Extending the database/limits of GIMPS

[NBtarheel_33]

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 billion-digit 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 billion-digit 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 built-in limitation on Prime95, or the fact that 1,000,000,009 isn't in the GIMPS database.

[Mini-Geek]

Originally Posted by NBtarheel_33

Has there been any work done between 1,000,000,000 and the first billion-digit 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 built-in limitation on Prime95, or the fact that 1,000,000,009 isn't in the GIMPS database.

That was just PrimeNet saying the assignment wasn't necessary, not Prime95 saying it couldn't do it. Prime95, IIRC, can handle exponents up to ~2 billion (this means that for the DB to include larger assignments, Prime95 would have to be modified or not used). For factoring on larger numbers, like the OBD candidates, there's Factor5.
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 future-proof 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.

[ET_]

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

[cheesehead]

Originally Posted by NBtarheel_33

Now that every exponent

between 8247300 and

1 billion has been TFed to at least 64 bits,

[wedgingt]

Originally Posted by ET_

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

What email address are you trying to use for me? wedgingt@garlic.com and wedgingt@acm.org should both work; others can be problematic. I rarely have time for forums, so email is better, but I did finally register here yesterday.

-- Will
http://www.garlic.com/~wedgingt/mersenne.html

[Mr. P-1]

Originally Posted by NBtarheel_33

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 billion-digit candidates)?

Alternatively, or perhaps additionally, how about expanding PrimeNet support for continued factorisation of already-factored Mersennes? In this post, I gave the example of M8000053, which has a 27 bit factor, undoubtedly discovered long ago by TF. Additional TF, P-1, or ECM might yield more factors. Unfortunately, the database doesn't tell us how much TF beyond 27 bits or P-1, if any, has been done on this number. Nor does it tell us whether any primality or PRP tests have been done on the cofactor

[wedgingt]

Originally Posted by Mr. P-1

Alternatively, or perhaps additionally, how about expanding PrimeNet support for continued factorisation of already-factored Mersennes? In this post, I gave the example of M8000053, which has a 27 bit factor, undoubtedly discovered long ago by TF. Additional TF, P-1, or ECM might yield more factors. Unfortunately, the database doesn't tell us how much TF beyond 27 bits or P-1, if any, has been done on this number. Nor does it tell us whether any primality or PRP tests have been done on the cofactor

Primenet and GIMPS seem to be interested only in Mersenne Primes and, to a much lesser extent, complete factorizations of the smallest Mersenne numbers.

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, P-1, 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

[wedgingt]

Originally Posted by NBtarheel_33

Has there been any work done between 1,000,000,000 and the first billion-digit 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 built-in limitation on Prime95, or the fact that 1,000,000,009 isn't in the GIMPS database.

The data I have includes lots of information about these larger exponents ... and about exponents considerably higher. There was some effort a while back to try to find factors of "repeated" Mersenne numbers like MM127 = M(M(127)), for example.

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.

[cheesehead]

Originally Posted by wedgingt

This includes known "gaps" in the trial factoring data, including due to bugs in prior versions of Prime95 and other (including my) programs.

Where should I look to find your data on those TF gaps?

[wedgingt]

Originally Posted by cheesehead

Where should I look to find your data on those TF gaps?

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 P-1 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