20171129, 20:07  #1 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
3·1,657 Posts 
Double checking of Results
....was wondering if we need to double check below 4000e15.
Last fiddled with by robert44444uk on 20171130 at 08:01 
20171129, 21:58  #2 
Jun 2015
Vallejo, CA/.
1011_{10} Posts 
That work was done by Tomás Oliveira e Silva of Aveiro University. While he only double checked randomly 400 x 10^{15} subranges or 10% of the 4000 x 10^{15} subranges, he contrasted the number of Primes discovered against the number of primes π(n) obtained by variants of the MeisselLehmer algorithm. In all 4000 intervals there was no discrepancy at all.
Last fiddled with by rudy235 on 20171129 at 22:03 
20171129, 22:18  #3 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
3^{2}×101 Posts 
It would be a possibly useful double check on our program, but perhaps best done as spot checks rather than duplicating the whole thing.

20171129, 23:07  #4  
Jun 2015
Vallejo, CA/.
3·337 Posts 
Quote:
We have 6000 e15 subranges. We could chose 600 e15 random ranges, I believe Mathematica has a Random Number Generation, and test them, stipulating that no one would check it's own work. That would go a great length to guarantee the soundness of this work. Last fiddled with by rudy235 on 20171129 at 23:20 

20171130, 00:58  #5 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
1110001101_{2} Posts 
Seems like a new thread for this makes sense. This is going far off topic.
I was thinking just check around windows of the gaps < 4e18. Our program should find the gap. I'm unsure as to the value but it is cheap as long as the windows are reasonably sized. For the spot check of *our* results, we could do the same (but I see no point), but what we probably want is checking that the recheck finds the same gaps as the original. Alternately as you suggest just do random ranges. What you want is random selections without duplication, which can be done using Perl/ntheory's randperm, Mathematica's RandomSample, numpy's choice (though it can easily blow up in time and memory), and more. Ensuring no double check of own work is probably manual with our current nonautomated methods. In theory it'd seem like we'd also want more like "a random 10% of each partipants work" rather than completely random, or we will likely do no double checking of some people's work. While it'd be nice to have full results from everything already done, I'm not sure how many people sent that info. What I believe we do have is the "largest gap" for reasonably sized subranges, so one could go through all the results and turn them into [version, parameters, expected value(s), participant id] tuples for small chunks. Version here is distinguishing between the "A,B" ranges vs. "A,B,M1,M2" modulo ranges. Then it would be reasonable to do the sampling from that set and assign the double checks easily enough. 
20171130, 03:03  #6 
Jun 2015
Vallejo, CA/.
3×337 Posts 
Danaj : if you feel this requires a new thread perhaps you could open a new one. I do have some comments of my own but I will keep then in pectore for the time being.

20171130, 07:54  #7 
Jun 2003
Oxford, UK
7A5_{16} Posts 
The weakest element of our work:
All of these weaknesses make the job of double checking hard because even if an error is found it may not impact the first instance gaps we find i.e. the robustness of the 25 or so gaps of this nature found to date and most will relate to the 3rd element listed above. The most critical error would be if there is a hole in the logic for Robert G's program, which would lead to systematic errors requiring a total recheck of the range. The program has been looked at in detail by any number of people so I have not listed this as a weakness. If there was one it would most likely relate to the way ranges are stitched together (is this guaranteed seamless?); to the changing of program variables during the testing of a range; or the generation of the "worktodo" file in stressful situations such as power cuts. Automating the reporting would go a long way to overcoming most of the weaknesses I have listed. There are 234,057,667,276,344,606 prime gaps below 10e18. I for one will want to leave these be for now! Onwards and upwards! 
20171130, 16:32  #8 
Jun 2015
Vallejo, CA/.
3F3_{16} Posts 
My principal concern lies with the fact that probably nobody will audit the results ever.
In other words if (for example) the gap 1382 lies somewhere among the 6e18 and 10e18 and we have let it slip then when someone does find it at a higher range and an exhaustive search is done this find will go as a CFC, when it might simply be just a simple gap without much significance i.e. the second (or worse third) occurrence of a specific gap. Of the many elements mentioned by Robert S I can only comment this. As to the intentional forging of data I truly don't believe that to be a major concern. There is almost no benefit in doing that. Any record will be checked by both Robert S and (presumably) Dr. Nicely and checking this is very easy to do. So, only the intentional omission of a find could be done without the chance of being found out. But what benefit would that do to the culprit? The other comment by Robert S does seem to be more pertinent. The lack of a centralized data repository I hope something can be done about this. 
20171130, 18:00  #9 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
3^{2}·101 Posts 
Robert: The weakest element of our work:

20171201, 07:31  #10 
Jun 2003
Oxford, UK
19×103 Posts 

20171208, 22:15  #11 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
3×1,657 Posts 
Out of cutiosity, are we going to search beyond 16950e15?
Last fiddled with by pinhodecarlos on 20171208 at 22:16 
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