Primality proof for n = 347582969077:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=10273.html>10273 is prime.</a>
<br>b^((n-1)/10273)-1 mod n = 152760838303, which is a unit, inverse 301429130273.
<p><a href=6827.html>6827 is prime.</a>
<br>b^((n-1)/6827)-1 mod n = 324937597743, which is a unit, inverse 108274241734.
<p>(6827 * 10273) divides n-1.
<p>(6827 * 10273)^2 > n.
<p>n is prime by Pocklington's theorem.