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Old 2009-08-18, 06:30   #9
gd_barnes's Avatar
May 2007
Kansas; USA

2×47×109 Posts

Originally Posted by mdettweiler View Post
YOWCH! Even with the new and improved PFGW, a test at that size for base 6 would probably take days to complete. Of course, that's not factoring in any expected increases in computer technology between now and when we get near that point.
That is a very big SWAG and this particular base has a somewhat unique issue that makes it a little trickier than one might expect for as prime as it is. That of k=1597. See last para.

I agree with your comments but believe me, that is very good for most of the bases here. I think there's a reasonable chance that we could prove it in 10-20 years depending on how much we dedicate to it.

That's for the Riesel side but on the Sierp side, with 28 k's remaining, it likely will not be proven in any of our lifetimes even allowing for computer speed increases and improvements in software unless new mathematical methods are discovered for searching the bases. Even if it was base 2, it would likely be more difficult than the Riesel side.

People don't realize how hard it is to knock out the final k's on these bases. Even for a fairly prime base like base 6, it's tough because the final few k's are almost always very low weight.

Consider that there are only 5128 pairs remaining for the entire n=150K-1M range for k=1597 on a sieve to P=6T. k=1597 will be the key as it is by far the lowest weight k remaining. If we can pick up a prime for it for n<=1M, then there's a reasonable chance that we could find them all by n=3M to 5M. If not, well, this may end up being yet another base that we have one k remaining on for an extended period.

All of that said, I still consider base 6 to be very exciting because it is the only truly "low" base that is kind of difficult to prove but not so overwhelmingly so that one side can't be done in our lifetimes. In this case, I define "low" as < 8. All other bases < 8 will be terribly difficult to prove in many lifetimes (Sierp base 2 has a chance but still a somewhat low chance at this point since it's already at n>10M with 5 k's remaining). I believe these "somewhat difficult" bases are the most interesting. An example is the Dual Sierp base 2 project with 3 k's remaining at n=~3M. I think that one has a good chance of being proven by perhaps the n=20M to 30M range. In other words, it's tough but not too tough, the most interesting kind.


Last fiddled with by gd_barnes on 2009-08-18 at 06:42
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