Primality proof for n = 24286359868392659038129333:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=72092088130766173.html>72092088130766173 is prime.</a>
<br>b^((n-1)/72092088130766173)-1 mod n = 15449338634632516943691367, which is a unit, inverse 10066637540387985466599456.
<p>(72092088130766173) divides n-1.
<p>(72092088130766173)^2 > n.
<p>n is prime by Pocklington's theorem.