[QUOTE=MyDogBuster;263100]Nice job Gary. That total jives with what I had. Only 2 ranges to go. Maybe I'll survive to finish it.[/QUOTE]

What!!! I thought that you would tackle R51! It only has 16753 k at n=10000.

[QUOTE]What!!! I thought that you would tackle R51! It only has 16753 k at n=10000. [/QUOTE]

Nah, I'm finished with the large CK bases after S51. I'm afraid if I take the laptop out to the garage and blow the dust out of it, the cloud created might pollute the air for a couple of miles.

[QUOTE=MyDogBuster;263118]Nah, I'm finished with the large CK bases after S51. I'm afraid if I take the laptop out to the garage and blow the dust out of it, the cloud created might pollute the air for a couple of miles.[/QUOTE]

Maybe Puzzle-Peter would like to take a crack at it. He's been working on S63. It would be about 1/4 of the work.

[QUOTE=rogue;263122]Maybe Puzzle-Peter would like to take a crack at it. He's been working on S63. It would be about 1/4 of the work.[/QUOTE]

Not enough k's. I'll go for R63 just to drive Gary crazy :devil:

[QUOTE] I'll go for R63 just to drive Gary crazy :devil:[/QUOTE]

I thought driving Gary crazy was my job.:grin: But any help is greatly appreciated.:help:

[QUOTE=rogue;263122]Maybe Puzzle-Peter would like to take a crack at it. He's been working on S63. It would be about 1/4 of the work.[/QUOTE]

Not sure about the 1/4 of the work. Here are the details I know.

I did the first 10K k's of S63 on 1 core I sieved to 250M testing from n=1K to 10K this took me 110 days to complete.

With R51 having 28520 k's on 4 cores (same machine as was used on S63) I sieved to 1G testing from n=3K to 10K this took me 180 days to complete.

End result

S63 [TEX]\frac{2444}{10000}[/TEX] = 24.44% remaining

R51 [TEX]\frac{16573}{28520}[/TEX] = 58.11% remaining

[QUOTE=Mathew;263130]Not sure about the 1/4 of the work. Here are the details I know.

I did the first 10K k's of S63 on 1 core I sieved to 250M testing from n=1K to 10K this took me 110 days to complete.

With R51 having 28520 k's on 4 cores (same machine as was used on S63) I sieved to 1G testing from n=3K to 10K this took me 180 days to complete.

End result

S63 [TEX]\frac{2444}{10000}[/TEX] = 24.44% remaining

R51 [TEX]\frac{16573}{28520}[/TEX] = 58.11% remaining[/QUOTE]

Note that your range for S63 was larger. You probably only had about 6000 remaining at n=3000. That implies about 40% remaining. If R51 has a removal rate of about 2/3 of S63, that would then put it somewhere between 1/3 and 1/2 of S63.

If I had my preference, it would be that we don't work on any new bases at all that will have > ~1000 k's remaining at n=10K or existing (already-worked) bases that already have > 1000 k's remaining at n>=10K. I would kind of prefer that we work on bases that can be possibly proven in our lifetimes or at least on ones that we can leave just a few dozen k's or less remaining for future generations to prove.

I do have one slight exception to the above. I have to admit I would be quite entertained to see all k's of R3 tested to n=25K (est. 300,000-330,000 k's reamining) and I'd do my best to keep up with statuses as they came in although might gripe and moan if they come in too fast. It is cool that it is up to k=1.2G now on a k=~50G conjecture. But it is so much work in bulk that I'm not going to formally promote it. Before I die, I'd like to see all of R3 tested to n=100K (est. 100,000 k's remaining) but I hope to live a while yet (I'm 49) so that's real low priority. :smile:

All of this said, at this point since the project has "matured" so to speak since all of the low-conjectured bases have all been tested to n>=25K, people should be free to work on whatever entertains them the most because one status is not going to overwhelm me like it did when dozens of bases were being completed in short order. That's what's great about the project now. You can find gillions of small primes or just a few huge ones or a medium amount of medium ones; whatever your taste is. Right now, my taste is to find medium amounts of medium ones so I'm taking several bases from n=25K or 50K to 100K. At other times, I test the large ones like when I took R4 k=19464 from n=500K to 1M recently. Any more, I grow quickly bored of finding a lot of small primes and probably won't consider any new bases in the future that I expect will have > ~200 k's remaining at n=25K.


