Primality proof for n = 82346938205356038105099017:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1131014973702835376677.html>1131014973702835376677 is prime.</a>
<br>b^((n-1)/1131014973702835376677)-1 mod n = 26712236373319478013273238, which is a unit, inverse 4008626004909148236229863.
<p>(1131014973702835376677) divides n-1.
<p>(1131014973702835376677)^2 > n.
<p>n is prime by Pocklington's theorem.