Gaps and more gaps on <300 site

[gd_barnes]

Let's talk gaps on the <300 site for a few minutes. This is something that I brought up for k=289 on the 'choose your own k' thread but I think gaps need their own thread now. I want to make sure that we get all gaps filled for all k < 300 so that no primes are missed.

Karsten, correct me if I'm wrong, but I believe that you informed me that when we see a notation on the <300 site like there is for k=289 that shows >> 77391, 90201 [300k Jeffrey], 501991, 509401 <<, that it means there is possibly a gap from n=300k to n=501991 and NOT from 90201 to 300k. I am taking that very literally when doing the following analysis of gaps.

I have now analyzed the entire <300 site and based on the above, I have observed the following gaps, several of which I have questions about:

k gap status of gap
1 17546k - 20996011 GIMPS working on
3 2710k - 3136255 321 working on
27 658k - 729314
45 640k - 645542
51 561k - 657705
57 561k - 565994
69 932k - 978209
77 1320k - 1467554
181 804k - 823853
207 460k - 481385
243 260k - 387836
255 604k - 635715
261 561k - 618918
267 561k - 607688
279 561k - 587881
289 300k - 501991 I am working on
291 561k - 565917
297 492k - 492450



Comment: I'm not concerned with k=1, 3, and 289 that either I or other major projects are working on.

Questions:
1. k=45; notation is: 368553, 528245 [VBCurtis at 640k], 645542. Does this really mean a very small gap from 640k to 645542? Or could it really mean a gap from 528245 to 640k? Or possibly no gap at all? It seems very strange to find a prime at 528245, have testing stopped at 640k, and then have testing started again at some unknown k after that only to find a prime almost immediately at 645542. This pattern of things occurs throughout these questions and it just doesn't seem correct.

2. k=57; same question as k=45; notation is: 239854, 450430 [RPS at 561k], 565994, 839446. Very small gap. Could the gap really be from 450430 to 561k? Could there be no gap?

3. k=297; Karsten, you are working on this one. Same question as the first two. The notation is: 283484, 378102 [kar_bon at 492k], 492450, 493726. What this means based on what I was told is that testing was completed up to 492k by you, then stopped, and then started again at some unknown place and then a prime was found almost immediately at 492450. That is what the notation is indicating but I'm thinking that it can't possibly be correct. Like above, could the gap instead be from 378102 to 492k or maybe no gap?

4. Same question on many others that have small gaps where the prime found before testing was stopped is much further from the stopping place then the prime found after it.


I'm wondering if my analysis here shows that the same notation may mean different things for different k's on the < 300 site. If so, can we establish some sort of standards for showing gaps there?

One thing that I previously suggested was to show (...) for gaps like is done on the summary site. I would really appreciate it if something like that was done because I'm still very confused by the current notation on the <300 site and would like to get all of the gaps filled or coordinate an effort to do so.


Thanks a bunch,
Gary

[Kosmaj]

Many of these are not real gaps. For example, k=45 currently tested by Curtis. From time to time he posts his status, and last time he said "k=45 tested to 640k." A little bit later he reported a prime at n=645542, without saying anything about the bound (limit) n_max that he reached. In the next update he will declare "tested to 650k" and after that I'll move the prime to the left side of the updated bound. But in the meanwhile I have no idea whether he checked all n's between 640,000 and 645,542.

The same applies for a number of k's you mentioned, like k=69, 181, 207 etc. including k=297. They are all in progress by our members.

For k=51, k=57 and some other k's from the 5th Drive, there is a person who reserved 561-562 a long time ago and I'm still waiting for his results.

k=27 is reserved by the "12121" project.

k=77 has a real gap between 1.32M and about 1.455M. The rest to 1.5M I tested.

k=243 has several real gaps, Rob told me exactly were they are, but he said he is working on some of them.

k=289, Bo is the only person who reported primes 3<=k<300 in the last few years with whom I'm not in touch. So, I have no idea where the gaps, if any, are located.

[kar_bon]

hi Kosmaj and Gray,
i can speek only for 'my' k=297: it's correct.
i submitted in post http://www.mersenneforum.org/showpos...&postcount=555 from March 22 that k=297 is at n=492k.
atfer that (next day) i found 2 primes at >492k and no new limit for n.
so the notation '<primes> (limit n) <primes>' is correct for whom reading this thread. i reserved k=297 from n=260k and now i'm at n=581k without any gaps.
the notation for k=1 (GIMPS) explains that:
the GIMPS-project is worldwide spreaded and many members working on it.
17546k means that all n lower this are tested at least once so you can be sure all primes are found. many other n's greater this are already checked and there are more primes above this limit.
GIMPS say's today:
All exponents below 15,188,500 have been tested and double-checked.
All exponents below 18,816,700 have been tested at least once.
Countdown to testing all exponents below M(20996011) once: 23
Countdown to testing all exponents below M(24036583) once: 277
Countdown to testing all exponents below M(25964951) once: 578
Countdown to testing all exponents below M(30402457) once: 5,645
Countdown to testing all exponents below M(32582657) once: 15,137
Countdown to proving M(20996011) is the 40th Mersenne Prime: 49,999
Countdown to proving M(24036583) is the 41st Mersenne Prime: 114,986
Countdown to proving M(25964951) is the 42nd Mersenne Prime: 156,093
Countdown to proving M(30402457) is the 43rd Mersenne Prime: 251,153
Countdown to proving M(32582657) is the 44th Mersenne Prime: 298,188

