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gd_barnes

Join Date: May 2007

Posts: 14017
#1

Come join us!

2007-12-14, 19:45

With this effort, we aim to prove many of the Riesel and Sierpinski conjectures for bases <= 1030 that are not currently being worked on by other projects or efforts.

Project definition:
For every base (b) for the forms k*b^n+1 and k*b^n-1, there is a k-value for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (-1 form) that is composite for all values of n >= 1.

Conjectures must have a finite covering set and cannot be a multiple of the base. k-values are not considered in instances where all n's are covered by one trivial factor, all n's are covered by algebraic factors or a combination of algebraic and trivial factor(s), or make Generalized Fermat Numbers (GFNs). See more details for conjecture requirements, inclusions, and exclusions in the links below to web pages about all bases.

Sub-project #1:
Assist in proving the Liskovets-Gallot conjectures for the forms k*2^n+1 and k*2^n-1 where n is always odd -and- where n is always even.

Sub-project #2:
Assist in proving the Sierp base 2 2nd conjecture for the form k*2^n+1. The 1st conjectured k where all n are proven composite is k=78557 and is extensively tested by the PrimeGrid Seventeen or Bust project. The 2nd conjectured k where all n are proven composite is k=271129. The range of 78557<k<271129 has been extensively tested by the PrimeGrid Prime Sierpinski Problem and Extended Sierpinski Problem projects. All of these projects have omitted even k's from testing. For the 1st conjecture there are no even k's remaining. For the 2nd conjecture some even k's remain. Therefore CRUS is testing even k's for the Sierp base 2 2nd conjecture.

Sub-project #3:
Assist in proving the Riesel base 2 1st conjecture and prove the Riesel base 2 2nd conjecture for the form k*2^n-1. The 1st conjectured k where all n are proven composite is k=509203 and is extensively tested by the PrimeGrid Riesel Problem project. The 2nd conjectured k where all n are proven composite is k=762701. The 1st conjecture project has omitted even k's from testing and some even k's remain. The 2nd conjecture has not previously been tested. Therefore CRUS is testing even k's for the Riesel base 2 1st conjecture and all k's for the Riesel base 2 2nd conjecture.

Goal:
Prove the conjectures by finding at least one prime for all lower values of k. Many of the conjectures have already been proven but much more work is needed to prove additional bases. Proving them all is not possible but we aim to prove many of them.

Here is what is different about this effort than others previously started outside of bases 2 and 5:

1. All known info. from all threads here and many other places on the web have been brought together and have been extended to base 1030. There are currently several web pages that contain all of the info. and others pages solely dedicated to reservation info. about all of the bases. Links to them are below. They will be updated daily or as needed.

2. There will be separate threads for important k to search, reservations, and sieving efforts. If you are new to the conjectures, you'll see a portion of the more important forms that we need primes found for. The reservations page will guarantee that there is no duplication of effort and the 'last status' date will keep the effort moving along.

3. We have well-sieved files for searching at all n-ranges. See links in the reservations web pages below.

4. There is a wide variety of k's for people of all tolerances. We have k's that can be started anywhere from n>=1M down to n=2500. There are also some bases that can be started from scratch where you can find millions of very small primes. (Not for the faint of heart!)

5. There are many conjectures where only ONE k needs a prime (and many more that need only two). If you find it, you could be the one to prove a conjecture! This is a big deal to us here.

6. Algebraic factors have been found for many k's, which prove them composite for all n, allowing them to be removed from searches. For me, there's nothing worse then searching a k for a long time that later is proven to have no primes.

7. For those who prefer to search the conjectures using BOINC, there is a BOINC effort called SRBase for the project. See SRBase.

Links to web pages about all bases:
Riesel conjectures
Riesel conjectures powers of 2
Sierpinski conjectures
Sierpinski conjectures powers of 2

Reservation pages:
Riesel conjecture reservations
Sierpinski conjecture reservations

Summarized statistics and
general short summary pages:
Condensed table of all conjectures
Overall progress
Top 20 lists
Unproven conjectures
Proven conjectures

BOINC effort (SRBase):
SRBase

The Liskovets-Gallot conjectures are shown as 'base 2 even-n' and 'base 2 odd-n'.

