Low weight stats page.
 

Since <300k is almost completed, I would like to set up a page on low weight candidates of the form [URL=http://www.15k.org/lowweight.htm]k*2^n-1[/URL] . If you could just tell me what work you have done on these. It would be nice not to duplicate work.

Joss

I haven't done any work on low-weight k's but I was thinknig to propose that we process one real but small 15k to 1M like k=15, 45, 75 or 105. After sieving such k's produce too many candidates for a single cruncher to process, but potentially they hide a good deal of primes so if we do it together there are good chances that many of us will find a large prime. With the latest LLR-P4 I think it can be done in a reasonable amount of time. What do you say?

I guess Mark could set up a team for some low 15k like he has done with 210885 and 2995125705. With the new LLRP-4, k=15 seems a good choice. Robert has been working on it for some times. We should ask him for team work first.

Joss

This is our first top5000 prime on Low Weight Candidate
3817*2^218917-1
It's a start!

Joss

I'm just announcing the find of two (big) primes of low weight k:

209826493*2^1140855-1 (ranking at position 50 of the Top-5000!)
209826493*2^1071303-1 (found a few months earlier)

-- Thomas L10

Wow thomas!!

Congratulations on your 2 big primes!!!! Good work!!!!

:bow: :bow: :bow: :banana:

These should had some weight to our project!
Great work :flex: Thomas :flex: !

Joss

How about another big one?

80857169*2^1251076-1 is prime! :w00t:

-- Thomas L10

Wow!

rank 37, whooo now we're talking.

congratulation

Joss

[B]Thomas[/B], congrats any many huge primes!

BTW, can I reserve one k, just to try? I'm not sure how to read the table at the [URL=http://www.15k.org/lowweight.htm]status page[/URL] but if available I'd like to take [b]k=32537227[/b]. It has no available data so I assume it's available(?) Can one reserve k's with some associated date in the table and/or provided sieve file?

Thanks and good luck!

Hi Kosmaj,

k=32537227 is all yours
I don't have any sieve file for it
It's not a very low weight at 2100 n's left at 20M but still a good choice.

Joss

k=32537227
 

No primes for n<=848k.

Some stats:
range 1-1M: 2226 candidates remain after sieving to 10 M.
range 1M-2M: 1280 candidates remain after sieving to 1.037E12 (1037G in your notation).

Since n=837k the FFT length has been 98304.

Joss, the status page now appears truncated at k=14321533 :surprised

I'd like to reserve k=131707 from the low weight page on 15k.org. I'm at roughly n=170,000 on my previous number, with the largest prime around n=120,000. I'll post the primes discovered on the small-primes thread once I compile the list from the machines that ran trials on it.
-VBCurtis

reserving k=167021 from the low weight page also. n=1M is a good target for low-weight numbers, right?
-Curtis

I tried only one low-wight k and I sieved to 2M, but checked only to about 1.25M. You can reach 1M quickly with a mid-range P-4 (2.4-2.6GHz) so I'd suggest at least 1.5M as the target.

Reserving k=171089 and k=175211 from low-weight page. I picked up a few machines from friends/students who think the project is interesting.
-Curtis

Reservations and updates: (all from low-weight page)
reserving 245561 (currently at n=580000)
reserving 13900807 (currently at n=320000)
131707 finished to n=1 million, sieving n=1m...3m currently (p=2.3T)
167021 at n=630000

No primes yet from this search.
-Curtis

Reserving k=9770317 from low weight page. I started work on this a couple weeks ago, but forgot to post the reservation.

-Curtis

Updates on low weight numbers:
131707 tested to n=1.15M, sieved to 6.5T up to n=3M. (working here now)
167021 tested to n=800k, sieved to 2.5T up to n=2M.
171089 tested to n=570k, sieved to 770B up to n=1M.
175211 tested to n=855k, sieved to 1.1T up to n=1M. (working here now)
167021 tested to n=800k, sieved to 2.5T up to n=2M.
245561 tested to n=1M, sieved to 1.5T up to n=2M.
9770317 tested to n=1.1M, sieved to 1.7T up to n=2M.
13900807 tested to n=600k, sieved to 1.2T up to n=4M.
-Curtis

Here is my low-weight number:
177941 tested to n=518k, sieved to 315B up to 1M. (feel should sieve it further)

Gribozavr-- how many candidates are left? I can give you a decent estimate of ideal sieving, if you can provide me the weight of the k-value (number of candidates left from n=518k to n=1M is sufficient).

If you have recent data on time per LLR or time per exponent sieved, that will help corroborate my estimation (I want to see if my estimations are accurate, so I'd use this data to double-check).

