Prime Gap News

[robert44444uk]

I am a bit surprised that there is no thread in particular for prime gaps. The purpose of this thread is to discuss and post information on prime gaps. The main focus here is likely to be adding to the record gaps kept at Prof Nicely's site, but also perhaps for discussions on the relative merits of gap finding techniques.

This is a continuation of the general posts made in the programming thread recently.

[danaj]

Originally Posted by robert44444uk

I think it is better to find these oddballs naturally. Somebody has to be last.

I was thinking of something like this page. So we don't have to keep posting these big lists. If I was ambitious I could crawl gapcoin's results, and have some way to submit data.

Other things to display:

• Overall top-20 gaps
• Record holders, with numbers of gaps and percent of total
• Stats about my new un-submitted gaps
• Graphs
• Interesting stats about gaps in the last month?
• Something else?

I also threw together a simple dynamic top-20 page. I can fill the other columns in with some simple mods.


In other news, I just found a small gap of merit 33.575. Another entry for the overall top-20.

[robert44444uk]

Originally Posted by danaj

I was thinking of something like this page. So we don't have to keep posting these big lists. If I was ambitious I could crawl gapcoin's results, and have some way to submit data.

Other things to display:

• Overall top-20 gaps
• Record holders, with numbers of gaps and percent of total
• Stats about my new un-submitted gaps
• Graphs
• Interesting stats about gaps in the last month?
• Something else?

I also threw together a simple dynamic top-20 page. I can fill the other columns in with some simple mods.


In other news, I just found a small gap of merit 33.575. Another entry for the overall top-20.

Well done on your new result. One of these days I will find another 30, but I realise these are like gold dust.

It would be great to maintain your suggested web pages either dynamically or updated weekly. If you are doing that, it would be also good to provide the top 20 in columnar form so that the relative positions can be related easily to the champion in that category.

[danaj]

Originally Posted by robert44444uk

It would be great to maintain your suggested web pages either dynamically or updated weekly.

They are dynamic in that the page is a Perl script that processes the merits file and my new gaps file, then generates the HTML output. So this morning I scp'd the new merits file, and both pages immediately have the new data (your entry for 157194, a new #1, is there now). Any holes that were filled by your new entries should be gone.

If you are doing that, it would be also good to provide the top 20 in columnar form so that the relative positions can be related easily to the champion in that category.

I was thinking of listing the overall top 20 similar to the first table here: JKA's Top-20 list

Did you have something different in mind, or did you mean a change in my current top20 page?

I'm out for a week so probably won't be doing any major updates.

[danaj]

I see my stats page is updating while I'm out of town, but apparently I mis-typed something before I left as it isn't adding any of my new gaps. It's uploading the new file, but the file has the same gaps as when I left. :)

[danaj]

Construction while I was gone cut power to a machine I was using as a file repo (and gap searcher), and it not being available made my script stop. All fixed for now (though sadly construction over the next month will keep cutting power to random machines).

I updated the top20 page to bold the #1 entries and fill in the full names. I still haven't started using the allgaps file to get the other two columns.

The stats page also uses full names now. It has more info on it. All the tables take into account the unsubmitted gaps I have, but I haven't written the code to scrape the unsubmitted gapcoin results yet.

Rob, you will probably get position 5 in most gaps found next week, passing Spielauer. Looks like Antonio Key started submitting k*n#/(2*3*5*11*m) this month, with 160 found so far.

[danaj]

New stats page update.

I changed the old "holes and merits < 10" table to a different format. This gives some of the data you wrote (gaps with merit < 20, merit < 15, etc.). I could add more columns. Looks like my new gaps set has found a fair number of these (indicated with the strike-throughs).

High wind today, lost power for 8 hours. My machine had been running for over 400 days and the UPS was good for 3 hours. Sigh. Restarting everywhere. No restart mechanism means a day or so of lost progress and a PITA. My girls' Windows 8 machines have been driving me crazy with this lately, with a combination of no UPS (construction takes them down), Windows 8 updates with restarts, and occasionally "my game hung so I rebooted."

