Riesel Primes k*2^n-1, k<300 [Part II]
 

[URL="http://www.mersenneforum.org/showthread.php?t=1767"]The original k<300 thread[/URL] was started in December 2003 and contains almost 600 posts. It is a great source of information about work already done, but I think we need a new thread for new posts.

The first post of the original thread contains some useful links to software used for primality search and to several stats pages listing all found primes. I'll continue to update that post, but almost all information is available on [URL="http://www.15k.org"]our web site[/URL] too.

Please post your new k<300 reservations, and your comments and observatons in this thread.

:exclaim: The latest search status, updated frequently, can be found [URL="http://www.15k.org/riesellist.html"]here[/URL].

Thanks,
Kosmaj:

Maybe we should close the original thread to avoid any confusion :question:

k=35 tested to 900,000. Continuing.

status and primes
 

k=209 llr at 704 k: 2 new primes:
209*2^692692-1 and 209*2^675232-1 (last prime at 60k!!!).

k=297 llr still at 581k (work next and let rest 209 a while)

105*2^530360-1 is prime.

k=289 now complete to n=470K without a gap
 

One of the cores on my high-speed dual machine has now completed k=289 for the range of n=260K to 400K. The other core that I've temporarily stopped for other activities had previously completed the range of n=400K to n=470K so this completes it up to n=470K with no gaps. No more primes have been found since n=90201. :yucky:

This leaves a remaining gap for k=289 of n=470K to n=501991. I have now re-started the other core and it will run all the way up to n=520K to complete filling of the gap and confirm some prior testing.


Gary

297*2^583464-1 (175643 digits)

Brief update regarding new issue...

207 is at 583k and pausing to work on 31.
31 is on hold at 567k. Currently working on 800k and up to race with Benson.
567k-800k gap will be filled soon.

-Steven

Status on k=289 and k=2145
 

I'm now complete on k=289 up to n=485K. Still no additional primes.

On k=2145, I've completed my own testing and am now testing from some sieve files given to me by Curtis. I'm now complete up to n=180K. Since my last status of n=120K, all previous primes listed on the summary site are correct and there were no additional primes found.


Gary

k=251
 

[B]Reserving k = 251 from 545,000.
[/B]I'll push this low weight a bit higher; only about 10.5 candidates per 1000.


Just a thought. Is it possible for a k to stop producing primes once it has produced one or more?

[QUOTE=Flatlander;110416]Just a thought. Is it possible for a k to stop producing primes once it has produced one or more?[/QUOTE]

No, I think it's proven that if k has a prime for one n, then there are primes for infinitely many. But the gaps between primes can be large. See for example k=253 and k=101.

[QUOTE=Kosmaj;110419]k=101.[/QUOTE]My favourite - the next prime is @ n=9M :wink:

Status on k=289; gap closed
 

I have now 'officially' closed the gap on k=289. I've now tested all the way from n=260K up past the next known prime at n=501991. I found that one prime that Bo had already found.

I'm actually testing all the way to n=520K to verify some prior results and LLR is currently at n=503K.


Gary

Unusual gaps between primes
 

[quote=Kosmaj;110419]No, I think it's proven that if k has a prime for one n, then there are primes for infinitely many. But the gaps between primes can be large. See for example k=253 and k=101.[/quote]

Good question by Flatlander. I think the term 'large' in describing the gaps between primes is a 'large' understatement. :smile: They can be flat-out enourmous!

I'll throw out a somewhat similiar situation in my gap-filling efforts...
Although it has many primes, k=289 is an excellent example of one of the more extreme gaps between primes that I've seen for a k that we would not consider low-weight. It has primes at 55693, 60243, 67891, 77391, 90201, then a 'monster' gap of no primes (now confirmed by me), followed by primes at 501991, 509401, 610737, 728205. This, I think, is far more unusual than a low-weight k having a gap between primes of more than 1M.