Also, do you have a P3 or Athlon to do the sieving? Ideal sieving depth if you only possess a P4 is nowhere near as deep as if you can sieve an athlon and LLR with a P4, since the P4 is relatively so much better at LLR than sieving. If you have only P4, I don't mind running a sieve for a week or so on an Athlon to give you a boost (you wouldn't have to credit me for any primes found).
-Curtis

Low weight update:
175211 complete to N=1M. No Primes.
Exponent returned-- I plan no further work on this number.
-Curtis

I just discovered k-value 245561 is being tested by Rieselsieve, so I wasted a few CPU-months testing this value to N=1 million. :squash:

Obviously, no further work is planned on this one!
-Curtis

[QUOTE]I wasted a few CPU-months testing this value [/QUOTE]

I feel your pain. I've done it, but at least you can now say it has been double checked! :smile: With no bugs found.

I would like to help with this portion of 15k, please help me get started. getting sieved files etc.

Citrix

PS: i know about all software's etc, so basically need help with the k's

I would like to reserve the following 4 k.

209102797
20168077
307715767
264039239

Sieved files, if any exist, are all with Joss. I have none. I'll try to update the status page but it's going to take a while. BTW, when you reserve new k's have a look at [URL=http://www.mersenneforum.org/showthread.php?p=60615#post60615]this thread[/URL] because some people report there low weight k's, not here. Also check that some of the k's are not already tested by RieselSieve. Many are marked but some are not, there was one such case recently. Check also already reported primes at Top-5000.

Unrelated to this I wrote to Joss yesterday to see whether he wants to continue moderating the forum. His last post was in April. If not we'll have to find a new moderator because I cannot handle everything.

[QUOTE=VBCurtis]I just discovered k-value 245561 is being tested by Rieselsieve, so I wasted a few CPU-months testing this value to N=1 million. :squash:

Obviously, no further work is planned on this one!
-Curtis[/QUOTE]


YOu can send your residues to rieselsieve for double check.

On the low-weight stats page, there are instructions for getting sieved files off the server.
Go to www.15k.org/Riesel/{your exponent here}_ktest.txt
to get the file.
Some are worthlessly sieved-- I found it faster to create a new file and sieve to 10 million than to download the file. However, the info on the server is still useful, since it shows how dense the candidates will be (sieving only to 10 million is sufficient to show weight).

Kosmaj-- I might be willing to moderate a small forum, if Joss no longer has time. Can you PM or email me with a short description of what it entails? email is vbcurtis at gmail. I'd also like to do a ton of presieving/updating on the low weight stats page, but I didn't want to trouble someone else with handling all the files. If moderating includes being able to upload sieve files to the server, I'd like to do so.
-Curtis

:)

Since LLR works best on K<2^20, I would like to work on a reduced problem.
k<2^20 and weight less than 100, and not being worked on by reisel sieve.

Could the moderators prepare such a page?

Citrix

17077 93
25229 98
48973 81
53741 51
70079 90
74201 92
77711 99
116531 99
124679 80
130139 81
131069 92
131707 99
138847 29
167021 95
171607 61
192509 88
216367 92
256453 86
275591 65
278077 95
278713 81
284579 83
313979 99
327163 73
332159 95
334331 81
342337 50
370421 99
403993 44
473279 91
487811 86
491891 66
516569 54
612509 74
643843 91
648433 95
671413 92
685183 99
700057 92
700477 84
780427 71
783073 75
784109 54
850931 62
893887 57
953429 95
961573 75
963643 48
967597 65
981493 49
1006469 79
1034503 66
1049917 37

53 numbers
Could a webpage be organized for these 53 with ranges already searched.
If no one else is intrested I would like to take them higher.

Citrix

The [URL=http://www.15k.org/lowweight.htm]low weight stats page[/URL] is now updated with reservations and results reported since May (mostly by VBCurtis). Please have a look and tell me if there is anything to change.

I also moved all posts related to "low weight" from "I'd like to help out" thread to this one. Plese post further reports related to "low weight" in this thread.

[B]Citrix[/B]
All k's you listed above are already on the [URL=http://www.15k.org/lowweight.htm]low weight stats page[/URL]. Creating another page will require updating two pages instead of one. But if you want to create such a page you are welcome, I can put it up on the server.

About reserving 53 values, I think it's not realistic. How many machines do you have? Some of these k's are already checked to 1M or more. So please have a look at the stats page and tell me what k's do you want to reserve so that you can have some results within a month or so.

