20080910, 16:45  #562  
Nov 2003
1110100100100_{2} Posts 
Quote:
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... 

20080910, 16:47  #563 
Dec 2003
Hopefully Near M48
2×3×293 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 20080910 at 16:49 
20080910, 16:49  #564  
Nov 2003
2^{2}×5×373 Posts 
Quote:
The process might be truly Poisson. But a small set of observations can neither confirm nor deny it. Statistical goodnessoffit 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. 

20080910, 16:51  #565  
Nov 2003
16444_{8} Posts 
Quote:
run separate tests on separate processors. And we can test parallel FFT's without testing M_p. 

20080910, 16:56  #566  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Tell me the scientific (or even mathematical) problem that is being solved by actually finding Mersenne Primes....... 

20080910, 17:04  #567  
Apr 2006
Down Under
59_{16} Posts 
Quote:
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. 

20080910, 17:06  #568  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
9,341 Posts 
Quote:
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 20080910 at 17:06 

20080910, 17:06  #569  
∂^{2}ω=0
Sep 2002
República de California
2·7·829 Posts 
Quote:
Sure, running in  is generally less efficient in terms of total throughput than singlethreaded  but it's precisely situations like the Mprime 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 cuttingedge 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 billiondollar 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. 

20080910, 17:15  #570 
Nov 2003
2^{2}·5·373 Posts 

20080910, 17:17  #571  
Nov 2003
2^{2}×5×373 Posts 
Quote:
GIMPS should be run without any monetary gain. 

20080910, 17:23  #572 
Feb 2008
40_{8} 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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