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Old 2007-12-19, 18:15   #3
gd_barnes's Avatar
May 2007
Kansas; USA

19·541 Posts

Originally Posted by Anonymous View Post
I voted to continue filling in bases <=32, but I was confused about one thing: why leave out bases 3, 7, and Sierpinski 31?

I imagine that quite a lot of the project's computing power will be thrown on the bases that are powers of 2 (simply because they're quite attractive to users)--though I don't think that in any way the project should be limited to those. In fact, most of the bases that are at all close to having their conjectures proven are not powers of 2.

Probably if we do any team drives in the future, we might want to focus them on power-of-2 bases, though, since those bases would be the most attractive to new users (team drives are great for "test-driving" a project)--and, in the case of Base 16 Sierpinski, are some of the farthest away from being proven.

We don't know the conjectures yet on bases 3, 7, 15, and Sierp 31. The first 3 are likely k > 10e10 and Sierp Base 31 is definitely k > 5e6. They're just too unmanageable with today's computing power and knowledge. That said, if people are open to the idea, I might suggest searching some of those up to k=100K at some point to get future generations of prime searchers started on those huge efforts. To me, the main thing is collecting data for us and for future generations to analyze.

I like the idea of a team drive for powers of 2, namely Sierp base 16. We will definitely look to do that in the future. It LLR's as fast as base 2 and we'll definitely get some top-5000 primes out of it with 57 k's remaining (55 not reserved). And we haven't even started on Riesel base 16. There's plenty of work to do on both sides.

As for team efforts for other powers of 2; we'd have to go up to base 64, 128, or 256, which is certainly an option. Base 2 is being worked by other projects as well as base 4 Sierp. Base 4 Riesel is down to 6 k's remaining for our effort so that is out. Base 8 is proven and base 32 is proven or cannot possibly be proven with today's knowledge.

We can even somewhat combine the first two choices in the poll while maintaining more focus on one or the other. We could open up bases 64, 128, or 256 for a possible team effort (I don't know the conjectures yet...most may be too low...I need to check) but keep our main focus on bases <= 32. I think that flexibility is important in this type of effort.

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