If you read my post it says if no one else is interested. I can always reserve work as needed from main thread as available if other people are also interested. But if no one else is interested, you reserve them for me.

Kosmaj, do you have a script to generate such a page. If you could generate such a page for me, I can update it myself.

Ill take 48973 to start with and when I am done, take more.

Thanks,
Citrix

Instead of working on all of them, I would like to search all of them for primes under n=100K. then take the best 2-3 candidates higher. Since I don't have enough power to work on all of them myself.

Citrix

Please help test these to 100K

48973 81 --4 primes // checked by citrix
74201 92
124679 80
131069 92
192509 88
216367 92
256453 86
278077 95
284579 83
313979 99
327163 73
332159 95
334331 81
370421 99
473279 91
487811 86
612509 74
643843 91
648433 95
671413 92
685183 99
700057 92
700477 84
780427 71
783073 75
953429 95
961573 75
967597 65
981493 49
1006469 79
1034503 66

[B]Citrix[/B]
Please stop this nonsense!

[QUOTE]48973 81 --4 primes // checked by citrix[/QUOTE] The above 4 primes have been already found by Joss, go and read the [URL=D:\minovic\proth\k15\webSite\lowweight.htm]Low weight stats page[/URL].

[QUOTE]74201 92[/QUOTE] k=74201 is already checked by Marcin to n=335k, 3 primes found.
And so on and so on. Your call is meaningless.

Now, with respect to the following:
[QUOTE]If you read my post it says if no one else is interested. I can always reserve work as needed from main thread as available if other people are also interested. But if no one else is interested, you reserve them for me.[/QUOTE] I'd like to inform you that this is not the way we discuss matters here! [I]Please[/I], calm down. Thank you.

[QUOTE=Kosmaj][B]Citrix[/B]
Please stop this nonsense!

The above 4 primes have been already found by Joss, go and read the [URL=D:\minovic\proth\k15\webSite\lowweight.htm]Low weight stats page[/URL].

k=74201 is already checked by Marcin to n=335k, 3 primes found.
And so on and so on. Your call is meaningless.

Now, with respect to the following:
I'd like to inform you that this is not the way we discuss matters here! [I]Please[/I], calm down. Thank you.[/QUOTE]

Sorry for the inconvinience. :no: :redface:

I have checked the k to 100K and there are no new primes to report.


Citrix

[QUOTE=VBCurtis]Gribozavr-- how many candidates are left? I can give you a decent estimate of ideal sieving, if you can provide me the weight of the k-value (number of candidates left from n=518k to n=1M is sufficient).[/QUOTE]

I have sieved to 1,5T and from n=518482 to n=1M there are 1610 candidates left.

[QUOTE=VBCurtis]If you have recent data on time per LLR or time per exponent sieved, that will help corroborate my estimation (I want to see if my estimations are accurate, so I'd use this data to double-check).[/QUOTE]

For n=518k LLR time is about 3500 sec.

[QUOTE=VBCurtis]Also, do you have a P3 or Athlon to do the sieving? Ideal sieving depth if you only possess a P4 is nowhere near as deep as if you can sieve an athlon and LLR with a P4, since the P4 is relatively so much better at LLR than sieving. If you have only P4, I don't mind running a sieve for a week or so on an Athlon to give you a boost (you wouldn't have to credit me for any primes found).[/QUOTE]

I'm doing sieving and LLR'ing on Celeron 1.2 GHz. But I also have an Athlon 64 3000+ 1.8Ghz here.

Sieving on a celeron is a waste of resources, if you have an Athlon.. The athlon is over 50% more efficient at the same speed (and yours is even faster than your celeron, so even faster, relatively!)
edit: you said celeron 1.2-- that's P3 based, I think, making it better even than an Athlon for sieving. Never mind!

1.5T should be plenty for sieving to n=1M, for any low-weight number. I'll find my formula notes at home tonight and see if I can find the p-value estimation.

The most basic equialence says to sieve until time per factor found is equal to LLR time on an exponent 70% of the way from min-n to max-n. For you, that's around n=850k. LLR time increases roughly with the square of n, so LLRing an 850k power should take you about 9000 seconds per power. If 10 or more factors are found in a day, you should continue sieving. If 8 or fewer, stop for sure. If 9 factors in a day, it's right at the "sieved enough" point, and you should do whichever you prefer, as the choice is not relevant from an efficiency standpoint.

-Curtis

Citrix:
[QUOTE=Citrix]Instead of working on all of them, I would like to search all of them for primes under n=100K. then take the best 2-3 candidates higher. Since I don't have enough power to work on all of them myself.