Go figure. I think an entire thread could be dedicated to record gaps between primes for different weights of k. These unpredictible gaps are what makes primes so fun! :smile:


Gary

k=101 question
 

[quote=Cruelty;110443]My favourite - the next prime is @ n=9M :wink:[/quote]

Hasn't that one only been tested to n=1M with its largest prime at n=900358? Just curious if I have missed something somewhere.

But that is a huge gap between n=94194 and 900358!


Gary

[quote=Kosmaj;110419]No, I think it's proven that if k has a prime for one n, then there are primes for infinitely many. But the gaps between primes can be large. See for example k=253 and k=101.[/quote]

But not proven for k=1?
[URL]http://en.wikipedia.org/wiki/Mersenne_prime[/URL]

[QUOTE=gd_barnes;110446]Hasn't that one only been tested to n=1M with its largest prime at n=900358? Just curious if I have missed something somewhere.[/QUOTE]You are correct, I have tested it 500000<n<1000000 so far. Shortly I will begin testing it in the 1M<n<2M range. When I have announced prime @ n=900358, Kosmaj suggested that the next one might be @ n~9M because last 3 "n"s for this k that start with "9" were primes :wink:

k=55 tested to 800,000. Continuing.

k=81
 

LLR at 840k. Continuing.

[quote=Cruelty;110451]You are correct, I have tested it 500000<n<1000000 so far. Shortly I will begin testing it in the 1M<n<2M range. When I have announced prime @ n=900358, Kosmaj suggested that the next one might be @ n~9M because last 3 "n"s for this k that start with "9" were primes :wink:[/quote]

Ah, I get it now.

Well...you should test k=101 from n=9M to 10M!! That'd be funny if you found one pretty quick. :smile: Of course it would take ages to process each candidate! :yucky:


Gary

[QUOTE=gd_barnes;110477]Well...you should test k=101 from n=9M to 10M!! That'd be funny if you found one pretty quick. :smile: Of course it would take ages to process each candidate! :yucky:[/QUOTE] Actually it takes ~2 days on 3GHz C2D :smile:

k=105
 

Cruelty, but that's great news, that you are already working on them!:smile:

BTW, Flatlander stopped n=105 at n=541300 and kindly sent me the rest of his file sieved to 4.2T. If anybody is interested in continuing tests, just let me know. Otherwise I'll send the block to about 570k to B'maxx. If there is enough interest I can open a thread for group testing as well.

How far does flatlander's file go? 1M? I'm willing to sieve it a little deeper if it goes that high, for future public LLR work. If the file goes to 700k or less, there's little point in more sieving.

Mini-update:
45 at 680k, paused for 800k work
93 at 680k, paused for 800k work
197 at 882k
201 at 640k

-Curtis

k=289 verification to n=520K complete
 

I'm finally done verifying the entire range of n=260K to 520K for k=289. No primes were found other than the two previously found by Bo at n=501991 and 509401.

The only consolation is that I got to report them on Prime Search since Bo is not coordinating with anyone. Ah well, it's nice to know that our list is complete to that point.

Needless to say, I'm not reserving this k. :yawn:


Gary

[B]Curtis[/B]
k=105 goes to 1.5M. If you want I'll send you the block from 600k. Up to there we'll do it as-is.

Edit: I just started a [URL="http://www.mersenneforum.org/showthread.php?t=8753"]new thread about k=105[/URL].

[B]Gary[/B]
Well done! I updated the k<300 stats page.

k=69
 

k=69 is complete to 1M and I'm now releasing this k.

k=173 checked in the 210k - 1M range.
k=253 checked in the 1165 - 1750k range.
Stopping and releasing both of them.

k=85 at 1015k, tests in progress.

status update
 

k=181 is at n=892k
k=223 is at n=1.88M

both are continuing

[quote=Flatlander;110416][B]Reserving k = 251 from 545,000.
[/B]...[/quote]
Please note that this k is incorrectly shown as unreserved on the k<300 page.

Will correct k=251 shortly.

During the update of k=253 I thought it was strange that k=251 was not marked but didn't have time to check...

k=251
 

k=251 tested to 600,000. Continuing.

monthly update
 

13 at 1.04M.
45 at 700k
93 at 680k
99 at 1.01M
127 at 1.02M.
197 at 950k
201 at 700k

Sheep has run the sieve for 13-45-99-127 to 125T.
2 cores on 45 and 99, 197 paused, 1 each on the rest. Megabits are slooww.
-Curtis

The exchange with DJones moved to [URL="http://www.mersenneforum.org/showthread.php?t=8935"]another thread[/URL].

k=139
 

Nuggetprime informed me that he doesn't have enough resources to continue his search of k=139 right now but he hopes he will be able to resume his search later this year.

I'll leave k=139 reserved for him for a while but if somebody wants to test it we can cancel his reservation.

Carlos decided to release k=33 for the time being.

k=19 has been tested to 1M. There are no new primes, but I'm continuing with it.

The last time I posted residues was at 940K, so the attachment contains residues from 940K-1M.

Kosmaj, are you still working on k=83? If yes then [URL="http://primes.utm.edu/primes/page.php?id=81948"]this[/URL] looks like something personal...

k=49
 

Update:
LLR complete to 950k.
No new primes.

k=81
 

LLR at n=900k.

No new primes since last update.

Please note that the search limits for k=19, 49, and 81 have not been updated on [url]http://www.15k.org/riesellist.htm[/url] , even though the page says that it has been updated on August 20th.

13 and 127 have hit 1.1M on LLR.
reserving 119 from 500k to 1M.
-Curtis

k=251
 

k=251 tested to 700,000. Continuing.

k=141,151,199,269 done till n=600000.
"Only" 5 primes for k=199 found in this range :wink:
I am releasing k=199, and continue testing 141,151 and 269 until I find a prime for each of these :flex:

Okay, I updated [URL="http://www.15k.org/riesellist.htm"]the stats page[/URL] accordingly (The first update after more than 10 days because the ftp server was down.)

k=199 is now up for grabs!

I'm afraid that for at least one of your remaining k's you will have to go into mega-bit exponents to find the next prime. But I know that's not a problem for you. :smile:

[QUOTE=Kosmaj;113480]I'm afraid that for at least one of your remaining k's you will have to go into mega-bit exponents to find the next prime. But I know that's not a problem for you. :smile:[/QUOTE]That's why I'm sieveing till n=2M :cool:

Cruelty- did you also sieve k=199 to 2M? If so, can you email it to me? Perhaps I can start a new form of team drive, testing 199 until I find a prime and then releasing it for the next person to reserve and continue. :yzzyx:

-Curtis

I haven't touched k=199 above n=600000. I am only sieving 141,151 and 269 till n=2M.

update
 

31 has reached 865k on the high part.

P4 is currently working back on 207 (at 586k).
Sempron is set to continue 31 from 865k and up.
Celeron is now LLRing 31 on the lower range, filling up the gap (at 570k currently).

EDIT: no new primes

-Steven

k=49
 

Update:
Sieving at 6T to 2M
LLR complete to 1M. Continuing.
No new primes.

k=39 is at n=1.135M
k=223 is at n= 1.99M

status
 

k=209 at 764k
k=297 at 615k

monthly status report
 

11 still no work yet- will be a while before sieving is ready.
13 at 1.14M.
45 at 740k.
93 at 710k.
99 at 1.04M.
127 at 1.12M.
201 at 775k.
no progress on 111 and 197.
:flex:

-Curtis

k=141 done till n=620000. I am releasing this k. If someone wishes to continue this work I have a sieve file till n=2M and p~2T.
I am continuing with k=151 and 269 until I find a prime for each of them :smile:

k=223 complete up to n=2M. Releasing this K!

k=55 tested to 900,000. Continuing.

k=269 tested till n=640000. I am releasing this k - if anyone wishes to continue I can provide a sieve file 640k<n<2M sieved till p~2.6T.

