20101025, 07:55  #1 
"Nathan"
Jul 2008
Maryland, USA
3×7×53 Posts 
Extending the database/limits of GIMPS
Now that every exponent under 1 billion has been TFed to at least 64 bits, leaving many folks searching for work for their older machines, and seeing the proliferation of GPU TF contributions to GIMPS, as well as the continued work over at the One Billion Digits project, is it perhaps time to again extend the limits of the GIMPS database to include exponents beyond 1 billion, say up to 4 billion (which would include a good number of billiondigit candidates)?
It seems as though this would (1) facilitate uniform tracking of results between GIMPS and OBD, while allowing OBD participants to make use of PrimeNet and receive GIMPS credit, (2) open up a vast new range of work for older machines and GPUs (think of how many exponents there are between 1B and 3.32B (OBD territory) that have had essentially no TF), and (3) ensure that GIMPS/PrimeNet is the premier repository for data on LL test results and factors of Mersenne numbers for the foreseeable future (and then some!). Has there been any work done between 1,000,000,000 and the first billiondigit candidate? I tried telling Prime95 to TF 1,000,000,009 and it balked, saying the assignment wasn't necessary, though I suspect that has to do with either a builtin limitation on Prime95, or the fact that 1,000,000,009 isn't in the GIMPS database. Last fiddled with by NBtarheel_33 on 20101025 at 07:57 Reason: Factors of Mersenne primes *d'oh* I mean Mersenne numbers! 
20101025, 11:46  #2  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:
Also: M1000000009 has a factor: 350544003154897 350544003154897 is 49 bits. 350544003154897=2*175272*1000000009+1 k=175272=2^3 * 3 * 67 * 109 As for the actual subject...I think that preliminary work ahead of the leading edge, except for when you plan to do an LL right away on that particular number, is quite inefficient, and shouldn't be encouraged (but, like OBD, if someone wants to do it anyway, there's no good reason to stop them). On the other hand, I agree that extending the bounds would futureproof the PrimeNet DB to keep it the best central source of Mersenne number info, and help out the OBD project by letting it use that to record results and coordinate work. But they (unless I'm mistaken) keep TFing exponents with known factors, which PrimeNet doesn't allow. So it might not be a perfect solution from that point of view. Last fiddled with by MiniGeek on 20101025 at 11:53 

20101025, 13:46  #3 
Banned
"Luigi"
Aug 2002
Team Italia
13·367 Posts 
Apart from PrimeNet, one of the best sources for Mersenne factors is Will Edgington's Mersenne Page.
Sadly, he seem to have changed his email, and I just can't send him our new found factors. As per your idea of PrimeNet extension, it would be wonderful in some years' time, but not now: data is still too sparse, in my opinion. And remember that George's private database has mostly all information about Mersenne numbers... Luigi Last fiddled with by ET_ on 20101025 at 13:47 
20101026, 02:14  #4 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×599 Posts 

20101126, 19:33  #5  
"Will Edgington"
Nov 2010
Utah, USA
2^{3}·3 Posts 
Quote:
 Will http://www.garlic.com/~wedgingt/mersenne.html 

20101126, 20:29  #6  
Jun 2003
1169_{10} Posts 
Quote:
Last fiddled with by Mr. P1 on 20101126 at 20:30 

20101127, 23:11  #7  
"Will Edgington"
Nov 2010
Utah, USA
11000_{2} Posts 
Quote:
On the other hand, I have been retaining all data related to Mersenne numbers for many years now and running my own Mersenne related programs for over 20 years now. My data includes what I've done or been told about in terms of how much trial, P1, and ECM factoring has been done, SPRP tests of cofactors, etc., for composite exponent as well as prime exponent Mersenne numbers. This includes known "gaps" in the trial factoring data, including due to bugs in prior versions of Prime95 and other (including my) programs. See my web site for much of the data that I have, at least for prime exponents. I haven't had a lot of time for this lately, but a few people still send me new data routinely.  Will Edgington http://www.garlic.com/~wedgingt/mersenne.html 

20101127, 23:59  #8  
"Will Edgington"
Nov 2010
Utah, USA
2^{3}×3 Posts 
Quote:
For exponents between the GIMPS limit and the OBD interest, I have 659297 lines of data for prime exponents; 658724 of those are factors. The other lines are all trial factoring limits for exponents near powers of two or multiples of large powers of 10. 

20101128, 19:28  #9 
"Richard B. Woods"
Aug 2002
Wisconsin USA
1110000010100_{2} Posts 

20101129, 06:19  #10 
"Will Edgington"
Nov 2010
Utah, USA
2^{3}×3 Posts 
The detailed data for the gaps is too large and changing to put on my web site, unfortunately. One of my computers is trying to close them as well as do SPRP of the smallest cofactors when new factors are found and do P1 and P+1 of the smallest composite cofactors.
The gaps & "joins" data is 1.8 GB presently. If you are interested in a particular exponent range, let me know and I'll see how much data that is. I can provide it in the "mers format" described on my web site or Prime95's worktodo.ini form; the smallest such gaps (in terms of the count of trial factors to close them) as of the 26th are appended but have likely already been closed by my computer. Also, note that the current version of Prime95 does not support this particular worktodo.ini format and it is imprecise since the start and end of any gap must be expressed as a power of two.  Will M( 333108899 )G: 36893488147419103232 36906115965890622881 M( 78747623 )G: 18446744073709551616 18450779679670020847 M( 85258253 )G: 18446744073709551616 18455991244270642297 M( 87657937 )G: 18446744073709551616 18462641129975539919 M( 72115151 )G: 36893488147419103232 36907425532122538489 M( 125596769 )G: 18446744073709551616 18471237005063409199 M( 120577403 )G: 18446744073709551616 18475614710353037177 M( 87585689 )G: 18446744073709551616 18472364893748042023 M( 77321987 )G: 18446744073709551616 18472695085247377801 M( 86028997 )G: 18446744073709551616 18476560532162118823 AdvancedFactor=35175541,35175541,54,56 AdvancedFactor=70351031,70351031,51,57 AdvancedFactor=70351027,70351027,51,57 AdvancedFactor=70351003,70351003,51,57 AdvancedFactor=35175433,35175433,54,56 AdvancedFactor=70350829,70350829,51,57 AdvancedFactor=70350823,70350823,51,57 AdvancedFactor=70350817,70350817,51,57 AdvancedFactor=35175407,35175407,54,56 AdvancedFactor=70350773,70350773,51,57 
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