Citrix[/QUOTE]
Getting all the powers up to some level isn't a bad idea, but why 100k? These candidates have such low weight that finding 3 small primes instead of 1 doesn't really indicate "best"ness for n-values above 50k or so. For proof, look at the number of bases that have no prime to even 500k, so running to 100k will not help in picking a "good" candidate.
If you want to LLR just small numbers, then sieve each candidate to 100G or so (for N-values up to 1M, since that is the standard on the stats page and server), LLR to your preferred cutoff, and post results. Doing this to 100k takes more time to post and admin than to actually run, so isn't very helpful. Choose a cutoff point that has you processing no less than 2 weeks on each number, and I'm happy to help admin/update the page/etc for your work. You can even email me the sieved-but-not-LLRed files, which I'll eventually post on the server.

I suggest n=500k as a nice balance between variety and depth, to keep you interested and the administration manageable. 400k is tolerable, but 300k will happen REALLY fast on each number--I think I used to get to 250k in a weekend on a P3-500, so a modern machine could sieve to 100G and LLR to 300k in something like 2 days. I imagine even 400k would happen in less than a week, thus my suggestion of 500k as your target. This would still get you through all 53 numbers by yourself in something less than 6 months, less if someone decides to join your method of progress.

Note that even 1M takes around a month on a mid-level (2.4Ghz) P4-- hardly a huge commitment. I have a bunch of public-school P3-class machines running, which is why my updates seem so much slower than these estimates indicate.

-Curtis

reserving k=403993, to help Citrix with his search. I'll put a P3 from school on it, and report times to sieve to 100G and LLR to 500k.
-Curtis

[B]Citrix[/B], no problems, please take a few at the time and keep on going.

But I agree that checking one k to n=100k will not be very helpful in deciding is it a prolific one. For example for k=80857169 for n up to about 1.3M (?) Thomas found only two primes, for n=4 and n=1251076.

Finally, I don't want to sound like a parrot :smile: :rolleyes: but k=403993 mentioned by Curtis has been already checked by Joss to 405k. Do you intend to double check? :cool:

This is just a status update.
The following 23 k have been testet to n=2M now. No new primes found so far...

19370947
59910449
80857169
143316643
162405629
175437131
189030223
203012861
209826493
224371169
243163663
245265883
248690527
260213857
265831619
276278983
290851087
298095191
300871183
308120317
308141737
315940139
326840893

-- Thomas :sleep:

Thanks, Thomas-- I was really hoping you'd weigh in with your research soon. I'll try to get those updates on the stats page soon. How far did you sieve these very low-weight candidates? I have two numbers similar in weight to the candidates you chose; it seems 4T is sufficient (plenty, even) for running to 2 million. Did you sieve deeper, and why?

Kosmaj:
I noticed Joss' work on 403993 after posting that reservation, so I grabbed the sieve file and plan to finish to 500k,which I admit isn't the best time trial for my suggestion. That said, my P3-550 has sieved from 35G to 110G in 20 hrs, so sieving for 1 day on a normal machine is sufficient to prepare LLRing to 500k; I'm still removing candidates at nearly one per hour, so I'll sieve to 150 or 200G before LLRing the 403-500k range.

I guess you guys are right, Why 100k? I just thought a low n peak estimate would be good, like you use n=5000 for 15k.

Anyway, I will not be working on these low k's because I tested LLR 3.62 and k<70 is twice as fast as compared to k>2000. Hence I see no point in working on k's greater than 70.

Thanks,
Citrix

Gribozavr:
My sieving-depth notes don't make as much sense now as they did in July, but my estimate is at p=1.5T, you're finding a factor about once every 2 hrs 10 min, with the efficiency cutoff at about 2 hrs 20 min. Thus, you've stopped sieving at almost exactly the right point for your chosen k-value.

If you have recent data about how often factors are found, I'd like to hear how good my estimate is. factors are not smoothly distributed, so anything from 2 hrs up to 2 1/2 hrs per factor in NewPGen will make me think my guesswork is accurate.
-Curtis

[QUOTE=Citrix]I guess you guys are right, Why 100k? I just thought a low n peak estimate would be good, like you use n=5000 for 15k.

Anyway, I will not be working on these low k's because I tested LLR 3.62 and k<70 is twice as fast as compared to k>2000. Hence I see no point in working on k's greater than 70.

Thanks,
Citrix[/QUOTE]

I am instead working on 47*2^n+1, though not part of this project, it has really low weight and each test is as fast as it gets. If anyone is intrested in helping, just PM me.