For details about conjecture requirements, inclusions, and exclusions, see the links above to web pages about all bases.

Since some of the exclusions are related to generalized Fermat numbers (GFNs), here is a link to GFN primes for bases <= 1030 up to n=2^22:
GFN primes

Thanks and come join us for the fun at..."Conjectures 'R Us".

Gary

Last edited by gd_barnes; 2024-11-13, 00:03. Reason: modern udpates
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michaf

Join Date: Jan 2005

Posts: 479
#2

2007-12-15, 00:04

Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>
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gd_barnes

Join Date: May 2007

Posts: 14017
#3

2007-12-15, 03:54

starting a new base...

Originally posted by michaf View Post

Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>

For starting a new entire base, I suggest PFGW. But you're talking about starting a single k on a new base. I don't recommend that because it would be highly inefficient and would take weeks just to search a few 1000 k. For instance on base 24 Riesel, it would require 32,335 separate searches (minus a small percentage with trivial factors).

For me personally, I would use PFGW to search all 32,335 k's at once up to n=3000. This would take it anywhere from 2-4 hours on one 3-Ghz P4 machine depending on how many k's it was eliminating in the early going. What's cool about PFGW is that it will stop searching a k after it finds a prime for it if you tell it to. The set up and recognition of the output wouldn't be too hard either because for base 24, there are few k's with trivial factors. (1 out of every 23 k's has a trivial factor of 23).

I think Robert did a good thing when he split up the base 16 Sierp effort into 4-5 pieces because that conjecture is k=66741. So that would be an option also. If you went with Robert's option, you might want to take the first 5000-7500 k's on base 24 to 'get your feet wet' on using PFGW and recognizing the remaining k's.

If you still want to bite off part of a new base like this, let me know and I'll send you a PM that will have detailed instructions on downloading PFGW and setting up the parameters properly. But if messing with proving many new primes, reporting k's remaining to me for others to search, etc., isn't to your liking, I have a suggestion just for you personally: You tested the remaining candidates on Base 23 up to n=34.5K. I've searched the Riesel side for them up to n=45K now. I have sieved files that go all the way up to n=100K that I can send you and you could start testing from there. As you may remember, there are 2 candidates remaining for both the Riesel and Sierpinski conjectures. (Top-5000 status is reached at ~n=74K for base 23.) If that's too long of a search per candidate for your tastes, there are many k's searched to much lower ranges such as for base 28 where there are a total of 23 k's remaining that have been searched to just n=5K.

If you're familiar with running LLR, that is what I recommend for all of the prime searches past about n=5K here after they have been sieved. Mine for base 23 have been sieved to P=600G, which is plenty sufficent, even for the longer running times of higher-n higher-base searches.

I will post what software to use including PFGW for all of the various searches and detailed instructions about their set up and how to use them in the next couple of hours but I won't go into how to start a new base like this, which would require way too many different instructions for the different situations on the many bases.

I know this doesn't answer your question completely but now that you know the above, if you can let me know how you want to proceed, I can taylor the answers more to what you want to do.

Gary
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Citrix

Join Date: Jun 2003

Posts: 1669
#4

2007-12-15, 06:11

Originally posted by michaf View Post

Is there a program available to 'start' a search easily?
i.e. get a program to search each number upto say n=1000, and let it report (and abort that k) whenever a prime is found.
(and also get an output file containing remaining k's of course)

I tried to make myself a ubasic program, but is seems waaaay slow, and it leaves about 1 in 10 numbers when I search only upto 100 in base 24, which would be too much to handle still :>

You can write a script in pfgw. There is some documentation of this feature in the package.

gd_barnes, if some previous threads could be locked/deleted if no one is using them, let me know. This will help organize the open projects section.

Thanks!
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gd_barnes

Join Date: May 2007

Posts: 14017
#5

2007-12-15, 07:20

Originally posted by Citrix View Post

You can write a script in pfgw. There is some documentation of this feature in the package.

gd_barnes, if some previous threads could be locked/deleted if no one is using them, let me know. This will help organize the open projects section.

Thanks!

