Quote:
Originally Posted by MrOzzy
Thanks for all the info.
I've been playing around with everything a little bit and I have a few more questions:
 covering.exe you a conjectured K and the primes considered to calculate the conjectured K, but it doesn't tell which primes are used when a solution is found. How do I calculate which primes are used for the covering set?

I think covering.exe gives a set of them that it used but those are almost always way more factors than what is needed and is not what we're looking for. What I generally do is do it manually by going to:
http://www.alpertron.com.ar/ECM.HTM. It is a great program that will prime factor large numbers up to 10000 digits.
I plug in the form and try n=1, 2, 3, etc. I then analyze the least set of factors that makes them all composite. You have to be careful because it's easy to get a factor in there that you don't need. To be mathematically correct, we want the smallest covering set that makes the conjectured k always composite.
To get a good feel for it, play around with a known small conjecture such as Riesel base 8 with a (now proven) conjecture of k=14 and a covering set of [3, 5, 13]. See how the pattern of factors repeats for 14*8^n1 with the different nvalues. Once you do that, you should be able to do it with any base.
Covering.exe is pretty good at coming up with the lowest conjecture if it is given reasonable parameters. It's not so good at coming up with the smallest covering set.
Gary