Citrix

VBCurtis:
The values of k I'm working on are all sieved to pmax=12T yet, with nmax=10M.
If you want to do n=0...2M, then pmax=4T should be quite sufficient.
One could also think of using SBFactor to do some P-1 factoring on candidates with n>1M.
I did some trials but found the sieving still more efficient. Maybe SBFactor will get another chance at even larger values of n.

-- Thomas

[B]Citrix[/B]
47*2^n+1 is extensively checked. Have a look [URL=http://www.geocities.jp/turbo_us_p/prime/47/status.html]here[/URL] for details.

[QUOTE=Kosmaj][B]Citrix[/B]
47*2^n+1 is extensively checked. Have a look [URL=http://www.geocities.jp/turbo_us_p/prime/47/status.html]here[/URL] for details.[/QUOTE]


Thanks for pointing it out to me. I have reserved the k from 1.8M onwards at prothsearch.net and plan to take it to 5M. Since this is the only k I am woking on, I think I can do that alone. Other than that the k is low wt and I really don't care any more about finding small primes. I want to find a prime that makes it to the top 10 list. Since with the few resources I have, the only way to do so is to gamble with a low wt k. Just hoping there is a prime for the k=47. I hope I am lucky.


edit: - I also checked on prothsearch.net, 'Nohara' has not reserved anything on prothsearch.net with n>1.8M , so I guess I am free to work on this k.

Thanks,
Citrix

[QUOTE=VBCurtis]If you have recent data about how often factors are found, I'd like to hear how good my estimate is. factors are not smoothly distributed, so anything from 2 hrs up to 2 1/2 hrs per factor in NewPGen will make me think my guesswork is accurate.[/QUOTE]

As far I remember, about 10 factors were found a day. 24 hours / 10 = 2 hours 24 minutes, so you were quite accurate!

Just an update: now I'm LLR'ing n=537154, time per iteration = 7.108 ms.

I'm currently working a bit on k=27791 and k=10813783. I will bring the k=10813783 to 1M, since it has only 550 n's left to test.
k=27791 has been tested until n=214k
k=10813783 has been tested until 315k
Both without new primes.

Working on 23437 and 11955659 ;)

[QUOTE=Citrix]
edit: - I also checked on prothsearch.net, 'Nohara' has not reserved anything on prothsearch.net with n>1.8M , so I guess I am free to work on this k.

Thanks,
Citrix[/QUOTE]

It's just my opinion, but I think you should contact Nohara as he's reserved a 0.02M range already. Seems like he hasn't seen your previous reservation...

Thanks for letting me know, I will write to him.

update on k=10813783 & k=27791
 

I'm still working on both of them.
k=10813783 has been tested until n=690k, 255 tests until 1M left
k=27791 has been tested until n=300k, 2264 tests until 1M left
Both without new primes. :sad:

k=380630849, 59493015971
 

k=380630849 and k=59493015971 have both been tested for n=0-2,000,000. No primes found. The later k is of extraordinarily low weight (Nash weight is 5), so I'll continue it a little bit further.

Update on reserved numbers
 

Here are the numbers I have reserved and/or done work on:
131707 done to 1.6M, sieved to 3M. in progress
167021 done to 1M, sieved to 2M, in progress
171089 done to 1M, no further work planned (unreserved)
403993 done to 900k, sieved to 1M, in progress
9770317 done to 1.5M, sieved to 2M, in progress
13900807 done to 1.5M, sieved to 4M. Not active, but still reserved.

New reservation: 24384313. Sieving to 2M, LLR currently at 100k. I have new access to a small army of P2-class machines at work, which just screams out for sieving duty. Sieving a new k does the trick.
-Curtis

I am currently working on k=11639819, tested until n=400000, 660 tests until n=1M left

k=59493015971
 

k=59493015971 is done to n=3M. I'll try to take it a little bit further...

403993 finished to 1 million, unreserved.
-Curtis

I have a question about one k I'm playing with.

For some time I work on k=2147483647 on my own (it's not on the RPS list of low weight k's). It is Mersenne prime (2^31-1). After I sieve range 350k-500k to 18G with NewPGen it remains 423 n values to test with LLR. It seems it is low weight candidate. I find two primes for this k, for n=97 and n=96001 (although I didn't test range 150k-220k, so it might be more primes in that region). I was thinking in testing this k to maybe n=2M, as after sieving I have relatively small number of n's to test.

But what bothers me is if somebody else was already done that. So, my question is does somebody maybe know where could I check if somebody test this k already? Or maybe if somebody is aware that someone else is working on the same k?