That was brought up to me before in a PM so it is a good idea. First I'd like to post a message in each of them, which I'll do in the next couple of days. The ones that I'd like to see locked are the conjectures for bases 10, 22, 23, and 6 thru 18. Rogue is still searching base 10 and Simelink is still searching base 22 per statuses in those threads in the last month. I have reservations shown for them on the web pages for this effort. What I'll do is ask that they coordinate their searches and reservations here; wait a few days for a response and then suggest that the threads be locked.

Initially I thought that base 4 Sierp could be locked and coordinated here but I noticed that it is an official prime search project as defined on the top-5000 site. So I'll leave that one alone and keep it on my list of sites and threads to observe from time to time to keep the pages up to date, similar to Riesel Sieve, Seventeen-or-bust, and base 5.

Detailed instructions on using software for this effort are coming up shortly, including the proper parameters and scripts to use for PFGW for a new effort. I had to download all of the latest versions of everything first!

Gary

Last edited by gd_barnes; 2007-12-15, 07:23.
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Citrix

Join Date: Jun 2003

Posts: 1669
#6

2007-12-15, 08:20

It would be nice if each project could just have one thread, this would make coordinating things easier. (is it possible to do this?). If you want to have several threads, a separate category might be helpful.
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gd_barnes

Join Date: May 2007

Posts: 14017
#7

2007-12-15, 09:03

Originally posted by Citrix View Post

It would be nice if each project could just have one thread, this would make coordinating things easier. (is it possible to do this?). If you want to have several threads, a separate category might be helpful.

I've asked xyzzy for moderator duties but I needed to get something started first. I think he implied that this could be moved over to the prime search projects forum and if the reaction to the effort was good, I may be able to be a moderator.

IMHO, separate threads are very much needed. If you look at the base 6-18 thread, there was a dukes mixture of reservations, k's remaining, k's being searched, statuses, you name it. People were getting mixed up.

That said...I think we do need to have the separate threads under a SINGLE project. Since this is 'Open projects', it does look a bit messy mixed in with threads from many other things. But if we had a stand-along project with just these 4 threads, I think it would look more like a well-structured directory structure on a computer.

Perhaps that's what you were implying that we needed a separate project for these several threads. I'm all for that. Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.

Software instructions now posted but 'how to's for this effort still to go. Fortunately those will be much quicker...Long night here.

Gary

Last edited by gd_barnes; 2007-12-15, 09:05.
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Citrix

Join Date: Jun 2003

Posts: 1669
#8

2007-12-15, 16:29

Originally posted by gd_barnes View Post

Perhaps that's what you were implying that we needed a separate project for these several threads. I'm all for that. Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.

Gary

Yes I do. Let me know if I can help with anything.
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mdettweiler

A Sunny Moo

Join Date: Aug 2007

Posts: 6436
#9

2007-12-15, 17:37

Originally posted by gd_barnes View Post

Citrix, do you have moderator priviledges for this forum? I kind of got that impression when you suggested having the other conjecture-threads locked. Just curious.
...
Gary

Hint: On the left, right next to where a post is in a thread, where it shows the username and other relevant information, there's a hint: The username is in blue if the user is just a regular user, green if they're a mod, and red if they're a forum administrator (sort of a super-mod, I think). The only exception (as far as I know) is Xyzzy, who shows up as a regular user but obviously has super-super-mod privileges.

Last edited by mdettweiler; 2007-12-15, 17:38.
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michaf

Join Date: Jan 2005

Posts: 479
#10

2007-12-15, 18:58

I was under the impression that Xyzzy was only a device used by the gerbils. Actually one gerbil and a spirit of one I believe.
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gd_barnes

Join Date: May 2007

Posts: 14017
#11

2007-12-19, 05:56

Come vote about this effort in the lounge...

I've posted a poll in the Lounge. Come vote and let us know if you think this effort is worthwhile enough to have it's own sub forum.

Thanks,
Gary
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Jean Penné

Join Date: May 2004

Posts: 652
#12

2007-12-21, 14:55

Two of the project rules may be conflicting!

Hi Gary,

The rules of the project include :

2) k must not be a multiple of the base.

and

3) Primes must be n >= 1

this last rule is quite mandatory : it is a part of the definition of Sierpinski and Riesel numbers.

