best Fermat search space program wanted

[jasong]

If you go here and scroll down, you'll find a link to the status of the search for Fermat factors. Basically, for any odd k, it lists which n have been searched up until now.

What I intend to do is to manually write a text file with the information, so that a program can be run that will take that file, generate a number corresponding to the k-value and lowest unlooked at n for that number, then compare them to recommend which is best.

First, I'll describe how I intend to make the text file:

The left side of the file will have the k-values, then there will be a space and the n value, which will actually be n/(10^6).

For the analysis program, here's my idea: As n increases by 50%, the time to do a test doubles. Also, according to what I've read, correct me here if needed, the odds a k will yield a factor for a Fermat number is proportionate to 1/k for any given n. So my idea is to calculate 1.5^x=n with n given, then calculate (2^x)/k with k given. The final value would be associated with the lowest unknown k/n pair. So, the k/n pair with the highest final value would be the "best bet" to find a factor.

One of the problems I see with this involves sieving, since the bigger the range of n sieved, the more efficient everything is. I'm not sure how hard it would be to add that circumstance to the computer.

Below is the file I've done so far, for ks that aren't represented, just think of them as being too high to be a "best bet."