Kosmaj, already point me to the Top-5000 and where can be seen that Broadhurst discovered 2147483647*2^96001-1 on May 2000. So, it's possible he serached further. Any info on that is very valuable to me, as it will help me to decide will I continue to test this k or not.

Thanks for any input.
Edo

If a k is not part of any organized search, checking the top-5000
is about all you can do. Have you tried contacting the people who reported
primes for that k?

Yes, I send an email to dr. Broadhurst asking him how far did he test this k. Hope he will answer.

Edo

If you decide to keep working on this k-value, we can add it to the low-weight stats page on 15k.org. At least that way there will be public record that you're working on it!
-curtis

Curtis, that will be great. If it is possible to add it there please do so. I would like to credit RPS for any potential finding, anyway.

Dr. Broadhurst wasn't sure how far he test this k. He said that it would be best to assume that he stopped work on that k as soon as he found this...
[URL="http://primes.utm.edu/curios/page.php?number_id=526"][COLOR=#800080]http://primes.utm.edu/curios/page.php?number_id=526[/COLOR][/URL]
(not sure what that mean, if anyone know please explain).

I will continue working this k up to 2M.

So, please include it in low-weight stats page.

Thanks.

I sent a low-weight update to Kosmaj just before checking the forum-- he'll get it on the server in a couple days. I hope/plan to update the page once a month, now that I understand how to edit the page without making a mess. Expect a mid-april update with your k-value as the bottom (largest) value on the low-weight page. I'll also add the k-values Thomas has referenced in his recent posts.

Post a reply when you've cleared the 150-220k range, so I can note that also.
-Curtis

Your [URL="http://www.15k.org/lowweight.htm"]page[/URL] is up!

One more reservation: 399239.
It produced a small prime at 253688 already. I'm running it to 1 million only on some slow machines.
-curtis

I have checked k=177941, n from 1to 1M. Found only two primes:
177941*2^34-1
177941*2^154-1

I'm unreserving this k.

I already test K=2147483647 from n=2 to 150k and from 220k to 350k, currently work 350k to 500k range. Plan to do it up to 2M. I find only two primes, for n=97 and n=96001.

Range n=150k to 220k for K=2147483647 is completed. Range n=350k to 500k will be completed in a few days.

No new primes.

Range n=350k to 500k for K=2147483647 is completed. No new primes.

New target... n=1M.

Monthly update:
131707 done to 1.75M, sieved to 3M
167021 done to 1.05M, sieved to 2M
399239 done to 400k, sieved to 1M
9770317 done to 1.7M, sieved to 2M
13900807 done to 1.7M, sieved to 4M.
24384313 done to 1.075M, sieved to 2M.
I'll update the webpage this week.
-Curtis

Here is a list of 31 k I'm currently looking at, and the primes I've found so far.
All have been tested up to n=475k, trying to reach n=1M sometime...

[CODE]
k primes
------------------------------------------------
20168077 --
24560197 1641, 145641
32859551 --
65581091 --
68816591 38, 4358
73595677 166825
73710809 --
80625343 1319
80889761 242, 4994, 10034
82742263 1311
95551177 329
100596217 --
106074103 475699
111081793 --
118130917 --
119543999 --
121273931 --
129833999 --
130562741 --
137609411 --
145097801 --
147453749 --
151791539 60
154074187 --
178293187 --
178348783 --
179337419 --
209102797 --
210037627 --
210215609 828
214943261 --
------------------------------------------------[/CODE]

I also like to reserve the following 5 k, formerly tested by Joss:
2308121, 4278899, 14961487, 26161207, 40293059

Due to the increasing interest on low-weight k, I'm releasing here some of the results I've got during the last 2-3 years. I've concentrated myself on the very-low weighted k.
The attached zip-file contains a list of more than 4500 k-values (up to k=238,000,000,000) with Nash weights equal to or below 15 -- all been tested for n=2-250,000 -- together with the primes I've found. The different weights are explained at the bottom of the list.

I hope that you will find the data somewhat useful for your own studies...

-- Thomas

P.S.: And just feel free to pick some of these k to test them beyond n=250,000...

Wow! This is real treasure! Thanks a lot for sharing this with us.

I'll pick following k...

59910449
380630849
442513453
535224337
536864983
811064503
953992993
1529129471
1545102311
1918825267

Initially, I'll test them from n=250k to n=1M, and after that will continue up to n=2M, and possibly even further, at least some of them.

[QUOTE=edorajh]
I'll pick following k...