On the other hand, the rule 2) may cause problem :

The reason given is that b*k*b^n+/-1 is k*b^(n+1)+/1

That is, indeed, always true, and more generally :

(b^q)*k*b^n+/-1 = k*b^(n+q)+/-1

But if the least exponent m for which k*b^m+/-1 is prime is <= q, then,
n = m-q <=0 in contradiction with the rule 3) !

The conclusion is that in this case, the multiplier K = b^q*k is still a candidate and must be tested...

There exists an open project which takes this in account :

http://www.mersenneforum.org/showthread.php?t=9444

Please, see also :

http://www.mersenneforum.org/showthread.php?t=9479

Also, I think that, in the Riesel base 4 project k = 19464 = 4*4866 has been omitted, probably because k-1 = 19463 is prime, but I am testing it and it is still surviving at n = 93672 base 4, so, I wish to reserve it also.

Best Regards,
Jean
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gd_barnes

Join Date: May 2007

Posts: 14017
#13

2007-12-21, 17:15

Originally posted by Jean Penné View Post

Hi Gary,

The rules of the project include :

2) k must not be a multiple of the base.

and

3) Primes must be n >= 1

this last rule is quite mandatory : it is a part of the definition of Sierpinski and Riesel numbers.

On the other hand, the rule 2) may cause problem :

The reason given is that b*k*b^n+/-1 is k*b^(n+1)+/1

That is, indeed, always true, and more generally :

(b^q)*k*b^n+/-1 = k*b^(n+q)+/-1

But if the least exponent m for which k*b^m+/-1 is prime is <= q, then,
n = m-q <=0 in contradiction with the rule 3) !

The conclusion is that in this case, the multiplier K = b^q*k is still a candidate and must be tested...

There exists an open project which takes this in account :

http://www.mersenneforum.org/showthread.php?t=9444

Please, see also :

http://www.mersenneforum.org/showthread.php?t=9479

Also, I think that, in the Riesel base 4 project k = 19464 = 4*4866 has been omitted, probably because k-1 = 19463 is prime, but I am testing it and it is still surviving at n = 93672 base 4, so, I wish to reserve it also.

Best Regards,
Jean

Thanks for checking things Jean. I agree with you completely. See the last para. of this post about the 'multiples of the base' issue where I state virtually exactly what you said about the possibility of k*b^n+1 yielding a prime at n=1 (or other small n), hence causing b*k*b^n+1 to yield a different prime.

For a DC effort like this, I thought that it was best to avoid them for now. In the bases 6 to 18 effort, there was much duplicate searching going on for k's that were multiples of the base and also much searching going on for GFn's such as 22*22^n+1 and 484*22^n+1, which seem unlikely to yield a prime in our lifetime. I wanted to INITIALLY avoid that with this effort until we all got 'used' to the problems inherent in such searches.

Another reason that I had initially decided to avoid them is that there is somewhat of a precedent. Both of the original Riesel and Sierpinski problems stated that it had to be odd k, i.e. eliminating the multiple of the base; in their case, 2. I don't want to claim that I know the exact history involved in why Mr. Riesel and Mr. Sierpinski made the conjectures for only odd k but it seems reasonable to assume that they may have also seen the same types of issues involved with searching even k.

That said, I do not want to ignore the math involved. I completely agree with you that we should not ignore multiples of the base. Therefore, I expect that within the next month, I will create a separate web page for b*k*b^n-/+1 where the expression yields a different prime than k*b^n-/+1 and begin some coordination and searches on those. With that effort, I of course will provide a link to the even Riesel and Sierpinski conjecture threads.

k=19464 for Riesel base 4 was omitted because it is a multiple of the base and you are correct that for k=19464/4=4866 was found to yield a prime at n=1 and so was quickly eliminated. But I will make sure that it is listed in the new page for searches on multiples of the base that yield a different prime.

Thanks for your input and detailed review of the pages. I'm always open to all suggestions for improvement. If you come across another stubborn k that is divisible by 4 for Riesel base 4, let me know because I will keep note of them when creating the new page.

Gary

Last edited by gd_barnes; 2007-12-28, 01:29. Reason: Changed posting link where multiples of base is discussed
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gd_barnes

Join Date: May 2007

Posts: 14017
#14

2007-12-21, 21:51

Powers of 2 on separate page now

I have now put bases that are powers of 2 on separate web pages as well as calculated the conjectures and searched them for all b=q^2 up to base 128. I've also computed the conjectures for base 256 but have not searched them. Riesel base 256 will likely be our next power of 2 base to go after as a team.

