Primality proof for n = 4310859807493:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=394049.html>394049 is prime.</a>
<br>b^((n-1)/394049)-1 mod n = 543675979413, which is a unit, inverse 1865434187540.
<p><a href=163.html>163 is prime.</a>
<br>b^((n-1)/163)-1 mod n = 2822299315753, which is a unit, inverse 501717291316.
<p>(163 * 394049) divides n-1.
<p>(163 * 394049)^2 > n.
<p>n is prime by Pocklington's theorem.