20050313, 13:57  #67 
Mar 2004
Belgium
29^{2} Posts 
Range: 333600000 333699999
from 1 => 50 bit depth complete. 
20050313, 21:23  #68 
"Curtis"
Feb 2005
Riverside, CA
2^{3}·5^{4} Posts 
Reserving 332193431 and 332193457 for "deep" searching (likely 67 bits).
Curtis 
20050314, 07:25  #69 
Mar 2004
Belgium
29^{2} Posts 
Code:
333400000 333499999 333500000 333599999 
20050314, 07:42  #70 
Mar 2004
Belgium
29^{2} Posts 
Correction:
I will take these ranges from 1 to 50 bit depth 
20050314, 07:45  #71 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
17·19·31 Posts 
Hold on, I have the results of those to that depth. I am working on a site update at this very mo. Check back in tomorrow for a full update.

20050315, 01:41  #72 
Oct 2004
23^{2} Posts 
Uncwilly, I think you have at least mostly understood my request. Thanks for trying to help me.
Cheesehead: thanks for repeating the general approximation formula from elsewhere. However this is precisely what I'm NOT satisfied with. As we only test primes as potential factors of mersenne candidates, we ignore all nonprime numbers. ie ignore Even ones obviously and also those we already established are composite. This means that in a given range of numbers we do not even begin trial factoring a number because it's not going to be what we look for. So in part, the probability of finding a factor when searching all exponents in a range A to B depends on the distribution of mersennes within that range. The distribution will determine how many there are to test. This in itself skews the probability. Then my major problem was that we might say in a range I found 20 factors, but have not counted up those numbers where no factor was found. Also expending more effort to TF deeper bit level makes it more likely to find a factor. As I understand it the current prime95 client makes a choice of what bit depth it will be worthwhile based on relative effort of its TF vs LL. Now, what if a modified algorithm or project had a better or worse TF/LL ratio. The optimal cutoff would therefore be somewhere else (more or less bits of factoring effort). I've read discussion elsewhere about actual calculations using the formula cheesehead put forward  using combinatorial probability rules for each bit depth. ie the probability of finding a factor from 2^63  2^68 has to take into account that someone already did testing from 2^3 up to 2^62 finding nothing. As a result I was trying to build a computer model or algorithm which would do this properly and very accurately. Since the TF/LL ratio varies between client architectures (eg SSE2) and even at different bit depths eg P4 above 2^64 uses SSE2 so is fast but below is slow. Therefore I wanted to benchmark factoring on a given machine then use these speeds combined with the PROPER probability results. For example prime95 can do factoring but so can Factor3_2. I have benchmarked these on various size numbers eg 10million digits, 100million digits, billion digits range etc. (up to a given bit depth anyway). I am hoping to obtain some of the data on probability of discovering a factor in a test from empirical research eg in your project. As I pointed out, I need to know a test was tried even if unsuccessful in discovering a factor. I hope the above gives some insight to my motivation. I will look on the website for any useful info you post there. Thankyou. 
20050315, 06:38  #73  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
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20050315, 06:53  #74  
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Quote:


20050315, 17:47  #75  
"William"
May 2003
New Haven
2^{6}×37 Posts 
Quote:
Thus the 1/n is not merely empirical observation  it is the expected result for random factors, and for sufficiently large factors Mersenne numbers are empirically observed to behave randomly. 

20050317, 22:25  #76 
Mar 2004
Belgium
349_{16} Posts 
Results:
Code:
333400000 333499999 5021 5021 . . in progress Done from 1 to 50 bit depth 333500000 333599999 5073 5073 . . in progress Done from 1 to 50 bit depth 333600000 333699999 5127 5127 . . Done from 50 to 52 bit depth 
20050318, 05:27  #77  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
(Memo to self: read more math FAQs.) 

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