Double checking discussion thread

[philmoore]

I have started a new sticky thread for double checking reservations. Double checking of the sequence 2ⁿ+40291 is currently complete for all n up to 1.25 million, with matching residues in every single case. Ben has run a few double checks of my ranges beyond that, as I was planning to quietly continue this work on the ranges I had not checked the first time, but Geoff recently requested some double checking work, so it seemed like a good time to start a new thread to coordinate everything.

That said, I still consider this work fairly low priority at the moment. We ran some sample double checks in the range 1.25-5.01M last year, and detected an error rate that seemed most likely to be a little under 1%. I would like to run some more sample double checks when we get up to around 7 million in first time checks, but since the range 0 to 2 million is no longer being sieved, it might make more sense to work in this lower range and let the sieving continue a bit further before taking up the second round of sample double checks. There is a discussion of the sample double checking results in the PRP discussion thread, and the conclusion was that most of the errors seemed to be coming from two computers. If you are running more than one computer, it may be helpful to assign unique computer ids to each one, so that if problems do surface, we know which tests should have priority for double checking.

Even lower priority, but still an eventual possibility, is double checking the four sequences in which we have already discovered probable primes. There is a small, but positive probability that we could have missed a smaller one, so if anyone wishes to explore that, feel free to post a reservation in that thread, and I can send you a work file. But indications so far are that my early work was pretty accurate, so finding a smaller one would really take a stroke of luck.

[Cybertronic]

Hello, why me make a double ckeck ? For what ?
Today , this numbers we can't prove and in few years we can maybe double checking this in few weeks.

Is it not better to search for higher PRPs ?

The two tiny numbers was maybe an inattation by the searcher.
Double checking only if we found an old PRP program , what say "is composite" instead of "3-PRP!".
My opinion.

[philmoore]

We certainly do have an error rate in our residues returned so far, although it appears to be low, perhaps a bit less than 1%. The main idea of double checking is that if we missed a prime, say of the size 2^2xxxxxx+40291, and the next one is not until 2^64xxxxxx+40291, that it will require far less work to double check this one sequence part way than to search all the way to 64M for example. Don't forget that Seventeen or Bust discovered two of their eleven primes through double checking. And so far, we are only talking about a modest effort that will take a small fraction of the resources that first time checks have taken.

The three small missed primes are a different issue, and very well may have been caused by errors in an early version of pfgw. Now that all of these sequences and prps have been confirmed, except for the six largest, I agree with you that double checking them should be a low priority, but it will eventually be done, hopefully with faster computers than we have now.

[Cybertronic]

Okay, I understand.

[philmoore]

Current status of double-checking is that 75353 and 28433 have been completely double-checked by Justin (enderak), and only 2131, 41693, and 40291 have not been completely double-checked. The effort to double-check these sequences is now being coordinated by PrimeGrid, which has made this their April PRPNet project, using Mark Rodenkirch's PRPNet software. They started 2131 at 1.25M, 41693 at 1.1M, and 40291 at 2.13M, and currently, the leading edge seems to be at 2.29M. It is pretty exciting watching progress go so fast, but sobering also, considering how long it took us! Way to go, PrimeGrid, and thanks to John Blazek and Mark Rodenkirch for setting this up!

[philmoore]

The details, for anyone who wants to participate, are at:

http://www.primegrid.com/forum_thread.php?id=3228
and
http://www.primegrid.com/forum_threa...rap=true#34414

[enderak]

Thanks for the heads up, Phil. I've been waiting for this to get started over there. Their forum seems to be down at the moment, but hopefully there will still be some tasks left in the morning!

With this and the new version of Primo on the horizon, this project might just have some life left in her after all! ;)

[SysadmAtNbg]

Originally Posted by enderak

... Their forum seems to be down at the moment, ...

seems to me you hit the daily downtime at 08:00 UTC

[Dead J. Dona]

Good day all.

Now when llrCUDA is available, and it's known that it's significally faster on larger numbers I want to ask - does somebody tried llrCUDA on this numbers?

[philmoore]

I moved your post to this thread, since llrCUDA does PRP testing, and would be useful for double-checking, but the other thread was more concerned with ECPP testing with Primo to prove that some of our probable primes were actually prime.

Certainly, llrCUDA seems promising, but I am not aware that anyone has yet tested it on numbers of the form b^n+k. I plan on building a new system this summer with a graphics board that will let me try programs running under CUDA, but if anyone else has any experience on numbers of this form, feel free to post here.

[philmoore]

PrimeGrid has finished checking the 2131 sequence and is on track to also finish 41693 as part of their April challenge, which now runs until May 5th. They would welcome any additional help:
http://www.primegrid.com/forum_thread.php?id=3228