Primality proof for n = 872357267323181399605475340121915583445030403:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=82357043705861571042799942460715218111.html>82357043705861571042799942460715218111 is prime.</a>
<br>b^((n-1)/82357043705861571042799942460715218111)-1 mod n = 843139640587047709490348777968176207648008206, which is a unit, inverse 561898945805988033203795926728656046250521671.
<p>(82357043705861571042799942460715218111) divides n-1.
<p>(82357043705861571042799942460715218111)^2 > n.
<p>n is prime by Pocklington's theorem.