Ultimate gap-busting file

[gd_barnes]

Karsten and Kosmaj,

Attached is what I call my 'ultimate gap-busting' file. Karsten, I warned you that this will be big...so here it is...now introducing...drum roll...a list of all primes where 1000 < k < 10000 and where n <= 10000; every last one of them, 4500 k's in all! Your task, should you choose to accept it , is to list all of these on the summary page in some fashion.

I previously posted a list of ALL twin primes in the TPS forum where k < 100000 and n <= 10000 so this is a natural extension of the twin primes list.

Now you may ask...Does it really bust gaps? Yes it busts entire gaps in some cases, although more often then not, it just REDUCES gaps. We have many gaps of n < 200000 for k's in the 1000 to 10000 range so this is my start to eventually wipe them out.

I don't want to leave you out in the dark on this so here are some things that I should bring up:

1. This was the list that I used to error-check all low n's for this range of k. So obviously you don't need to recheck existing ones and you can just ignore them on my list. But most (> 90%) are not on the summary site and would need to be listed. I included all k's in the range because I wanted to check the existing ones at the same time.

2. The political stuff about reservations. This should not be an issue for anyone that I can tell. Everyone that I see that has k's reserved in this range are all searching for higher primes and I can't see that any of them would have a problem having primes listed from n=1 to 10K that were found by someone else. But just in case, the people searching for higher primes on their k's are: Benson, Amphoria, Flatlander, and Thomas. Other reservations are for Cruelty, SB2, and you (Karsten) but all of those reservations are for k's where all of their primes for n<10000 are already listed so those k's wouldn't be affected. If you think the first group of people should be contacted before adding the small primes for 'their' k's, I will be glad to assist in contacting them. Note that probably over 80% of the k's are either unreserved or have never been searched.

3. The file is one big "regular" LLR file starting with k=1001 and continuing all the way through k=9999. If I can format it in a better fashion or split it up so that it would make your task easier, I will be glad to. Just let me know what you need.

This is the first time I've zipped an attachment for this site. Let me know if you have any problem opening it.

So there you have it...My next task on this effort...extend the file to n=25K, although that will be quite a while yet. I don't plan to add any more k's to the effort in the future. 4500 of them should be sufficient!


Gary

[gd_barnes]

I just wanted anyone and everyone to know that I'm not somehow 'reserving' the k's in the gap-busting file in any way nor do I want to step on anyone's toes for already reserved k's. Anyone can still reserve any unreserved k in the range and search them however (s)he wants.

Even if I extend the file up to n=25K in the future, everyone should know that I'm only interested in listing the low primes for them. If I want to do a search on one or more of the k's for higher primes or for the entire ranges of particular k's, I'll reserve them like anyone else would.


Gary

[kar_bon]

oh, eeehmmm, not to do in 15 min!!
but i can do that. reading zip is ok: 86924 primes at all you listed.
i think first i delete the primes listed already at the summary-pages.
another point of interest: the resulting size of the pages!? if they are too big and the download is therefore too long i'll have to split it in perhaps more pages with 1001<k<2999, 3001<k<5999, 6001<k<9999 or something like that.
i'll see, post the progress and then we can decide!
in the meanwhile i'll make 'normal' updates every day and send the new pages to Kosmaj.
Karsten

[amphoria]

Gary, I have no problem with you posting the primes for the k's I have reserved.

[Kosmaj]

Well done Gary! I checked a number of primes on your list and it appears they are all correct and that for respective k's there are no other primes n<10000.

I can find the place for the file on the web but it will have to be in a publishable form, in the format we are using for k<300 or something similar. I suggest that we publish the file (or several of them if we divide it in smaller parts) separately of other files currently on our home page. (It will be nice to have a script in Perl or awk to convert the row input into a publishable form.) Karsten can, when he finds time, add primes not on our summary page for k<10000 (for a number of k's on the summary page all n<10k primes are already listed).

Finally, I'm not sure why you call it the "gap busting" file: we never intended to cover all those k's and until recently we didn't work on k's in the 1-10k range except for a few low-weight and heavy-weight ones. Also, our summary page is a new one, recently started by Karsten. I know that some people, for example Larry, computed all primes to n=50k for a number of k's but they are not on any web page. And as you found out by yourself, with latest software and hardware it's very easy to compute them.

[gd_barnes]

Kosmaj,

Thanks. I double-checked about 20 to 30 of them myself. What's great is that for this effort, it was the first time that I had used Srsieve instead of NewPGen for sieving. When I found out what it does with sieving multiple equations in one range, the choice was clear. And as you probably know, srsieve does not remove low values of n like NewPGen does. When I saw that I could get accurate candidates to test after sieving without having to add back erroneously removed candidates, that make the decision easy to do it.

And thanks for not just ignoring this. I think some sites would just say that they don't have the time nor is it worth the effort to do this.

On calling it a 'gap-busting' file, I agree that it depends on the definition of a gap. If someone starts at n=200K to search for primes, then by my 'broad' definition of a gap, that is a gap, even though others may not consider it as such. And that is a large part of what is happening in that range. So we can say that those gaps are now reduced from n=1 to 200K to n=10K to 200K.