there's a (low) chance of finding primes below 20996011 (here only 23 are not tested yet). and doublechecking to prove the 40th prime there're 49999 n to test.

hope it's a little bit clear now.
Karsten

[gd_barnes]

NOW I see the light! OF COURSE if someone finds a prime but they are in the middle of testing a large range, they aren't going to report how far they've tested until they hit some round number like 562k or 600k or whatever. Thank you both Karsten and Kosmaj for the detailed explanations.

I was aware of the situation on GIMPS. I tested one exponent for them before I found this effort but with only 2 machines at the time, I quickly decided that I didn't have the patience for it. I think in order to do testing for exponents that high and not go crazy, I'd have to have at least 20-30 machines. :-)

I don't currently have the available machines to fill any more gaps until I'm done with k=289 without giving up other efforts so here's what I'd like to do over the next few weeks to rid ourselves of the gaps for k < 300:
1. Finish the gap on k=289.
2. Start a thread to coordinate an effort to knock out the gap on k=77 since that will take a while at such a high n.
3. Check with Rob and see where he's at on completing the gap for k=243.
4. Check with the person who has not reported back their results on the range of n=561K to 562K for several k's on the 5th drive.

Kosmaj, you can help me in a couple of ways here:
1. Could you give me a link or point me in the direction of the person named Rob who is working on k=243? I'll follow up with him to verify what gaps remain and if he's still working on them, I'll just leave him alone and let him finish it. Or if he has some ranges that he won't be able to get to, I'll take them after I'm done with k=289, which I'm thinking will be just a little over 2 weeks.

2. Could you give me a link or tell me who it was that had reserved the ranges of n=561K to 562K for several k's on the 5th drive and hasn't reported back in a long time? If I can't get a response, since he hasn't reported in a long time, I'll temporarily take one of my machines off of another effort and personally do them all myself. A 1K (or 2K) range at that value of n won't take too long to complete even for a lot of different k's and it'd be nice to have the final gaps filled on so many k's.


On another note... can the notation for k=1 (GIMPS) be updated to show (GIMPS at 18817K) based on what Karsten pasted here? Just thought I'd check.

One final note, you can see my progress on k=289 by checking the ranges completed on Primesearch for that k. I have n=260K to 520K reserved there and here. I've split the range in two for my dual processors on one machine. One is working on n=260K to 400K and the other on 400K to 520K so you'll initially see them completed a little out of order. I realize that I'm probably duplicating at least some effort for it but I'll be extra happy to know for sure that the gap is filled.


Thanks again,
Gary

[VBCurtis]

Originally Posted by gd_barnes

One final note, you can see my progress on k=289 by checking the ranges completed on Primesearch for that k. I have n=260K to 520K reserved there and here. I've split the range in two for my dual processors on one machine. One is working on n=260K to 400K and the other on 400K to 520K so you'll initially see them completed a little out of order. I realize that I'm probably duplicating at least some effort for it but I'll be extra happy to know for sure that the gap is filled.

Thanks again,
Gary

Your method of splitting work on two cores is exactly how some primes are reported above the current limit. I often have 2 or 3 machines on LLR on the same k, and the higher-range might find a prime first. 197 is presently running 700-800, 800-900,900-1000,1000-1100 on 4 separate machines. If I get lucky and 1020xxx is prime, that will be posted long before the been-checked range is up that high. You should only be concerned with unreserved k's for your gap-filling.

Kosmaj's example of 45 happens to be the one k I currently have only one machine on, so I could have reported that prime and the new been-tested limit as that n, but I prefer to do as Kosmaj explained, posting new limits once a month or so.

Overall, the k<300 page is the best-organized of any prime search I've seen on the Net; in no small part because of Kosmaj's frequent updating, combined with his efforts to make sure it was accurate when he took over maintaining it.

-Curtis

[Kosmaj]

The latest version of our k<300 status page is on the server. Many gaps due to work in progress have been closed thanks to Gary's initiative and people who reported their latest status. Two missing primes k=201 and k=279 added. Also, I visited the 12121 project web page and found that they filled the k=27 gap. Gimps new limit updated as well.

Kosmaj

[Kosmaj]

The last news I got from Rob about k=243 can be found here. I'll try to contact him again to see where is he now.

