Primality proof for n = 2291998858935929043684562366356035548933:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=82346938205356038105099017.html>82346938205356038105099017 is prime.</a>
<br>b^((n-1)/82346938205356038105099017)-1 mod n = 2249321467603453650220320055829948929527, which is a unit, inverse 10979720823912652656268176817449481162.
<p>(82346938205356038105099017) divides n-1.
<p>(82346938205356038105099017)^2 > n.
<p>n is prime by Pocklington's theorem.