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2008-09-10, 16:45   #562
R.D. Silverman

Nov 2003

11101001001002 Posts

Quote:
 Originally Posted by Fusion_power There is no current efficient implementation of a factoring algorithm that works near the sqrt (Mp). DarJones
What does it mean for a factoring algorithm that "works near the sqrt (Mp)".
Do you mean test numbers that are ~sqrt(M_p) as potential divisors?
I suggest that you count the size of this set... If you don't mean trial
division, what do you mean? I also suggest that you study Dickman's
Function.

Do you mean a difference of squares algorithm? This method works
when the divisor is very close to the sqrt of the composite being factored.
If so, I suggest you estimate the number of steps it will take to
succeed on even a modestly sized Mersenne number.

If you mean something else, then I haven't the foggiest notion of
what it could be...

 2008-09-10, 16:47 #563 jinydu     Dec 2003 Hopefully Near M48 110110111102 Posts I step away from the forum for less than 10 hours and flaming starts... At least it appears to have subsided a bit. How is Gilchrist's verification of MSept going? Last fiddled with by jinydu on 2008-09-10 at 16:49
2008-09-10, 16:49   #564
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by T.Rex Bob, knowing more Merseonne primes is also interesting in order to check if the observed repartition of Mersenne primes is following the expected (but not proved) Poisson process, with the 1/e^gamma slope. Tony

The process might be truly Poisson. But a small set of observations
can neither confirm nor deny it. Statistical goodness-of-fit tests are
woefully weak. And finding (say) more/less primes than expected in one
interval doesn't say much. We are still a long way from oo.

2008-09-10, 16:51   #565
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by T.Rex Verifying these numbers with big machines with many cores is also a way to measure how efficient are both the software FFT-parallelizing techniques and the machine scalability. Tony
But this is an inefficient way to use these machines. The best way is to
run separate tests on separate processors. And we can test parallel
FFT's without testing M_p.

2008-09-10, 16:56   #566
R.D. Silverman

Nov 2003

1D2416 Posts

Quote:
 Originally Posted by Orgasmic Troll I'm satisfied with this answer, I stopped running the GIMPS client years ago for similar reasons. However, the prize money is not meant to further new research, "The Electronic Frontier Foundation (EFF), the first civil liberties group dedicated to protecting the health and growth of the Internet, is sponsoring cooperative computing awards, with over half a million dollars in prize money, to encourage ordinary Internet users to contribute to solving huge scientific problems"
I approve of the stated goals of EFF. Now reduce my ignorance.
Tell me the scientific (or even mathematical) problem that is being solved
by actually finding Mersenne Primes.......

2008-09-10, 17:04   #567
rgiltrap

Apr 2006
Down Under

89 Posts

Quote:
 Originally Posted by Prime95 This is probably the cutting edge of Mersenne research now. Maximizing the efficiency of parallel FFTs would have wide-spread benefits. Will we (Ernst, myself, Guillermo, Tony, etc.) be the ones to make improvements in the area? Maybe, maybe not, but it does show why continuing a "not important" search for Mersenne primes could turn out to be unexpectedly useful.
For the Mlucas compiles on Solaris (both SPARC & x64) we're using the SunStudio C compiler (which generally gives a nice boost over GCC). Being at the cutting edge has meant we have identified two new obscure bugs in SunStudio. One has already been resolved that affects inline assembler optimizations on x64 systems.

Sorting these bugs out paves the way for more "important" HPC activities and also allows us to continue to push the boundaries further and further.

2008-09-10, 17:06   #568
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

2·4,597 Posts

Quote:
 Originally Posted by R.D. Silverman Now reduce my ignorance. Tell me the scientific (or even mathematical) problem that is being solved by actually finding Mersenne Primes.......
"How many MP's are there? What is their disribution pattern? What more can we learn by knowing more about them?"

Remember that data sets are important to the developement and testing of theories. Field researchers gather data that others use. GIMPS is gathering data. Known factors of M#'s are also a nice data set. By trying to eliminate those with small factors (so that LL tests are not done), a nice side data set is generated.

Last fiddled with by Uncwilly on 2008-09-10 at 17:06

2008-09-10, 17:06   #569
ewmayer
2ω=0

Sep 2002
República de California

2×5,791 Posts

Quote:
 Originally Posted by R.D. Silverman But this is an inefficient way to use these machines. The best way is to run separate tests on separate processors. And we can test parallel FFT's without testing M_p.
The whole point is to try to make it *more* efficient than it has been - and I would say that getting 10x speedup running in || on 16 processors is not that inefficient - at my work they are happy to get 4x for their logic-placement code on 16 CPUs.

Sure, running in || is generally less efficient in terms of total throughput than single-threaded - but it's precisely situations like the M-prime verify runs, "when you really want the answer as quickly as possible" [a concept the commercial software industry understands very well] that || applications are appropriate.

As to your "there are other ways to test parallel FFTs" statement - sure there are, but it seems the cutting-edge work in this area is mostly being done by the "amateurs" around here. Your own major field of interest, NFS factoring, could be described similarly - "there are other ways to test massively parallel linear algebra routines than via NFS". Does that mean the NFS folks should simply give up coding and let someone else show them how it's done?

"Other ways" does not equate to "better ways."

And "No billion-dollar industrial application" does not equate to "not worth spending time on".

As a working mathematician and computational number theorist, I would expect you of all people to embrace doing something interesting without an immediate prosect of monetary gain.

2008-09-10, 17:15   #570
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Uncwilly "How many MP's are there? What is their disribution pattern? What more can we learn by knowing more about them?" .

Finding a small set of Mersenne Primes through calculation does nothing

2008-09-10, 17:17   #571
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by ewmayer As a working mathematician and computational number theorist, I would expect you of all people to embrace doing something interesting without an immediate prosect of monetary gain.
I thought that this was the point I was making!!!!

GIMPS should be run without any monetary gain.

 2008-09-10, 17:23 #572 Housemouse     Feb 2008 25 Posts Importance of prize money I think it will be interesting to see if there is a significant decrease in throughput after the 10M digit is confirmed. I think decrease will be less than 5%.

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