Primality proof for n = 172054593956031949258510691:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=4434155615661930479.html>4434155615661930479 is prime.</a>
<br>b^((n-1)/4434155615661930479)-1 mod n = 81982237619807054769897706, which is a unit, inverse 154275350521713489305385904.
<p>(4434155615661930479) divides n-1.
<p>(4434155615661930479)^2 > n.
<p>n is prime by Pocklington's theorem.