Locking the headers on and putting links to sieved files on the pages still to go.

Gary
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gd_barnes

Join Date: May 2007

Posts: 14017
#15

2007-12-24, 05:11

Reservation/status posts moved

I have moved all posts in this thread related to reservations and statuses to that thread.

Gary
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gd_barnes

Join Date: May 2007

Posts: 14017
#16

2008-01-14, 12:02

Multiples of bases now on pages

The project definition and web pages have been updated to include multiples of bases and exclude generatlized Fermat #'s.
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m_f_h

Join Date: Feb 2007

Posts: 432
#17

2008-05-19, 21:34

sorry for posting in spite of feeling somehow clueless about what's going on, but.... according to http://www.rieselprime.org/Liskovets-Gallot.htm
it seems that the remaining k's are all "reserved", is this correct ?

Q2:
for b=27 (Riesel), I see
706 (100K) 706 (available) sieve-riesel-base27-100K-1M.txt
does this mean that if I download that txt, fire up the right proggy and wait some time, then I will enter as celebrity in Math history for having proved that 804 is the smallest Riesel k for base 27 ??
sounds very attractive to me. (sorry if I got it completely wrong...)
PS: I'd like to RTFM, but where is it ?

Last edited by m_f_h; 2008-05-19, 21:35. Reason: formatting
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gd_barnes

Join Date: May 2007

Posts: 14017
#18

2008-05-20, 07:29

Originally posted by m_f_h View Post

sorry for posting in spite of feeling somehow clueless about what's going on, but.... according to http://www.rieselprime.org/Liskovets-Gallot.htm
it seems that the remaining k's are all "reserved", is this correct ?

Q2:
for b=27 (Riesel), I see
706 (100K) 706 (available) sieve-riesel-base27-100K-1M.txt
does this mean that if I download that txt, fire up the right proggy and wait some time, then I will enter as celebrity in Math history for having proved that 804 is the smallest Riesel k for base 27 ??
sounds very attractive to me. (sorry if I got it completely wrong...)
PS: I'd like to RTFM, but where is it ?

Hello mfh, welcome to the effort!

The Liskovets-Gallot web page is outdated right now. Karsten (kar_bon) will update it when he has time. To see updated reservations for ALL bases, see my following reservations web pages. The Liskovets-Gallot conjectures are shown as 'base 2 even n' and 'base 2 odd n'.

Riesel conjectures reservations
Sierpinski conjectures reservations

As for the Liskovets-Gallot reservations, there are technically 4 k's available for Sierp odd-n that have been tested to n=600K but I was planning on reserving them in the next 1-2 days and taking them up to n=800K.

But you are correct on Riesel base 27. If you find a prime for it, you will be celebrated as the person to prove a conjecture, which is a big deal to us here! I'm not sure about the math history thing but it would certainly be important here!

You can take the sieved file and start testing although you may want to see if it needs to be sieved further. The particular file in question might be sieved far enough for n=100K-150K but will likely need to be sieved further if you want to test higher. That's only a guess.

If you have any questions about sieving and how to determine how far a file needs to be sieved before primality testing, let me know. There's plenty of info. in the various threads about different things and everyone is quite helpful around here.

BTW, what is RTFM? Is that some software? I haven't heard of it. We generally use LLR or PFGW here for primality testing although more recently, there is a program that is faster for many bases called Phrot. One of our big testers named Rogue, who has recently proven 2 conjectures with some huge primes, has been using Phrot a lot.

Good luck!

Gary

Last edited by gd_barnes; 2009-07-11, 05:52.
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S485122

Join Date: Sep 2006

Posts: 2173
#19

2008-05-20, 10:48

Originally posted by gd_barnes View Post

BTW, what is RTFM? Is that some software? I haven't heard of it.

If you had searched you would have found "Read The Forgotten Manual". Sometimes another F work is used.

Jacob
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masser

Join Date: Jul 2003

Posts: 2108
#20

2008-05-20, 15:16

Originally posted by gd_barnes View Post

BTW, what is RTFM? Is that some software? I haven't heard of it.

