Primality proof for n = 27413359092552162435694767700453926735143482401279781:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=104719073621178708975837602950775180438320278101.html>104719073621178708975837602950775180438320278101 is prime.</a>
<br>b^((n-1)/104719073621178708975837602950775180438320278101)-1 mod n = 6041092171163918423393132352399868606647826176154688, which is a unit, inverse 4031111370769809914916647399004588060065488295890678.
<p>(104719073621178708975837602950775180438320278101) divides n-1.
<p>(104719073621178708975837602950775180438320278101)^2 > n.
<p>n is prime by Pocklington's theorem.