20100127, 05:42  #1 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
1010001100000_{2} Posts 
Double check of factoring??
I understand that LL/DC errors (i.e. incorrect results) are generally caused by hardware errors.
Is it not possible, likewise, for similar hardware errors to cause invalid factor results; i.e. reporting a factor when there really isn't one and thereby eliminating the exponent from LL/DC, erronously? 
20100127, 05:51  #2 
Aug 2002
North San Diego County
2E6_{16} Posts 
IIRC, the server checks the validity of the factor when reported.

20100127, 06:00  #3 
Aug 2006
3×1,993 Posts 
It's easy to check that the submitted factors are correct. The only kind of error you'd need to worry about is that no factor is reported when there is, in fact, a small factor. But even then the only cost is that the number will need to be LL'd.

20100127, 07:39  #4  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Quote:
Last fiddled with by cheesehead on 20100127 at 07:44 

20100127, 18:34  #5  
If I May
"Chris Halsall"
Sep 2002
Barbados
3^{2}·5^{2}·47 Posts 
Quote:
This will detect false positives, but not false negatives... 

20100127, 19:00  #6 
"Richard B. Woods"
Aug 2002
Wisconsin USA
7692_{10} Posts 
... which is exactly what the OP meant by "i.e. reporting a factor when there really isn't one and thereby eliminating the exponent from LL/DC, erronously", which I quoted in my reply. :)
Last fiddled with by cheesehead on 20100127 at 19:45 Reason: New Year's resolution: Remember the [strike]Alamo[/strike][strike]Maine[/strike] emoticons! 
20100127, 19:06  #7  
If I May
"Chris Halsall"
Sep 2002
Barbados
10575_{10} Posts 
Quote:
But... a LL is *very* expensive. Thus, while a false negative won't allow a prime to be missed, it would waste resources. I have always wondered why Prime95 doesn't return a residual for factoring work which could only be produced by doing the full amount of work without error. This would allow "spot checks" of factoring producers (at least, those using Prime95), which was the point I was trying to make. 

20100127, 19:41  #8  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
2×3×23×31 Posts 
Quote:
Let's say you've got hardware that has a 2% chance of a single error over 30 days of work (be it TF or LL). For simplicity's sake, we'll assume an error on a TF always produces a negative for the factor being checked. Let's say you make one computation error during a TF to 2^64. There's a 1/64th chance (assuming http://www.mersenne.org/various/math.php is right) of there being a factor anywhere in there. According to http://mersennearies.sili.net/throughput.php?cpu=AMD+Athlon%28tm%29+64+X2+Dual+Core+Processor+4800%2B5120&mhz=2500, there are about 1,136,364 TF iterations in that range. I'm not sure if 1 iteration=1 factor, but let's assume so. So there's about a 1/(64*1,136,364) chance that the one computation error was during a factor, rendering a false negative. That's a 0.000001375% chance of a missed factor for every error your computer makes. And this CPU could do about 389 TFs to 2^64 per 30 days. That means that there's a 2% chance that one out of 389 TFs would have a tiny chance of a missed factor, or a 0.000000000275% chance of a missed factor. Unless I'm making some false assumptions, or have done something really stupid here, I'd say that's well worth the risk, despite the large cost difference between LL and TF. 

20100127, 20:31  #9  
If I May
"Chris Halsall"
Sep 2002
Barbados
294F_{16} Posts 
Quote:
These were only found by way of statistical analysis (and perhaps this is the most optimal way  I don't know). But I stand by my argument that it *might* be good if the Prime95 client returned a unique residual even for TF work. After all, if LL and DC work fails to execute deterministically on the CPUs out there, surely TF (and P1 and ECM) work does as well? And I'm not arguing for a standard "Doublecheck" of TF work. Simply the ability to do so for participants and/or machines which *might* be questionable. After all, a single bad machine can result in *many* bad results. And a bad participant can result in many *many* bad results. Those far more learned than myself might be able to speak to this question more deeply. Last fiddled with by chalsall on 20100127 at 20:41 Reason: Added "And I'm not aruging... 

20100127, 20:55  #10  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
What if there's a computation error affecting the increment between candidate factors or the screeningout of candidates divisible by small primes? Then one error could affect many candidates by causing large numbers of potential factors not to be tested. Up to a whole bit level  zillions of candidates  could be erroneously reported negative, when not a single candidate on that level was actually tested. My guess is that there is much less chance that a single error systematically affects large numbers of candidates than that it affects only the test of a single candidate. But that smaller chance should be multiplied by the large number of candidates affected if it happens, to properly judge the impact. 

20100127, 21:09  #11 
Jul 2006
Calgary
110101001_{2} Posts 
I'd think the (slim) chance of accidental false negatives wouldn't warrant massive double checking. The subsequent LL test(s) will settle the matter of primality after all. Only if you're keen to find factors of known composites would it be of interest.
Also the P1 and ECM searches seem to perform an implicit check for missed factors. If there is systematic false negatives either a bug or fraud, they should show up in statistics I think since the odds of finding factors are fairly well known aren't they? If there's any statistical outliers by account or by program/version then rechecking a sampling might be warranted. 
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