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Old 2007-12-21, 14:55   #12
Jean Penné
 
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Default 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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Old 2007-12-21, 17:15   #13
gd_barnes
 
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Quote:
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 fiddled with by gd_barnes on 2007-12-28 at 01:29 Reason: Changed posting link where multiples of base is discussed
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Old 2007-12-21, 21:51   #14
gd_barnes
 
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Default 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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Old 2007-12-24, 05:11   #15
gd_barnes
 
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Default 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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Old 2008-01-14, 12:02   #16
gd_barnes
 
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Default 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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Old 2008-05-19, 21:34   #17
m_f_h
 
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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 fiddled with by m_f_h on 2008-05-19 at 21:35 Reason: formatting
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Old 2008-05-20, 07:29   #18
gd_barnes
 
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Quote:
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 fiddled with by gd_barnes on 2009-07-11 at 05:52
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Old 2008-05-20, 10:48   #19
S485122
 
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Quote:
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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Old 2008-05-20, 15:16   #20
masser
 
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Quote:
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 fiddled with by masser on 2008-05-20 at 15:17
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Old 2008-05-20, 17:51   #21
m_f_h
 
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Quote:
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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Old 2008-05-21, 03:04   #22
gd_barnes
 
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Quote:
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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