59910449
380630849
442513453
...
[/QUOTE]

I should have added the note that some of the k of my list have already been tested much further, e.g. I have tested k=59910449 and 380630849 up to n=2M. And k=442513453 has been tested by myself to somewhere around n=2M and was later continued by Jean Penne.
k=535224337, 536864983, 811064503 have also been tested somewhat further. I'll need to look into my records.
Nevertheless, everything above k=1,000,000,000 should be available (e.g. at least those k haven't been tested by me any further -- this means all but k=59493015971).

You should also check [URL="http://www.15k.org"]www.15k.org[/URL] before wasting your cpu(s)...

-- Thomas

Ah, I see. In that case I would like to cancel my reservations.

Thanks for the great source, Thomas. Since people (myself included) seem to like to search really low-weight k-values, I'll add some of the lowest-weight work to 15k webpage.

If you have time/energy, send or post another zip of work completed above n=250,000, so we avoid duplication.

-curtis

I had been indeed two other "big" low-weight runs about 1-2 years ago.

The first one, which I call "LowNash2", has reached n=1.1M and contains the following 36 k (together with the primes I found):
[CODE]overall nmax tested: 1100000

k primes
------------------------------------------------
389152177 --
410314627 --
414322661 2114
432043439 --
443200949 --
463395913 --
482987411 --
491362811 --
493412999 --
494660219 --
531115657 --
535224337 --
536864983 --
540196717 --
552455201 25862
564510097 11345
567143683 4027
578625847 --
589877983 --
609937687 1561
651488009 156, 10956
660879671 702
667868189 --
673503191 --
691459721 --
713633533 --
725433403 --
738297163 --
759833699 --
801584081 182
811064503 --
814419757 --
835596479 --
851324377 --
855686399 162836
857656417 4953
------------------------------------------------[/CODE]

The second one, called "LowNash3", has reached n=500k and contains the following 32 k:
[CODE]overall nmax tested: 500000

k primes
------------------------------------------------
253104569 348
255333787 21
257250883 326, 9359, 74879, 109919
257878177 --
260334281 --
264039239 --
268346437 156061
270274153 --
272294801 --
273507613 --
279599587 --
280970467 --
287742253 --
289797523 115, 45619, 256435
291996611 350058
294660907 37, 901, 35653, 52741, 362773
307715767 --
307876003 --
315419827 --
316203817 --
316371073 --
323063771 205578, 219114
324539233 35, 155, 90035, 136475
325434251 2050
332827783 103, 125383
332847659 89828
334490381 7382, 36902, 127478
338381947 --
340130729 --
343172617 --
346694111 --
348970301 --
------------------------------------------------[/CODE]

Both blocks have been sieved much higher, e.g. "LowNash2" has originally been prepared for nmax=2M, and "LowNash3" up to nmax=1M.
I'm currently digging out those old sieve files and want to take them further. In principle "LowNash3" has already reached the optimal sieve depth to be LLR tested up to n=1M, and I'm planning to combine it with the 31 k values I reported on earlier this week.

"LowNash2" still needs about one or two weeks to reach it's optimal sieve depth for testing up to n=2M. But testing all the 36 k by myself would be very demanding. So, one could think of a distributed attack, e.g. the "3rd RPS drive".

And then, there are the 23 k values (I call them the "original LowNash" or "LowNash1") which already have reached n=2.27M (<-- note this as a status report). I spent thousands of hours for sieving them, e.g. they are preparated for n up to 10M, and the sieve is around n=14T.
These k are already well prepared for LLR testing them into the million digit region (which start around n=3.3M). This could also be taken as the "3rd drive".

So, just let me know, if there is some interest in a distributed low-weight search. I already suggest such project about two years ago, but there wasn't any reply. Nevertheless, I'm still willing to prepare the necessary input data for either case. In principle, this could be an easy way for finding a megabit prime. But, of course, there is no guarantee that the ranges contain any prime at all. Nevertheless, I'm still quite confident that there is at least one prime for "LowNash2" in the n=1.1-2M range. And after that large gap for the "LowNash1" (e.g. no prime between n=1.25-2.27M), there should be one really soon...

I can provide you quite a few lists of low-weight k. The problem is that during my search for even lower weights I generated a few giga-bytes of raw data, which obviously cannot be distributed through the internet. And the raw data wouldn't be very useful to someone else.

So I generated a few files, which are hopefully of some interest for you:

First of all, there a file of 32314 k (up to 400,000,000,000) which have Nash weights up to 20.
Note again, that some of the lower k have already been investigated by myself or others. So check [URL="http://www.15k.org"]www.15k.org[/URL] before duplicating work.

I'm game! Sounds like the best way to get some mega-bit primes.

