20080831, 13:19  #1 
Sep 2006
Brussels, Belgium
2×5×167 Posts 
EFF prize and error rate
I just queried the v5 database for all LL results for 10M digit mersennes under 33,5M. Some of the figures are not encouraging :
 there where 5684 unverified exponents, 657 of those had two or more unmatched residues for a total of 712 unmatching residues. 12,5 % of bad results.  there where 647 results with error codes, most of the errors codes where bad. 11,4% of possible bad results.  there where 730 verified results and 55 bad results. Some of the verified results have been computed up to 6 times ! The first 10M exponent, 33219281, for instance.) 7,5% of bad results. This compares with an error rate of under 5% on average... It to me seems as if the EFF prize did bring a lot of participants, but a large proportion of them do not have stable hardware (or are to greedy ?) Jacob 
20080831, 17:03  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 

20080831, 22:40  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Perhaps it would be illuminating to compare LL error rates for justunder10Mdigit numbers, which may have fewer fortuneseekers.

20080901, 05:47  #4 
Sep 2006
Brussels, Belgium
11010000110_{2} Posts 
From 32,9M to the last Mersenne under 10M digits the data is not as complete.
The query revealed the following data :  there were 5872 unverified exponents, 65 of the 5937 tests had two unmatched residues for a total of 65 unmatching residues. At least 1,1 % are bad results.  there were 180 results with error codes, only 4 "FF" error counts. 3,0% are possible bad results.  there were 113 verified results concerning 55 different exponents and 0 confirmed bad results so far. There is less data, but one comparison can be made : the rate of tests with error codes for the first 10M digit exponents is about 4 times higher. Jacob Last fiddled with by S485122 on 20080901 at 05:51 Reason: (Hoping this post contains less embarassing spelling errors. As for the syntax ... At least I try.) 
20080901, 15:50  #5 
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Mightn't the tests just above 33219280 have been performed, on average, on older and slower CPUs than the ones just below 33219280? We'd expect a higher error rate among tests that take longer, all else being equal.
Any one have data on whether new CPUs nowadays are less errorprone per unit of time (or per, say, quadrillion CPU cycles) than new CPUs were a few years ago? Can we compare error rates for tests just above 33219280 (I'm trying to memorize this number :) to tests reported around the same dates for the thenleadingedgebelow10M LL tests? Last fiddled with by cheesehead on 20080901 at 15:54 
20080901, 16:01  #6 
Bemusing Prompter
"Danny"
Dec 2002
California
2·3·397 Posts 
Even if the error rate is quite high, the chance of an error generating a perfect residue of 0 is very, very low. Any error that occurs will most likely just change the residue to another nonzero residue.
Last fiddled with by ixfd64 on 20080901 at 16:04 
20080901, 16:05  #7 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 
But the change of an error missing a perfect residue of 0 is higher.

20080901, 17:11  #8  
Sep 2006
Brussels, Belgium
2×5×167 Posts 
Quote:
Jacob 

20080902, 06:02  #9  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Quote:
Last fiddled with by cheesehead on 20080902 at 06:06 

20081224, 16:58  #10 
Sep 2006
Brussels, Belgium
686_{16} Posts 
Error rate per exponent range
I just compiled a spreadsheet with the error rates per range. My hypotheses about the bad influence of the EFF prize stands.
Do not conclude to quickly that from 18M upwards he error rate goes down dramatically : the unconfirmed results contain many results that will turn out to be bad. Jacob 
20081225, 15:28  #11 
Sep 2006
Brussels, Belgium
2×5×167 Posts 
Error rate per exponent range
I completed the analyses. There are new columns in the spreadsheet containing the minimum number of residues that will turn out bad once the double check is complete.
The average error rate in the finished (and almost finished) ranges seems to drop a bit, to just less than 10% after a peak of 11,1% at 15M. Among the ranges for which there is not much data the 33M and 34 M spring out. The number of “surnumerary”^{*} residues is already very high. I stand by my conclusion that a lot of overclockers tried to win a quick buck, without realising what the job represents. Jacob * Not an English word but I mean something like “residues to many” : there is only one correct residue per exponent. 
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