Primality proof for n = 35581458644053887931343:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=44925942675193.html>44925942675193 is prime.</a>
<br>b^((n-1)/44925942675193)-1 mod n = 24115266892333603123314, which is a unit, inverse 35517264014749958086007.
<p>(44925942675193) divides n-1.
<p>(44925942675193)^2 > n.
<p>n is prime by Pocklington's theorem.