Gary

STFW. GIYF.

Last edited by masser; 2008-05-20, 15:17.
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m_f_h

Join Date: Feb 2007

Posts: 432
#21

2008-05-20, 17:51

Originally posted by gd_barnes View Post

Hello mfh, welcome to the effort!(...)
But you are correct on Riesel base 27. If you find a prime for it, you will be celebrated (...)
You can take the sieved file and start testing although you may want to see if it needs to be sieved further. The particular file in question might be sieved far enough for n=100K-150K but will likely need to be sieved further if you want to test higher. That's only a guess.
If you have any questions about sieving and how to determine how far a file needs to be sieved before primality testing, let me know. There's plenty of info. in the various threads about different things and everyone is quite helpful around here.
We generally use LLR or PFGW here for primality testing although more recently, there is a program that is faster for many bases called Phrot.

Thanks for the heartly welcome & answers.
Thus, reservation / synchronization / job processing is somewhat less automatized here than elsewhere (gimp, riesel & sierpinski p.s.)...
I'll have a look to see if I can get a phrot exec working on my PentiumD or compile it from source. (I hope it will read the same txt file. If I'm not wrong, this ressembles the LLR worktodo formats, but not the ABC format(?))
Yes, I'd appreciate some more tech info about how far to sieve, but I don't want to monopolize you too much ...
OTOH it might be worth while making a "digest" (summary) of such info available in the other threads (and update when concensus or "confirmed results" occur), since AFAICS often opinions diverge (on depth of sieving vs testing, also depending on amd64 vs dual & quad core pentiums etc ; maybe sometimes due to outdated information for some authors).

Concerning the cited base=27, I saw that in spite of some confusion about +1 resp. -1 , it finally seemed to be nevertheless reserved... (now I don't find that thread again :-(!)
or am I wrong ? (just to avoid useless duplication of work...)
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gd_barnes

Join Date: May 2007

Posts: 14017
#22

2008-05-21, 03:04

Originally posted by m_f_h View Post

Thanks for the heartly welcome & answers.
Thus, reservation / synchronization / job processing is somewhat less automatized here than elsewhere (gimp, riesel & sierpinski p.s.)...
I'll have a look to see if I can get a phrot exec working on my PentiumD or compile it from source. (I hope it will read the same txt file. If I'm not wrong, this ressembles the LLR worktodo formats, but not the ABC format(?))
Yes, I'd appreciate some more tech info about how far to sieve, but I don't want to monopolize you too much ...
OTOH it might be worth while making a "digest" (summary) of such info available in the other threads (and update when concensus or "confirmed results" occur), since AFAICS often opinions diverge (on depth of sieving vs testing, also depending on amd64 vs dual & quad core pentiums etc ; maybe sometimes due to outdated information for some authors).

Concerning the cited base=27, I saw that in spite of some confusion about +1 resp. -1 , it finally seemed to be nevertheless reserved... (now I don't find that thread again :-(!)
or am I wrong ? (just to avoid useless duplication of work...)

You can't monopolize me too much. I'm always willing to help as best I can.

Riesel base 27 is NOT reserved and the sieved file for it is just as you saw it on the Riesel reservations web page so feel free to reserve it. Sierp base 27 is reserved by Rogue.

Check out our instructions thread for instructions on all primality testing and sieving software that we use for this project with the exception of Phrot. There is quite a bit of information there but Phrot wasn't in use, to my knowledge, when the project started.

I believe you can use the standard .txt sieved file format for use with Phrot but you might contact Rogue regarding the program.

As for how far to sieve, for a large range of n=100K-1M like is in the file for Sierp base 27, breaking it off in powers-of-2 pieces (i.e. 100K to 100K*2^1, 100K*2^1 to 100K*2^2, etc.) is, I think, the best way to go for primality testing, although you should still sieve the entire file at once. You should sieve until the removal rate is the same as the primality testing (i.e. LLR or Phrot) time at 70% of each break-off n-range.

To put it more clearly for a range of n=100K-1M:

1. Run an LLR or Phrot test for a remaining candidate at n=170K to see how long it takes. Note that we are going to 'break off' the 'piece' of n=100K-200K first and 170K is 70% of this piece.