I don't mean in any way to say that your summary page is somehow deficient in some manner. It is one of the must amazing and comprehensive list of primes anywhere on the web and I am happy to be involved with this effort. I am fully aware that you never intended to cover every k possible for any range of k's. I knew that you could only post what people had already posted somewhere somehow on the world wide web. But it had become increasingly clear to me, especially after Benson started searching that large range of k's between 1000 and 2500 starting at n=200K that eventually all k's would be searched in a much wider range than anyone had ever anticipated before. And as computers become faster and faster, perhaps all k's < 1M will eventually be searched! :surprised

I also knew that you would probably have to divide up the pages again in some fashion. Splitting them up in ranges of 2000 is an excellent idea. I won't inundate you with any additions until long after you're done with this effort. Probably what I'll do if I extend the effort to n=25K is search and then send them to you in multiple ranges of 2000 k's. However you divide the pages up is how I'll send them to you. That way, you could just work on them one page at a time.

Unfortunately I know little about web programming. I am a mainframe computer programmer. I would know little about Perl or awk. But if there is something, anything, that I can do to divide up or format the file that I sent, please let me know. I have taught myself a little about Visual Basic for Excel. By doing some cut-and-pastes and messing around with that, I may be able to format its current vertical format to the horizontal format with commas in between that you need it in within each k.

Next on gap-busting activies...REGULAR entire-range gap-busting, which is probably what you had expected anyway. That is, I'll take about 10-12 unreserved k's with some sort of gap < n=150K and search their entire gapped ranges. Examples include k=12045, 8311875, 19217385, and 334639305.


Gary

[kar_bon]

i know the original purpose of 15k.org is to search for 3 different kinds of k:
1. k with very high nash weight so many candidates to test and also many primes to expect (mostly 15k (the name!) or 2145k or 2805k)
2. the opposite of 1.: low weight k's with rare primes
3. k<300

when i compiled the summary pages i saw that there're many persons searching also k*2^n-1 but no overview of these k's are available nor their search limits or primes listed at once.

my suggestion: i update the summary with missing prime from your gap-busting file and create a new page (think of a new link in the 15k.org menu) with all k's and primes not falling under the conditions of 1. to 3.
i think i can write a little program to convert a (the) llr result file into something like the summary:
k with number of primes and the primes n listed with comma. perhaps the nash weight could be useful too.
takes some time but i'm willing to do so.
karsten

[kar_bon]

i wrote a little awk-script to convert the llr-output into a standalone naked html-page (see attachment).
as i mentioned there's a table with every k, number of primes and the n-primes itself and nothing else yet.
now i can include missing primes in the summary pages.
next step is trying to include the nash weight per awk.

[gd_barnes]

Originally Posted by kar_bon

i wrote a little awk-script to convert the llr-output into a standalone naked html-page (see attachment).
as i mentioned there's a table with every k, number of primes and the n-primes itself and nothing else yet.
now i can include missing primes in the summary pages.
next step is trying to include the nash weight per awk.

Karsten,
Looks great! You are FAST! Now I'm guessing that the hardest part for you is merging the primes already found on our summary page in with this list.

I don't know how you are ultimately going to split up the primes pages and I know the amount of space available makes a big difference, but I will make a suggestion that I think would make it easiest for people to view them in the future. I would suggest a slight modification to what you had suggested earlier. That is:
Page 1: < 300
Page 2: 301-999
Page 3: 1001-2999
Page 4: 3001-4999
Page 5: 5001-6999
Page 6: 7001-9999
Page 7: > 10000

About Nash weight. Can you forward me a link to a program that computes the Nash weight? I think it would be interesting to know for any new k that is worked on. But more importantly, if I can get a Nash weight calculator, I could perhaps help you do some of the Nash weights for the new k's on my list.


Thanks,
Gary

[amphoria]

Originally Posted by gd_barnes

About Nash weight. Can you forward me a link to a program that computes the Nash weight?

Google "psieve3" and you will get the link.

[kar_bon]

look in the forum here at this thread by Thomas: http://www.mersenneforum.org/showthread.php?t=7213
that's what i use.

gap file:
yeah, now i'm filling for every k in that list all primes you found (if the k is in the summary) per hand!
this takes some time and hope to bo ready for all k<3010 in a few days (now at k=1241).
so then for every k<3010 there will be an entry with primes, nash weight and search limits.
the nash weight i calculate 'on the fly' when i insert the k-value. nothing to do for you (could make a file with start- and end-k and their weights, see above link).
i'm thinking about your suggestion of splitting the ranges up to 10000. the other hand is, that if you plan to going higher with k, say 100000, it becomes slightly confusing.
perhaps i could fill in the summary>3010 the missing primes and create a new site with the rest of your k's.
so when someone reserve a k from this big site i could shifting it in the summary. the summary keeps clear.
perhaps anyone has another suggestion. hope i read some here!

Karsten