The second file is for Nash weights up to 30. Due to the filesize limitations this is only up to k=50,000,000,000.

[QUOTE=lsoule]I'm game! Sounds like the best way to get some mega-bit primes.[/QUOTE]

Indeed! I've got 3 in 2004 between September and December...

The following file is for "real" experts only!

It contains k of Nash weights up to 5. These are very big k (up to 17 digits). This means that you'll need to use ksieve. The chances are very, very low to find any prime at all.
Probably quite a few of them are Riesel numbers, e.g. they will never produce a prime.
But, nevertheless, these kind of numbers can be tested beyond n=1M quite easily, since typically only about 100 candidates per million (or even less) survive the sieve...

I am also interested in a distributed low-weight search (something like "3rd drive"). I think it's a great idea.

[QUOTE=edorajh]I am also interested in a distributed low-weight search (something like "3rd drive"). I think it's a great idea.[/QUOTE]

Okay, then let me know your opinion on the following choices:

(1) taking the 23 k ("LowNash1") already tested to n=2.27M and drive them to n<=10M
(2) taking the 36 k ("LowNash2") already tested to n=1.1M and drive them to n=2M
(3) preparation of a complete new selection of k

Personally I would vote for either (1) or (2), since these are just ready to start with.

If we intend to start such an effort in earnest, then one of the moderators should start a separate thread for this sub-project. And I would need an opportunity to upload the presieved files to the 15k.org server.

For start, it seems to me that option 2 might be better. Latter on we might start another drive with option 1. Just a thought... why not take k's from 2nd option up to n=2.27M... then next drive could combine k's from option 1 and option 2, and take them to n=10M.

Re option 3... maybe latter on when we reach 10M for options 1 and 2.

[QUOTE=edorajh]Just a thought... why not take k's from 2nd option up to n=2.27M... then next drive could combine k's from option 1 and option 2, and take them to n=10M.
[/QUOTE]

k's from the 2nd option ("LowNash2") have only been sieve for nmax=2M. Combining them with "LowNash1" would mean that these k need to be completely resieved for n=2-8M up to around p=14T. This would require again [B]thousands[/B] of cpu hours...

Nevertheless, I would agree with you, to start with the smaller candidates (2nd option) and drive them to n=2M. Later on we might switch to "LowNash1" beyond n=2.27M.

P.S.: Just to give you a measure on how long a single test lasts in that region: on a 2.4GHz P4 it will take about 1.5 hours around n=1.1M and more than 6 hours around n=2.27M...

You are right Thomas. I didn't take into account sieving time. In that case I think it's the best to start with 2nd option, and once we complete this we can start 1st option. Hope this subproject will become 3rd drive.

I'm aware of how long one test lasts in that range of n's. Did some tests for "my own k".

I also vote for option 2-- taking a batch from 1.1M to 2M isn't a huge project at this weight, yet has the tantalizing chance of a Big Prime (tm).
If there is no moderator with time to administer the RPS-drive-style checkout pages, perhaps the 2-4 of us who are interested in this could commit to a 100k range of n to check, and all just grab Thomas' file, parsing it for our committed range ourselves.
Ideally, a mod sets up checkout ranges like the other projects, but I imagine that's a serious time undertaking. If anyone considers setting this up, I'd personally be comfortable with larger file-pieces; 2-3 weeks on a P4 isn't unreasonable, as there will be few people working on this, and frequent progress updates aren't as relevant, with the small chance of finding a prime.
Thomas-- thanks again for sharing your sieving work with us.
-Curtis

Curtis, I like your idea... that each of us take a 100k range of n to test, and parsing it ourselves.

But, before we go that way maybe we could send PM to admins if they are interested to set up this project as 3rd drive. I'll send PM to Kosmaj and Larry.

Low weight (3rd Drive) sounds good and I also vote for option 2. I'm not sure do you need extra sieving or not. If you do, we have a small "sieving squad" that might be able to help.

I'll suggest to Larry to start a new drive thread as I already run two others. As for uploading files to the server I'll talk to SlashDude but he is often slow to respond. In the meanwhile, if you can either mail me the files (zipped), or place them somewhere so that I can access them, I'll put them on the server. [EMAIL="kosmaj@yahoo.com"]Let me know [/EMAIL]what file size are we talking about. I second Curtis' idea for larger blocks, but ideally it will be nice to have medium-size ones too.

I cannot wait to see those low-wieight megabit primes! :cool: :w00t:

That's great Kosmaj! So we can have this low weight search as RPS 3rd drive.

It would be nice to catch one of those megabit primes! :w00t: