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John Forum moderator
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About the extended Sierpinski Problem
In 1962, John Selfridge discovered the Sierpinski number k = 78557, which is believed to be the smallest such number. The Sierpinski problem attempts to prove that it is, in fact, the smallest Sierpinski number. In 1976, Nathan Mendelsohn determined that the second provable Sierpinski number is the prime k = 271129. The prime Sierpinski problem attempts to prove that this is the smallest prime Sierpinski number.
Should both of these problems be solved, k = 78557 will be established as the smallest Sierpinski number, and k = 271129 will be established as the smallest prime Sierpinski number. However, this would not prove that k = 271129 is the second provable Sierpinski number. Since the prime Sierpinski problem is testing all prime k's for 78557 < k < 271129, all that's needed is to test the composite k's for 78557 < k < 271129. Thus, the extended Sierpinski problem is established.
As of March 2010, there remain 30 composite k's for which no primes have been found. They are as follows:
85013, 91549, 94373, 98749, 99739, 107929, 123287, 131179, 147559, 154801, 161041, 163187, 167957, 168587, 185449, 187681, 193997, 198677, 200749, 202705, 208381, 209611, 211195, 219259, 225679, 227723, 229673, 238411, 250463, 261203
For a more detailed history and status of the extended Sierpinski problem, please visit Wilfrid Keller's The Sierpiński Problem: Definition and Status.
To participate in the search, add the following server/port to your prpclient.ini file (adjust project share accordingly):
server=ESP:100:5:pgllr.mine.nu:9000
NOTE: For those new to PRPNet, please see the Welcome to PRPNet post.
NOTE: If you are using v3.2.1-beta, please comment out pfgw in your master_prpclient.ini file as there is a bug.
Initial work is for n<500K with additional work for n<1M.
Stats can be viewed here:
Server Stats
Pending Tests
User Stats
User Primes
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Cool. Just started 2 dual cores and a quad core on this. =)
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The server stats page shows the value of K=263329 as being one of the k's being searched. But your post, and the Sierpinski problem web page you reference both list 261203 as the highest K to be searched (and it was eliminated just today by Lennart!!!).
What's the story with 263329?
Thanks,
Mike
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JohnForum moderator
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The server stats page shows the value of K=263329 as being one of the k's being searched. But your post, and the Sierpinski problem web page you reference both list 261203 as the highest K to be searched (and it was eliminated just today by Lennart!!!).
What's the story with 263329?
Nice catch!!!
In the preliminary work to prepare the project, we double checked all primes to establish minimal n. There's one remaining prime left in that effort. Referencing The Sierpiński Problem: Definition and Status page, you can see that k=263329 was found prime at n=406934 by Kevin O'Hare on 05 Aug 2006.
All other primes have been confirmed minimal for their specific k.
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I guess I might as well shoot for really understanding the rest of it...
On the server stats page, what is the difference between the "lowest primes" and "PRPs/Primes" columns? For that matter, what does PRP stand for?
Similar or identical question on the user stats page: What's the difference between "PRPs found" and "Primes found"?
Lastly, on the user primes page, what's the difference between candidates and the primes?
Thanks again,
Mike
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JohnForum moderator
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First note that PRPNet is still under development so there are still bugs being worked on.
On the server stats page, what is the difference between the "lowest primes" and "PRPs/Primes" columns? For that matter, what does PRP stand for?
Lowest prime is the lowest n for that k that results in a prime. The PRPs/Primes column is a count column identifying how many PRPs/Primes have been found. PRP stands for "probable prime". Some of the tests available in PRPNet only test for probable primes. They must further be tested for primality.
For the page referenced, the PRPs/ Primes column should display a 1 for where primes have been found. This is a bug that's already fixed in the next release.
Similar or identical question on the user stats page: What's the difference between "PRPs found" and "Primes found"?
See answer above.
Lastly, on the user primes page, what's the difference between candidates and the primes?
Candidate is a term given to numbers that are being tested for primality. Thus, a candidate can either end up composite or prime.
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 HAmstyVolunteer tester
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i've got mail from john and it clears my confusion.
i saw geeknik had the last prime pending for over 4h, but then it disappeared and pilgrim got the task and reported it as prime.
wouldnt it be fair, if both of them get the prime as dc accounted?
EDIT: which version of prpnet should be used instead of 3.2.1b?
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JohnForum moderator
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i saw geeknik had the last prime pending for over 4h, but then it disappeared and pilgrim got the task and reported it as prime.
wouldnt it be fair, if both of them get the prime as dc accounted?
EDIT: which version of prpnet should be used instead of 3.2.1b?
Yes, we can find a way for them to share credit as double checkers. Note that the prime was already found by Kevin O'Hare on 05 Aug 2006. This was just a DC effort to confirm that it was the minimal prime for that k.
As for which version to use, 3.2.1-beta is fine as long as you comment out the pfgw call in the master_prpclient.ini file:
Windows
pfgw=pfgw.exe
Linux
pfgw=./pfgw
By commenting out pfgw, this client will not be able to participate in the Factorial and Primorial prime search ports.
port 12002: FPS
port 12008: PRS
However, it will work on all other ports.
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I'm shutting down PRPNet on all of my machines. I'm going to install BOINC on all of the machines since that project is stable and I will get credit for all of the work that I do. I have over 30 cores running various PrimeGrid projects and I can't keep track of what version is on what machine, so I'll just simplify the issue and run BOINC. =)
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HAmstyVolunteer tester
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grats geeknik, you've found a new one.
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Grats, Geeknik, for knocking off one of the k's!!!
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Thanks for the congrats! If it wasn't for the posts here, I wouldn't know that I knocked one of the Ks out of the search. :) According to my PC, I found 263329*2^406934+1 at 6:31AM local time (11:31 UTC). Server shows Pilgrim got credit for it at 13:44 UTC. But whatever, I'm not going to lose sleep over it. These machines will be doing BOINC by tomorrow morning. :)
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Thanks for the congrats! If it wasn't for the posts here, I wouldn't know that I knocked one of the Ks out of the search. :) According to my PC, I found 263329*2^406934+1 at 6:31AM local time (11:31 UTC). Server shows Pilgrim got credit for it at 13:44 UTC. But whatever, I'm not going to lose sleep over it. These machines will be doing BOINC by tomorrow morning. :)
Nope, you actually found 2 primes. The one we were congratulating you about was the other one; the one you found all by yourself (k=167957).
The rest of us mere mortals are jealous!
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HAmstyVolunteer tester
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Pilgrim killed another k, k=185449.
Congratulations
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HAmstyVolunteer tester
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grats lennart.
you eliminated another k, k=208381 ... 26 remaining...
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grats lennart.
you eliminated another k, k=208381 ... 26 remaining...
Thanks :) I hope we can nock out some more today :)
Lennart
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Congratulations Everyone!
The leading edge has now reached "Top 5000" reportable. Well done!!! Since 14 March when this effort was in its prep stage, 8 new primes have been found (3 in the last two days). There are now 26 candidates remaining.
Up to n=1M has now been loaded into the database. Thank you to everyone for contributing to this effort. :)
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Excellent!
Please post top5000 reporting details? I'd guess finder, PrimeGrid, SrSieve, LLR ? ie same as PPS LLR?
(only asking since the server publishes the prime data)
I presume the usual Fermat Number divisibility checks should be done at some point too?
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JohnForum moderator
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Please post top5000 reporting details? I'd guess finder, PrimeGrid, SrSieve, LLR ? ie same as PPS LLR?
(only asking since the server publishes the prime data)
I presume the usual Fermat Number divisibility checks should be done at some point too?
Since primes are reportable to the "Top 5000", we are experimenting with the prime suppression feature available in PRPNet. It is set, so now primes should not be displayed. Let's find one now and test it out. :)
Yes, reporting will be what you guessed: prime finder, PrimeGrid, Srsieve, LLR. And yes, with PFGW commented out, we are testing for xGFN divisibility outside PRPNet.
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Just to be clear, if we're actually to solve the "extended Sierpinski problem" (proving that 271129 is the second Sierpinski number) , we not only need to find primes for all the k's in this project, but we also have to have found primes for all the k's in both the Sierpinski problem (SoB) and the prime Sierpinski problem.
Is that correct, or is there some other inherent value in proving that these composite k's not covered by the other two projects have primes?
Mike
P.S. And congrats to whomever just found the latest prime for k=168587! (The stat pages are acting up so I'm not sure whom it was.)
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HAmstyVolunteer tester
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Steve_Martin@SETI.USA seems to be the lucky one.
grats Steve
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JohnForum moderator
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Steve_Martin@SETI.USA seems to be the lucky one.
Yes, congratulations to Steve Martin. Unfortunately, the suppress feature did not work. Whenever anyone attempted to access the user_primes.html page, it would take down all the stats. Therefore, we had to disable the feature. All stats pages are working fine now.
Now if we can just get Steve to see his emails. :) He's got 2 primes, 1 also from PRPNet PPSE.
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the problem persists, stats are down and lennart found another prime :)
grats lennart, again
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JohnForum moderator
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the problem persists, stats are down and lennart found another prime :)
Yes, it would help if we updated the correct ini file. The ESP port was still set for suppress. It's corrected now.
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JohnForum moderator
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Just to be clear, if we're actually to solve the "extended Sierpinski problem" (proving that 271129 is the second Sierpinski number) , we not only need to find primes for all the k's in this project, but we also have to have found primes for all the k's in both the Sierpinski problem (SoB) and the prime Sierpinski problem.
That's it in a nutshell. :)
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Looks like the stats pages are down again.
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Looks like the stats pages are down again.
Yes but now it is up :)
as before it was a new prime causing the downtime
It does not help to set unhide=0
becuse it will be marked hidden when it is recived , after that it can take up to 10 min befor server unhide the primes.
We are working with Mark on those problem.
Thank's to all who help us here. I think it is fun :)
Lennart
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I'm getting "pgllr.mine.nu:9000 connect to socket failed" trying to get new tasks to crunch.
EDIT: And, of course, moments after posting that, it starts working again!
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Steve_Martin@SETI.USA seems to be the lucky one.
Yes, congratulations to Steve Martin. Unfortunately, the suppress feature did not work. Whenever anyone attempted to access the user_primes.html page, it would take down all the stats. Therefore, we had to disable the feature. All stats pages are working fine now.
Now if we can just get Steve to see his emails. :) He's got 2 primes, 1 also from PRPNet PPSE.
Have the e-mails, There is a mix up with reporting passwords, John B. is helping out with the problem. I hope he can fix it.
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Steve,
Congrats on finding another prime!
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I have been watching this thread and seeing the primes fall rather quickly. Was this expected to happen so fast? It sounds like this problem has existed for quite a while, and all of a sudden BAM! a ton of them are eliminated. Just was wondering. Great job by all!
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I have been watching this thread and seeing the primes fall rather quickly. Was this expected to happen so fast? It sounds like this problem has existed for quite a while, and all of a sudden BAM! a ton of them are eliminated. Just was wondering. Great job by all!
I don't know enough about the subject to comment on the expected distribution of the primes for the various k's, but one thing is obvious: The processing time for the lower n's is MUCH faster than for higher n's. As a result, in the first few days, a tremendous number of k/n pairs were tested. Even if the distribution of primes over the range of n's is constant, you would expected the rate (as compared to time) of discoveries to drop off rapidly, even if the rate of discovery vs. the number of WUs remains constant.
Processing time today for each task is almost quadruple what it was when the project went public a few days ago as a result of n increasing from the 300K range to the 700K range.
On the positive side, every prime we find knocks a k out of the pool for future testing, so while each test takes longer, there's less testing to be done.
On the negative side, Seventeen or Bust still has 6 k's remaining and n is in the 17 million range, with task run-times roughly 1,000 times longer than the ESP tasks we're running in the 700K range. I don't think anyone expects this to be completed quickly.
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Well the search is for the 2nd lowest sierpinski number. That's not quite like searching for the first.
Are the 3rd and 4th lowest of same interest? |
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Actually, it's worse than searching for the first, because we need this project *and* SoB *and* PSP to complete to be able to prove this is the 2nd! And I suspect that all 3 projects will likely need to continue to ludicrous levels to kill off each of the last primes.
I don't see the 3rd or 4th being of particular interest at this time. ESP is effectively an opportunistic "fill-in", and that's a good thing in my opinion.
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Is there anyone else running a PS3 here in PSA?
I would just love to get a prime on mine
Steve
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Is there anyone else running a PS3 here in PSA?
Not at the time, but sometimes especially for challenges PS3 is very helpful.
Mine seems to have a fan problem and gets very loud, although I'm removing the dust inside from time to time.
BTW I provide the prpclient-bundle for PS3, so if you ever experience trouble with that just let me know.
If you're interested I also got a genefer version which runs on the SPUs or even CUDA although I only tested the latter one in emulation-mode. But they're both a little bit unstable.
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You guys running PS3s, don't upgrade to Sony's new 3.21 firmware. It kills the Other OS option on ALL pre-slim PS3s. :)
http://blog.eu.playstation.com/2010/03/29/ps3-firmware-3-21-coming-april-1st/
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You guys running PS3s, don't upgrade to Sony's new 3.21 firmware. It kills the Other OS option on ALL pre-slim PS3s. :)
http://blog.eu.playstation.com/2010/03/29/ps3-firmware-3-21-coming-april-1st/
Mixed emotions over this. One, sadness that Sony could pull such a dick move. Two, glee: if I can't have prime crunching fun on my PS3 (I own a Slim), no one can. I'm a bad person. |
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Two, glee: if I can't have prime crunching fun on my PS3 (I own a Slim), no one can. I'm a bad person.
Maybe you can in future, as soon as the firmware is modded to even boot linux on a slim.
$ony declared the war, now they have to bear with the consequences. Bad marketing as always on $ony's side. |
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JohnForum moderator
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Actually, it's worse than searching for the first, because we need this project *and* SoB *and* PSP to complete to be able to prove this is the 2nd! And I suspect that all 3 projects will likely need to continue to ludicrous levels to kill off each of the last primes.
I don't see the 3rd or 4th being of particular interest at this time. ESP is effectively an opportunistic "fill-in", and that's a good thing in my opinion.
Yes, as Vato points out, the extended Sierpinski problem is the most Challenging of the three projects. All three projects must complete in order to prove that k=271129 is the second Sierpinski number.
Regarding the next few Sierpinski numbers, Wilfrid Keller has shared the following information:
I have just verified that between 271129 and 271577, the 2nd and 3rd proven Sierpinski numbers, there is certainly no other. So the 2nd and 3rd are anyway known to be _consecutive_.
The list continues as follows:
k = 78557, 271129, 271577, 322523, 327739, ...
Then, for 322523 and 327739 I could also quickly show that they are consecutive Sierpinski numbers.
Therefore, should the extended Sierpinski problem prove that k=271129 is the second Sierpinski number, then 271577 will also be proven as the third Sierpinski number.
To prove the fourth Sierpinski number, it must be shown that no prime k*2^n+1 exists for 271577<k<322523. In doing so, the fifth Sierpinski number, k=327739, will also be proven. However, at this time, there is no particular interest in proving that k=322523 is the fourth Sierpinski number.
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ESP Update
The initial goal of n=500K was quickly achieved and soon the secondary goal of n=1M will be reached. What started out as an interesting side project has now grown into a full-fledged search. Thank you to everyone who has contributed so far.
However, at n=1M, the project will be suspended as further sieving is required. Due to limited resources, only 1M-3M is being sieved. This is definitely not ideal. If further interest remains with this project, then a consideration will be given to establishing an ESP sieve effort in the sieving thread and expanding the max n.
Thank you once again for making this such a successful search.
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Number of tests went down. will there be a lucky punch on one k? ;-)
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All tests have been sent out. :)
[2010-04-02 08:48:36 GMT] ESP: INFO: No available candidates are left on this server.
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Yep ! ;-) just right in time to move over to the PFDMC and get some work done before 18UTC
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If further interest remains with this project, then a consideration will be given to establishing an ESP sieve effort in the sieving thread and expanding the max n.
Yes please!
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I have eliminated k=107929. 303413 digits. Not bad. =)
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I have eliminated k=107929. 303413 digits. Not bad. =)
Well done :)
Congrats .....
Lennart |
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If further interest remains with this project, then a consideration will be given to establishing an ESP sieve effort in the sieving thread and expanding the max n.
Yes please!
I would also be very interested in helping sieve for this project.
P.S. Congrats on the latest k, geeknik!
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I don't sieve anymore (unless I get a badge for it), but I will support those who do, so please, get some people sieving so I can knock a few more Ks off the list. =)
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ESP Sieving
ESP sieving has been opened in the PST forum. You can access it here: ESP Sieving Reservation
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Prime Found!!!
Another k eliminated: 98749*2^1045226+1 is prime! Found by Pilgrim on Fri Apr 9 12:23:05 2010. The prime is 314650 digits and currently enters the Top 5000 list at 295th place.
20 k's remain
Congratulations to Pilgrim and to everyone else participating.
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will there be any PSA Credit awarded for this effort?
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JohnForum moderator
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will there be any PSA Credit awarded for this effort?
Yes, ESP is within the PSA.
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Prime Found!!!
Another k eliminated: 219259*2^1300450+1 is prime! Found by Lennart (sm5ymt} on Thu Apr 29 09:02:01 2010. The prime is 391480 digits and currently enters the Top 5000 list at 188th place.
19 k's remain
Congratulations to Lennart and to everyone else participating.
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Nice! I look forward to the new sieve file. :) |
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Nice! I look forward to the new sieve file. :)
a new sievefile is done.
ESP3M_60T.abcd
In HFS
Lennart |
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Prime Found!!!
Another k eliminated: 154801*2^1305084+1 is prime! Found by Roger (Pilgrim} on Thu Apr 29 23:45:44 2010. The prime is 392875 digits and currently enters the Top 5000 list at 187th place.
18 k's remain
Congratulations to Roger and to everyone else participating.
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Prime Found!!!
Another k eliminated: 250463*2^1316921+1 is prime! Found by Roger (Pilgrim} on Fri Apr 30 04:31:18 2010. The prime is 396439 digits and currently enters the Top 5000 list at 183rd place.
17 k's remain
Congratulations to Roger and to everyone else participating.
Lennart |
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stop it Roger .. leave some for the rest of us.. :p
but seriously.. keep up the good work.. |
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stop it Roger .. leave some for the rest of us.. :p
OK Roger, you can start finding primes again. :)
After the early success, it looks like we've settled down into the stubbornness of this conjecture. Hopefully this will make the next prime, when found, that much more rewarding.
Thank you to all who continue to plug away with this search. Best of Luck!
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