Primality proof for n = 23314383343543:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=228572385721.html>228572385721 is prime.</a>
<br>b^((n-1)/228572385721)-1 mod n = 20351814924464, which is a unit, inverse 1293503794781.
<p>(228572385721) divides n-1.
<p>(228572385721)^2 > n.
<p>n is prime by Pocklington's theorem.