Gary

[QUOTE=Puzzle-Peter;263127]Not enough k's. I'll go for R63 just to drive Gary crazy :devil:[/QUOTE]

I think you should do base 280...both sides for good measure. :smile:

[QUOTE=rogue;263134]Note that your range for S63 was larger. You probably only had about 6000 remaining at n=3000. That implies about 40% remaining. If R51 has a removal rate of about 2/3 of S63, that would then put it somewhere between 1/3 and 1/2 of S63.[/QUOTE]

Fortunately I have all of the primes for both R51 and S63 from n=1K to 10K so let's get an apples to apples:

S63 has 56548 k's remaining at n=10K.
There were 60285 primes from n=3K-10K.
So there were 116833 k's remaining at n=3K.
Removal rate = 60285 / 116833 = 51.60% (or 48.40% remaining)

R51 has 16573 k's remaining at n=10K
There were 11947 primes from n=3K-10K.
So there were 28520 k's remaining at n=3K.
Removal rate = 11947 / 28520 = 41.89% (or 58.11% remaining)
[exactly what Mathew said]

So...R51 is not very far behind S63 in its "primeness". S63 is actually fairly weak for the "very prime" 2^q-1 bases. Bases 3, 7, 15, & 31 are all far better.

Extrapolation:

S63 has 56548 / 16573 = 3.412 times as many k's remaining

S63 takes [log(63)/log(51)]^2 = 1.11 times as long to test as R51 (since it is a larger base) at the same n-value.

So S63 would take 3.412 * 1.11 = 3.787 times as long if the base was of the same "primeness". This doesn't take into account any extra time due to extremely large k's, which is fairly minimal for k>1M.

This is where it gets tough and with my mathematical knowledge, only a rough estimate can be provided: S63 removes k's at a 51.60 / 41.89 = 1.2318 or 23.18% faster rate than R51. Does this mean that S63 should take 23.18% less time to test for the same # of k's for n=10K-25K? Absolutely not. It depends greatly on the n-range tested. (After all if we tested only an n=100 range, the difference would be almost non-existent.) We can always say that S63 should find 23.18% more primes for any given n-range than R51 but to estimate the time savings is much more tricky. If the range we were testing was exactly like the example, i.e. n=3K-10K or an n-max to n-min ratio = 3-1/3rd or in this case n=10K to 33.3K, and we make a slightly erroneous assumption that the primes are evenely dispursed throughout the n-range, we could say that the time taken should be 23.18% / 2 = 11.59% less for an n-max to n-min ratio of 3-1/3rd. But since they are not evenly dispersed, it's probably more like 13-15% less time since a majority of the primes will be found in the earlier parts of the range, due to a greater chance of prime at lower n-ranges.

If you're staying with me there, I use the above logic to assume that for n=10K-25K (i.e. an n-max to n-min of 2.5 vs. 3.33) for R51 vs. S63 would take S63 ~8-10% (vs. 13-15%) less time for the same # of k's due to its greater "primeness" (we'll use 9%).

Therefore I estimate that:
S63 will take 3.787 / 1.09 = ~3.475 times as long to test as R51 for n=10K to 25K. So Mark wasn't too far off when he gave a rough estimate of R51 being 1/4th of the work of S63. It's more like 1/3.5.

Interestingly if you had just ignored the fact that S63 is a larger and "more prime" base and used the ratio of k's remaining, you would have come quite close to this. My suggestion for figuring out estimates like this for bases of similar size is to just use the ratio of k's remaining. If you know that one base is extremely "more prime" or that one base is much larger than the other, then you can make adjustments accordingly. Here the size of the bases and "primeness" of the bases were not extremely different and actually worked to mostly offset one another.


Gary

[QUOTE=gd_barnes;263149]If I had my preference, it would be that we don't work on any new bases at all that will have > ~1000 k's remaining at n=10K or existing (already-worked) bases that already have > 1000 k's remaining at n>=10K. I would kind of prefer that we work on bases that can be possibly proven in our lifetimes or at least on ones that we can leave just a few dozen k's or less remaining for future generations to prove.[/QUOTE]

I agree about new bases. My thinking is that I would like to see all bases that have been started get to n=25000. Since R51 and R79 have been completed to n=10000, they are not as big a task as R3 and S3.