2. Since you're only running one k-value, use sr1sieve to sieve the entire range of n=100K-1M until the factor removal rate is the same as the testing time in #1. (sr1sieve is the fastest for a single k-value)

3. 'Break off' n=100K-200K and do primality testing on that range.

4. If no prime is found in #3, repeat step 1 for testing a candidate at n=340K (70% of n=200K-400K), step 2 for sieving n=200K-1M, and step 3 for primality testing n=200K-400K.

5. If no prime is found in #4, repeat step 1 for testing a candidate at n=680K (70% of n=400K-800K), step 2 for sieving n=400K-1M, and step 3 for primality testing n=400K-800K.

6. If no prime is found in #5, repeat step 1 for testing a candidate at n=940K (70% of n=800K-1M), step 2 for sieving n=800K-1M, and step 3 for primality testing n=800K-1M.

The above is likely to be several CPU years of work so hopefully a prime will be found somewhere in there. Keep in mind that you can reserve any sub-range you want of this. I might suggest starting out with n=100K-200K or n=100K-400K to start with.

As for what machines to use for testing and sieving, I suggest using the fastest machine you have for primality testing and the fastest machine you have for sieving when making the comparison. Athlon's are very good at sieving. P4's are very good at primality testing. Others can provide more detail as to why and how much.

As for automation: With the tremendous amount of work with so many different bases, it would be even more work to automate every base and would likely be counter-productive, at least until we have more searchers, because our resources would be spread so thin and many would have no work done on them for months at a time. The projects that you are referring to solely concentrate on one specific base and, as such, are more 'closed ended' so to speak, and so have plenty of searchers on them at any one time. This project, while finite in nature, is so much larger than a single base that we need many searchers for just about every base to justify automating everything. Note that each base requires a different server.

With the above said, we do have some automation: We have an LLRnet server set up for Sierp base 6. See this thread for info. about helping us out with that. Also, if you like testing for HUGE primes, we also have a server set up for Sierp base 4 where you can test a single k-value from n=925K-1M (n=1.85M-2M base 2). Check out this thread for info. about that.

We used to have LLRnet servers set up for Riesel base 16 and Sierp base 16 but interest waned. Anonymous and I have continued manually testing the bases and there are manual LLR files available in both of those threads.

If you feel like you'd like to help us with base 16 and would like an LLRnet server to do so, I'm sure I could ask our server guru, Ironbits, to set one up for you. That's where we're at right now. If people request a server to run a specific base or process, Ironbits is glad to set up a server to do so.

There is no specific automatic notification of primes found so you need to check the LLRnet GUI interface or the results file for primes from time to time. Anonymous processes results files and matches them up to the original sieved files to make sure no k/n pair goes untested.

Gary
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m_f_h

Join Date: Feb 2007

Posts: 432
#23

2008-05-22, 05:17

Dear Gary,
thanks again for all that additional info!
I'll try to see what proggies I get to run correctly on my machine, how they perform, and keep you informed as soon as I am ready to seriously reserve something.

Originally posted by gd_barnes View Post

Riesel base 27 is NOT reserved and the sieved file for it is just as you saw it on the Riesel reservations web page so feel free to reserve it. Sierp base 27 is reserved by Rogue.

well at
[URL]http://www.mersenneforum.org/showthread.php?p=133164#post133164[/URL]
I read:

[IMG]http://www.mersenneforum.org/images/statusicon/post_old.gif[/IMG] 09 May 08, 07:48 PM #[URL="http://www.mersenneforum.org/showpost.php?p=133164&postcount=275"][B]275[/B][/URL]

Quote: Originally Posted by [B]rogue[/B] [URL="http://www.mersenneforum.org/showthread.php?p=133156#post133156"][IMG]http://www.mersenneforum.org/images/buttons/viewpost.gif[/IMG][/URL]
[I]OK, then I'll take Sierpinski base 27.[/I]

OK, I'll put you down for Sierp base 27 and Riesel base 26.
Thanks guys.