I will be submitting my set of 2931 gaps tomorrow, after ECPP check of endpoints goes a little farther.

[robert44444uk]

Originally Posted by danaj

I will be submitting my set of 2931 gaps tomorrow, after ECPP check of endpoints goes a little farther.

Its not a record unless you submit

That's why I do that weekly. Then at least some of them last as a record for a week or two.

[danaj]

I find it works better for me to do 3-4 weeks between submissions. I have enough searches going on in the same space that I get a lot of overlap of gaps just within that time period.

Things I should work on include:

- restart. Some of the tasks take > 4 days just to catch back up. I need a way to either skip forward in the first entry or better yet, give it the output file and let it figure it out.

- threaded verifier. 1 thread can keep up with weekly new gaps and make a little progress on the backlog, but not much progress. Running 8 threads at a time for a while would help.

- graph of gaps to 100k.

[robert44444uk]

Originally Posted by danaj

Things I should work on include:

- restart. Some of the tasks take > 4 days just to catch back up. I need a way to either skip forward in the first entry or better yet, give it the output file and let it figure it out.

I can't figure out what your problem might be. I have to restart a fair bit (especially on my work laptop) and I only have to go back to the start of the last factorial tackled. I run only 75 multipliers in any thread. (my end minus my beginning), whereas I think you run 300 multipliers, even for very high factorials. This way I rarely have to duplicate more than 1 hour of work.

[danaj]

Originally Posted by robert44444uk

I can't figure out what your problem might be. I have to restart a fair bit (especially on my work laptop) and I only have to go back to the start of the last factorial tackled. I run only 75 multipliers in any thread. (my end minus my beginning), whereas I think you run 300 multipliers, even for very high factorials. This way I rarely have to duplicate more than 1 hour of work.

Yes, some of those are easy, and the tests with k=1..1 starts pretty quickly, although they have grown to where the time per test is not insignificant.

k*n#/30 where k = 100M to 200M can take a while even with very small n... The computer I have doing that range is too flakey to handle it so I dropped it down to 10M at a time.

Even just 1..25 when n is almost 40000 can take a long time -- it takes hours just to test one number.

You are also not running the k*n#/(235*m) version, which adds an inner loop. As n grows, so does the number of divisors. So 75 multipliers becomes tens of thousands.

Doing runs like k*n#/30 where n is fixed and k continues to grow indefinitely, which is what most of Rosenthal's patterns are, is super easy to restart. Just start with k being one higher than the last record found, and very little time is lost.


I have stuff running all over the place, not just a single fixed pattern. I believe with k*n#/30 I've run or have running:

1-25
26-50
50-100
100-300
300-10k
10k-20k
20k-30k
30k-40k
40k-50k
50k-100k
100k-1M
1M-10M
10M-100M
100M-200M

For the 23, 235, 2357, and 235711 patterns I don't have as many levels, but there are a few. Some of them are still catching up after being started 3+ days ago (again, because of the extra inner loop, a range of 1000 can become 1M tests).

Different computers run different sets, and some have been put on hold. The 1-25 range has gone very far, and the others move at slower rates. I guess it depends on where you want to concentrate. Records under gap=10k are harder to find since so much more searching has taken place, but the programs will still regularly produce results (which Spielauer and Gapcoin may take away). Up in the 200k range the tests are slow but almost anything you find is a record since it's very sparse. Looking higher has more possibility of a "ooo aaa a top-20 result" at the expense of slow tests. The sweet spot for production seems to be in the 60k-100k range where the testing-effort vs. ease-of-getting-a-record curve is most favorable.

I've been not worrying so much about where they fall, but just test lots of levels so I get broad coverage. It also gives me more to work with in looking at the performance of my code, which was really the point of all of this for me, rather than the gaps themselves.