Cruelty- please email me your orphan sieve files. I'm not sure I will complete them, but I'll likely do at least a little work from them. Email is this handle at gmail.
-Curtis

[QUOTE=VBCurtis;114854]Cruelty- please email me your orphan sieve files. I'm not sure I will complete them, but I'll likely do at least a little work from them. Email is this handle at gmail.[/QUOTE]You've got mail :wink:

I am unreserving k=137. This should be marked as reserved by David Broadhurst. From what I've found out he has notified Wilfrid Keller about his reservation last month.
He is also working on k=137137.

Cruelty
 

I'm sorry to hear about your sieving of k=137 in vain. David will tell you ranges he tested if you ask him, but he is not coordinating his efforts with us so there was no way to know. Also, currently there is nothing about his reservation on the Keller's page. If you sieved high enough, for example to n=3M, you can consider testing some higher ranges. But there are also meny other promising k's, and I'm sure you will hit your next mega-bit prime soon. So, don't despair, just keep on going! :smile:

Edit: Keller just updated his page, and k=137 is listed as checked all the way to n=1849260 (the prime was at n=1849238).

Of course I will keep going :smile:

Cool! :cool:

BTW, would you be interested in k=281 ?
It's the only k<300 with no primes with more than 100k bits, the largest was at n=93850 and no more up to n=600k.

I was planning to investigate such numbers further as right now I am looking for a prime for k=151 (141 and 269 already done) :cool:

I'm reserving 109, 131, 211, 221, 233, 245, 263, 281, 283 and 299 for 600000<n<2M. Right now I only have some spare sieving resources but after finding k=151 prime I will be also able to LLR them :wink:
BTW: k=151 has been tested till n=700000, and I am still working on it :tu:

Cruelty,

I just marked on the stats page all 10 Ks you reserved on Oct. 1. Although they are all low to medium weight I'm afraid it's too many to run efficiently even on several machines at once. True, better unefficiently than not at all, but somebody else might be interested in trying some of them later...

Kosmaj,
I am already at p=0.5T so don't worry :smile:
Also, I think that k=141 and 269 should be marked as reserved by VBCurtis - as I have sent him the sieve files till n=2M.

I won't start on them for quite a while, and don't mind if someone else reserves them or wants to work the sieve files, so there's no need to mark them reserved for me. If someone else takes 'em, I'll forward the files along.

-Curtis

Milestone report:
k=25, 59, 101 (and 617), have been tested till n=1.1M (I am still working on those).
k=141 and 269 will be merged into my 10k sieve making it a 12k sieve ;-)

Arminius completed k=49 to n=1.05M. No new primes were found.
The last one was at n=691469.

Monthly update
 

13 at 1.20M.
45 at 780k.
93 at 850k.
99 at 1.10M.
127 at 1.20M.
201 at 825k.
no progress on 11, 111, and 197. :cool:

-Curtis

k=151 tested till n=800000, I'm still working on it.

k=19 has been completed to n=1050K, and no new primes were found.

I'm still working on it, and I've attached the residues from 1M (my last status update) to 1050K.

I would like to know if there's a sieve file available up to n=1M for the following k's: 295, 293, 287 and 275.
I think my strategy from now on will be to LLRing all k<300 up to 1M.

Thanks in advance,

Carlos

No, as far as I know.

I have sieved files for:
k=125, from n=870k to 1M, currently sieved to about 8T and
k=97, from n=930k to 1M, sieved to 3T (or more, not sure)

k=125 I can send you in a few days, k=97 I can send you in a few hours.

Carlos, I believe no work has been done past 600k on these numbers, including sieve work. If you are interested in already-sieved k's, choose one of the k's marked as tested by Masser to 700k. Reserve it here, and I will mail you the sieve file. His sieves run to 1M, conveniently. If you want, I can also send you the lowest- (or highest-) weight k from Masser's group, instead of picking one at random.

-Curtis

Kosmaj,

I'll take those two.

Curtis,

Please pick up two from Masser's group.

You both can send them to me within a week. I still have 3 days with k=5 and 5 days with k=105.