(ok here it's me who mixed up sierp vs riesel... and before I read KEP's reservation but not the latest msg about him releasing it again + sieve file from the base 3 crunching) - bottom line: better ignore all of that to avoid confusion

Last edited by m_f_h; 2008-05-22, 05:28. Reason: strikethru my misreading
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m_f_h

Join Date: Feb 2007

Posts: 432
#24

2008-05-22, 06:14

Originally posted by gd_barnes View Post

Also, if you like testing for HUGE primes, we also have a server set up for Sierp base 4 where you can test a single k-value from n=925K-1M (n=1.85M-2M base 2). Check out this thread for info. about that.

what do you call HUGE?
These seem far from being 10M digits, which I used to crunch up to now :)
(I started having a look at this since it was definitely the simplest to start with, using crus.ironbits.net:4 - I hope it's OK with my mers'forum username [not as with rieselsieve])

I never got the llrnet-GUI to work on my P.D in spite of some efforts by Anon ; now I unzipped llrnet on some other machine, and it still didn't work, but in fact it works if I launch first the llrnet.exe (w/o GUI) and then, having this running, I launch the remoteGUI.
On that token, I'm trying out this on a quad core (remote desktop server ;-) but during nighttime this should not bother my colleagues too much [I hope...] - tomorrow morning I'll have to move it to my own machine ;)
well, I notice that it's horribly core-swapping. Is there nothing like CPUaffinity setting (for the worker thread) or so in llrnet ?
(not found in clientconfig)

PS: oh, what I wanted to say, I got two WU with even n's - AFAICS this corresponds to base 16. I hope there's nothing wrong with that... (I mean, I hope the k for these n/2 are not crunched by s.o. else in the base 16 subproject) (in fact the even n is used as exp. of 2 so it's an odd n for base 4 - however, the k also is even, so k*2^n = k*4^(n/2) = (k/2)*2^(n+1) ...?)

PPS: the patched client_server.lua from http://www.mersenneforum.org/showthread.php?t=7152 should definitely replace the buggy version in the original distrib.

Last edited by m_f_h; 2008-05-22, 06:54.
Comment
gd_barnes

Join Date: May 2007

Posts: 14017
#25

2008-05-22, 09:34

Originally posted by m_f_h View Post

what do you call HUGE?
These seem far from being 10M digits, which I used to crunch up to now :)
(I started having a look at this since it was definitely the simplest to start with, using crus.ironbits.net:4 - I hope it's OK with my mers'forum username [not as with rieselsieve])

I never got the llrnet-GUI to work on my P.D in spite of some efforts by Anon ; now I unzipped llrnet on some other machine, and it still didn't work, but in fact it works if I launch first the llrnet.exe (w/o GUI) and then, having this running, I launch the remoteGUI.
On that token, I'm trying out this on a quad core (remote desktop server ;-) but during nighttime this should not bother my colleagues too much [I hope...] - tomorrow morning I'll have to move it to my own machine ;)
well, I notice that it's horribly core-swapping. Is there nothing like CPUaffinity setting (for the worker thread) or so in llrnet ?
(not found in clientconfig)

PS: oh, what I wanted to say, I got two WU with even n's - AFAICS this corresponds to base 16. I hope there's nothing wrong with that... (I mean, I hope the k for these n/2 are not crunched by s.o. else in the base 16 subproject) (in fact the even n is used as exp. of 2 so it's an odd n for base 4 - however, the k also is even, so k*2^n = k*4^(n/2) = (k/2)*2^(n+1) ...?)

PPS: the patched client_server.lua from http://www.mersenneforum.org/showthread.php?t=7152 should definitely replace the buggy version in the original distrib.

Some of this is a bit Greek to me. Our techie moderator Anon can help you with any technical questions regarding the LLRnet server(s).

What I can answer: Yes feel free to run our port 4 server on what I called 'HUGE' primes at n=~1.9M+ base 2 (obviously not big for someone who's been testing for 10M-digit primes). I'm sure your user name will be fine. I don't know of any restrictions on user names in the servers except for spaces.

I think I kind of see what you're saying on Sierp base 4 vs. Sierp base 16. On base 16, we are only testing at n=~132K (n=~528K base 2). The only k-value remaining for Sierp base 4 is not remaining for Sierp base 16 so there would between those efforts.

Running the Sierp base 4 LLRnet server would be one of the better ways for you to help us here. There are not too many people here that are fond of such long tests...long by our standards anyway. lol

Gary

Last edited by gd_barnes; 2008-05-22, 16:56.
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