258510691)-1 mod n = 9148758478138211201771971577098600188171, which is a unit, inverse 16371654433361644093796961727196399386194.
<p>(172054593956031949258510691) divides n-1.
<p>(172054593956031949258510691)^2 > n.
<p>n is prime by Pocklington's theorem.