Carlos

Releasing:

k=97, tested 800-930k, one prime found at n=843205 (January 2006)
k=189, tested 700-770k, no primes

update
 

207 is pausing, focusing all 3 cores on 31

(630k-570k) P4 LLRing 31 at 645k
(750k-800k) Sempron LLring at 751k
(870k and up) Celeron LLRing at 871k

-Steven

Steven, I'm not sure how to interpret your first line:

[QUOTE](630k-570k) P4 LLRing 31 at 645k [/QUOTE]

Does it mean you tested the 570-645k range?

nice big one for k=243
 

After just a little more than 3 days of searching n=500K-600K on core #4 of my k=243 search, I finally hit pay dirt for all of my gap filling and double-checking efforts. Rob missed a nice one by not searching all of the ranges of k=243 and then going virtually AWOL for nearly 2 years...

243*2^510491-1 is prime (153676 digits) :surprised

Nearly 120,000 bits bigger than my previous biggest. :smile:

This makes a pretty good case for checking all of the ranges, not just the ones shortly before a fftlen increase.

I'll call this my payback for a barren double-check stretch of k=289 from n=90K-500K.

4 cores are on it, one each started at n=230K, 333.3K, 400K, and 500K. The ranges completed so far are on my web page.


Gary

yes. the number inside the parentheses is the exponent which is assigned to the machine. and the there's typo in the first line. it suppose to be 630 to 750k

-Steven

David informed me that he tested k=137 all the way to n=2M and stopped there.

Cruelty, if you want you can continue frome there...

[QUOTE=Kosmaj;117634]David informed me that he tested k=137 all the way to n=2M and stopped there.

Cruelty, if you want you can continue frome there...[/QUOTE]Tempting but no thanks :wink:

k=243 strikes again for n>500K only n=8K larger
 

243*2^518736-1 is prime! (156158 digits) :surprised


Someone really missed the boat on this one!

Gary-
please post primes in the "post primes here" thread, not in this thread. This is for status updates, not for prime-posting. This keeps threads less cluttered.
-Curtis

k=81 Status
 

k=81 at 1025k. Continuing.

k=67
 

Reserving k=67.

k=147
 

Reserving k = 147 please.

Gryphon informed me that he had tested k=255 to n=820k and is continuing.

I'll update the k<300 stats page over the weekend.

I'd like to try k=33 for a while, if it's not currently being tested. This is complete through 750K? Thanks.

k=243 status
 

Here's a permanent status record for k=243 off of my web page:

Double-checking for n=230K-260K and 300K-400K is complete. No problems were found. Citris tested the n=260K-300K range for RPS here.

Consecutive testing is now up to n=472.6K. Other ranges tested so far are n=500K-558.1K and 600K-615.5K.

I added the core from the double-check range to the 400K-500K range for a total of 2 to more quickly fill the lower gap. 1 core each are on the others. When 400-500 is done, I'll put 1 more each on the 500-600 and 600-650 ranges. I should be complete up to n=650K within 7-10 days.


Gary

k=251
 

k=251 tested to 800,000. Continuing.

k=49
 

Update:
Sieving at 14T to 2M
LLR complete to 1.09M. Continuing.
No new primes.

milestone report for k=151
 

k=151 tested till n=900000, I'm still working on it

k=243 status
 

k=243 has now been fully tested up to n=642K.

2 cores are working from n=642K-745K. The other 2 cores are working 745K-800K and are at 752.3K. When the latter 2 are done, they will join the other 2 in double checking the 650K-745K range.


Gary

Justin reserved k=69 from n=1M.

K.

k=139 again
 

As I mentioned in [URL="http://www.mersenneforum.org/showpost.php?p=111941&postcount=34"]post #34[/URL] of this thread, k=139 is not strictly reserved, and the name of Nuggetprime attached to it is only a placeholder meaning that he may return and keep on working on it soon.

If anybody wants to work on k=139 now he is free to do so. Actually Nugget said that he tested it to "about" 419500 but I'd like to suggest starting at 400k.

:coffee: