Primality proof for n = 173308343918874810521923841:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=361725589517273017.html>361725589517273017 is prime.</a>
<br>b^((n-1)/361725589517273017)-1 mod n = 9183761016836624269894001, which is a unit, inverse 112963131467374717304890528.
<p>(361725589517273017) divides n-1.
<p>(361725589517273017)^2 > n.
<p>n is prime by Pocklington's theorem.