Primality proof for n = 97859369123353:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=379979.html>379979 is prime.</a>
<br>b^((n-1)/379979)-1 mod n = 94986100431262, which is a unit, inverse 41608912195100.
<p><a href=271.html>271 is prime.</a>
<br>b^((n-1)/271)-1 mod n = 93325906734243, which is a unit, inverse 24193097608682.
<p>(271 * 379979) divides n-1.
<p>(271 * 379979)^2 > n.
<p>n is prime by Pocklington's theorem.