Candidates remaining and how high to top RPS?
 

[quote=em99010pepe;126392]Gary,

How many candidates do we have until n=600k?

Carlos[/quote]

It depends on where you start from. Total in the files is 3,918,344. So starting from n=360001, it would be 3,918,344-1,144,127=2,774,217. Starting from n=370001, it would be 3,918,344-1,258,856=2,659,488.


Here's another bit of information that someone was wondering about in another thread. How high would we have to search in order to overtake RPS? And I had to ask myself, is that even a reasonable goal? I did some searching on the top-5000 site for k<300 for n=333.3K-600K. I found 246 primes for 150 k-values. Of course this assumes no missed primes in non-double-checked ranges and not quite all of their k's have been searched to n=600K yet (but most have).

So we have the following:

246 primes / 150 k's = 1.55 primes / k. (Assume 1.6 primes / k-value to allow for a small amount of additional searching that they still need to do.)

1.6 primes / k * 351 k-values = 562 primes in our k-ranges

Two adjustments need to be made now for the # of primes for our ranges that are found by others that will not be reporting them as Primesearch, either past or present.

Adjustment #1:
94 total primes previously found in our range
- 57 primes previously found by Prime Search in our range when the project started

Loss of 37 primes

Adjustment #2:
There are 12 k's that we are not fully searching. One of which we're not searching at all, one we're only searching for n>400K, and the rest were only searching for n>500K. Assume a loss of 1 prime each on those, i.e. 1.6 - 1 = 0.6 primes / k-value on those.

Loss of 12 primes


So at n=600K, assuming that none of our primes have dropped off the list, we would have:

562 - 37 - 12 = 513 primes.


RPS currently has 558 primes. They had been averaging about 1 prime/day up until the last month when they dropped to about .75 prime/day. With the rate we're adding primes, all n=333333 primes should be gone in < 3 months. So if they continue for 90 days at their current rate, they'll add another ~67 primes for a total of 625 primes.

The question is, how many primes will we have in 3 months? Is 3 top-5000 primes/day possible? That would make 270 more primes for a total of ~380 primes for Primesearch 3 months from now. We've added ~50 in 30 days so far but we've only recently had the full-power of Free-DC working for us.

Regardless, when primes start dropping off, both projects will still be gaining ground. We'll just be gaining ground > 3X as fast. As ranges get higher primes/day will drop, so assume that we continue gaining ground on RPS at 3 (us) - 0.75 (them) - 1 adjustment = 1.25 primes / day gain on RPS. So if we're trailing 625-380 in 3 months, it would take us 240 / 1.25 = 192 days or ~6.5 months to catch them after the 3 month period is up at the end of May, i.e. mid-Dec 2008!!

So in conclusion, it does not look like we can overtake RPS by n=600K like I had originally thought BUT if we can search beyond n=600K by the end of 2008, then we can catch them by the end of the year. I'm thinking we'd have to go to somewhere around n=750K-800K by the end of 2008. Is anyone up for that challenge? I am! :smile:

BRING ON THE TOP-5000 RALLIES in the future!! lol

We'll have ranges available to n=1M for 300<k<400 starting in March for selected k's that have already been searched to n=600K.


:smile: Gary

[quote=gd_barnes;126424]...

So in conclusion, it does not look like we can overtake RPS by n=600K like I had originally thought BUT if we can search beyond n=600K by the end of 2008, then we can catch them by the end of the year. I'm thinking we'd have to go to somewhere around n=750K-800K by the end of 2008. Is anyone up for that challenge? I am! :smile:

BRING ON THE TOP-5000 RALLIES in the future!! lol

We'll have ranges available to n=1M for 300<k<400 starting in March for selected k's that have already been searched to n=600K.


:smile: Gary[/quote]
Well, I can say I'm up to the challenge, at least for what little bit I can do with my current resources. :smile:

As for n=600K-1M ranges for 300<k<400, those sound especially interesting, since primes at that level won't be dropping off the list for quite a while to come yet. :smile: Also, those high-n ranges will be especially well suited to LLRnet: LLRnet is great for high-n searches, because it deals with k/n pairs individually, and thus you can do them in exactly as small or large quantities as you want, rather than having to worry about whether you can finish a reasonably-sized block of high-n numbers in a reasonable amount of time (if, say, you've got an older machine, or your computer isn't on much). Thus, IMO we should have LLRnet focus on the higher-range numbers when they become available.

[quote=Anonymous;126425]Well, I can say I'm up to the challenge, at least for what little bit I can do with my current resources. :smile:

As for n=600K-1M ranges for 300<k<400, those sound especially interesting, since primes at that level won't be dropping off the list for quite a while to come yet. :smile: Also, those high-n ranges will be especially well suited to LLRnet: LLRnet is great for high-n searches, because it deals with k/n pairs individually, and thus you can do them in exactly as small or large quantities as you want, rather than having to worry about whether you can finish a reasonably-sized block of high-n numbers in a reasonable amount of time (if, say, you've got an older machine, or your computer isn't on much). Thus, IMO we should have LLRnet focus on the higher-range numbers when they become available.[/quote]


I agree in the long-run but in the short-term I REALLY :smile: want a rally to get 300<k<400 up well out of the danger zone near n=333333. With only 50 k's minus 4-5 reserved by others, we could blow away n=333K-380K or higher in a single rally. That'd be perfect. For individual files for the range, they'll be in either n=1K or 2K chunks. Same # of candidates as now would be had in a n=1200 piece. With 10% of k's removed though and the fact that even individuals are blowing through the files so fast, I may just post in n=2K chunks and if people want smaller, they can ask for it.

Gad...so much to do with a range that has been SO far behind for years.


Gary

[quote=gd_barnes;126433]I agree in the long-run but in the short-term I REALLY :smile: want a rally to get 300<k<400 up well out of the danger zone near n=333333. With only 50 k's minus 4-5 reserved by others, we could blow away n=333K-380K or higher in a single rally. That'd be perfect. For individual files for the range, they'll be in either n=1K or 2K chunks. Same # of candidates as now would be had in a n=1200 piece. With 10% of k's removed though and the fact that even individuals are blowing through the files so fast, I may just post in n=2K chunks and if people want smaller, they can ask for it.

Gad...so much to do with a range that has been SO far behind for years.


Gary[/quote]
Oh, okay. Yeah, I agree--we should get 300<k<400 out of the "danger zone" first, then move LLRnet to the higher range once we're all clear on the lower end, to try to put a lot of high-n top-5000 primes in the list that won't drop off for a long time.

The following have been completed by LLRnet:
350.4K-352.4K
354.0K-355.5K

lresults for both have been emailed to Gary. :smile:

Gary,

Please start preparing another 20k range for the LLRnet server port 300.

Carlos

[quote=em99010pepe;126513]Gary,

Please start preparing another 20k range for the LLRnet server port 300.

Carlos[/quote]


Done. n=372K-392K has been posted for reservation by LLRnet.

[quote=gd_barnes;126532]Done. n=372K-392K has been posted for reservation by LLRnet.[/quote]

Thank you Sir. I'll add it to the server within 2-3 days.

Taking 353.4-353.6.

taking 353.6-353.8

Another Update
 

llring 337.6-337.8 is over 3/4 done
i am up to:
645*2^337754-1