I already mailed John, who is testing 561-562 from the 5th Drive, about a week ago, still waiting for his reply.

I'm still working on k=77 to fill the gap, but currently I have only one machine running, and only on weekends.

BTW, k=135 is included in the 5th Drive, we started at n=300k.

[gd_barnes]

Originally Posted by VBCurtis

Overall, the k<300 page is the best-organized of any prime search I've seen on the Net; in no small part because of Kosmaj's frequent updating, combined with his efforts to make sure it was accurate when he took over maintaining it. -Curtis

I couldn't agree more. Especially the amount of information that gets into the summary page in such rapid fashion. Very nicely organized.

[gd_barnes]

Originally Posted by Kosmaj

The last news I got from Rob about k=243 can be found here. I'll try to contact him again to see where is he now.

I already mailed John, who is testing 561-562 from the 5th Drive, about a week ago, still waiting for his reply.

I'm still working on k=77 to fill the gap, but currently I have only one machine running, and only on weekends.

BTW, k=135 is included in the 5th Drive, we started at n=300k.

Great to see the updates Kosmaj. I see those gaps falling little by little! :-)

That sounds good on the gap for k=77. No hurry since it's a gap at such a high value of n. I'm more interested in seeing the lower gaps filled.

You guys have mentioned the '4th drive', '5th drive', etc. many times. Having only been at this a couple of months, I've read some past threads about them but don't know what all they have entailed without spending a lot of research time. So can I assume by your statement here that the 5th drive is testing k=135 consecutively from n=300K up to the next prime at n=437544? Although certainly possible, there's 175K between primes at that point and there's a fairly high density of primes on both sides of it so it looks pretty questionable.

Here's what I'll do to finally knock the other gaps out. If you don't hear back from Rob or John by the time I'm done with k=289 in < 2 weeks, I'll check with you first and then reserve them all in the 'choose your own k' forum and start doing them myself because all but one will take little time. The ones with the small gap from n=561k to 562k will go quickly so any place where I see (561k xxx) on the <300 site, I will take and test them real quick. I think there's 10 or more of them but I'm thinking just 2-4 days or so at most to complete them all.

k=243 would take a long while to do unless Rob has filled a lot of the gaps indicated by your last post. Rob's post is 9 months old and since you haven't heard anything from him, it makes me wonder if he intends to complete all of the testing. Your statement at the time about what ranges he had tested said: "Rob kindly informed me that he is still working on k=243=3^5. So far he tested the following ranges: 300-400k, 650-745k, and 800k-1M." This indicates huge gaps including n=260K-300K, 400K-650K, and 745K-800K. The gap of 400K to 650 is most troubling. Hopefully he's completed at least some of that range.


Thanks again,
Gary

[gd_barnes]

Originally Posted by VBCurtis

You should only be concerned with unreserved k's for your gap-filling. -Curtis

I appreciate the info. but I think it really depends entirely on the situation. In many circumstances, I don't think we can ignore gaps on reserved k's, Curtis, especially when they get more than 6 months old without any reporting. That's how gaps and hence primes get missed. People reserve stuff and get busy with other projects and sometimes just forget about them. I have to be careful not to let some of my other reservations go more than 1-2 months without activity. See the last post. It's been 9 months since Rob reported any activity on k=243 and then there's the whole 561k-562k gap on 10+ primes for k's<300 that are for one person with a reservation that I believe is at least that old. Once the 561k-562k gap is filled, many of the k's will be complete to well over 600k. And then there's the whole issue with k=289 that Bo supposedly had reserved. He started finding primes at n=500K+ but we have no idea where he started and little info. about how to contact him and there were no reservations on the Primesearch site past n=260K. All of these k's that I'm referring to are currently reserved and could go on with a gap and potential missing primes indefinitely if they aren't followed up on. And if we wait too long to follow up, the thread where they were originally reported may no longer be around or may be very difficult to find.

I can see how these 'temporary gaps' come about. Sure primes get found out of order when splitting work across multiple machines or processors. I was simply initially confused by the notation but understand it now. Karsten and Kosmaj set me straight there.


Gary

[Kosmaj]

You guys have mentioned the '4th drive', '5th drive', etc. many times. ... So can I assume by your statement here that the 5th drive is testing k=135 consecutively from n=300K up to the next prime at n=437544?

Yes, in the 2nd, 4th, and now in the 5th Drive we have tested a total of 55 different k<300 from respective n_min consecutively to n=600k (2nd and 4th) and to 1M (5th). For details please refer to top posts of each drive thread, as follows:

2nd Drive: 20 k's all from 210k to 600k, completed, 56 primes found, all LLR residues available on 15k.org.
4th Drive: 21 k's from respective n_min>=250k to 600k, completed, 35 primes found, residues 250k <= n <= 400k available on 15k.org
5th Drive: 14 k's, from respective n_min>=250k to 1M, in progress, 32 primes found so far.

You are welcome to join us in the 5th Drive