k=243 testing ??

[gd_barnes]

Due to the problems in getting all of the ranges tested for k=243, I think it's worth it's own thread now. The latest information that I received from Kosmaj and Karsten on the 'gaps and more gaps on <300 site' thread is that this k possibly has gaps that have not been tested for the ranges of n=260K-300K, 400K-650K, and 745K-800K. So even though the highest prime shown is n=744442, obviously there must have been some testing above above n=800K.

It has been 9 months since they have received any information from Rob on what ranges have been tested and he has been sent several messages asking him where he is at in testing and has not responded.

What I'm asking for is Rob's and anyone else's assistance. If Rob will please respond to the messages that have been sent and let us know what ranges he has tested, that would be the most helpful. But if anyone else knows if any of the above ranges of n have been tested for k=243, please let us know.

If we can't figure out if any of the above ranges have been tested, then I would like to coordinate an effort to get them all tested. I believe this is the only k<300 that is divisible by 3 that has not been tested to at least n=300K. Just testing it from n=260K to 300K would bring it's testing up to n=400K.


Thank you,
Gary

[ValerieVonck]

I volunteer to test the range from 260k to 300K

[gd_barnes]

Originally Posted by CedricVonck

I volunteer to test the range from 260k to 300K

Cedric,

Great; test away. Thanks for getting us started. That's the best range to start with. Finishing it will make the k complete to n=400K.

Karsten or Kosmaj, should we reserve the ranges of this k in some other forum or will this be sufficient?

I'll wait a few more days to hear from anyone else on this and if we don't hear anything, I'll start doing some sieving on the large range of n=400K to 650K. After that is done, I'll divide up the sieve into apporpriate chunks and people can take them depending on their availability for testing.



Gary

[Flatlander]

I vaguely remember something about NewPGen missing factors for 'k that are powers'. I was told I could safely remove certain candidates from my sieved files for k=81 and k=125. Not sure if this also applies to sr1sieve and k=243???

link:
http://mersenneforum.org/showpost.ph...&postcount=440

[R. Gerbicz]

Originally Posted by Flatlander

I vaguely remember something about NewPGen missing factors for 'k that are powers'. I was told I could safely remove certain candidates from my sieved files for k=81 and k=125. Not sure if this also applies to sr1sieve and k=243???

link:
http://mersenneforum.org/showpost.ph...&postcount=440

That was my post.
Here: for k=243=3^5 you can remove all n values, where n is divisible by 5, because if n=5*d then k*2^n-1=243*2^(5*d)-1=(3*2^d)^5-1 so it is divisible by 3*2^d-1 so it is composite.

[gd_barnes]

Originally Posted by R. Gerbicz

That was my post.
Here: for k=243=3^5 you can remove all n values, where n is divisible by 5, because if n=5*d then k*2^n-1=243*2^(5*d)-1=(3*2^d)^5-1 so it is divisible by 3*2^d-1 so it is composite.

Thanks for the great analogy! It seems so elementary and obvious when someone points something like that out but I wouldn't have thought of it. It has usually been my experience that NewPgen ends up with very little n's of this nature that it 'could have' removed but didn't because it uses the 'brute force' approach so I ran a quick test. I did a 'preliminary' sieve for k=243 for the range of n=400K to 650K up to p=1G.

There were 22,717 candidates remaining of which 292 of them (1.3%) had an n that was divisible by 5. This seemed to confirm my thinking that the impact is minimal but that thinking was incorrect. At these higher n values, the time saved will be significant. At an estimated average of 10 minutes per candidate to test in that range, that's 2920 minutes or over 2 total days of CPU time! (Will be somewhat less after sieving further but still significant.)

So anyone doing any sieving on this effort, if you feel it is worth the trouble, you can remove n values that are divisible by 5 after sieving. Note that they all end in a digit of 5. There are no values of n left after sieving that are divisible by 10. Any sieved files that I provide others for testing will have them removed.


Thanks a bunch,
Gary

[Kosmaj]

Although I'd like to see all these gaps filled and this and all other k's processed to higher exponents, I'm afraid you are over-reacting a little bit here. Rob has reserved k=243 and he is free to divide the work as he likes. Please observe that some people's main objective is to find large primes, not to fill all the gaps. Rob told me last time that he had been working on n>1M and to fill remaining gaps. Yes, that was in September last year (2006) but I don't consider that to be a distant past. Everybody is busy and the search for primes is low on one's priority list in real life. I mailed Rob on Saturday and I hope he will reply soon (meaning within a week or two).

In conclusion, I see no harm in filling the 260-300k gap, because the primes from the range (if any) cannot be reported to Top-5000. But I cannot support your proposal to fill the 400-650k gap because doing so will be in direct disregard of the k<300 reservation list we are trying to maintain.

Kosmaj

[ValerieVonck]

ok then I start the sieve.

[biwema]

Originally Posted by R. Gerbicz

That was my post.
Here: for k=243=3^5 you can remove all n values, where n is divisible by 5, because if n=5*d then k*2^n-1=243*2^(5*d)-1=(3*2^d)^5-1 so it is divisible by 3*2^d-1 so it is composite.

Oh, this property could also be useful for me. (On +1 Numbers, it only works when the mantissa has an odd exponent)
I am working on 243 * 2^k+1

In my case I can remove all exponents that are divisible by a multiple of 10
(k with 5 mod 10 are divisible by 11 and already removed)

Thank you for the hint...

[gd_barnes]

Originally Posted by Kosmaj

Rob told me last time that he had been working on n>1M and to fill remaining gaps. Yes, that was in September last year (2006) but I don't consider that to be a distant past. Everybody is busy and the search for primes is low on one's priority list in real life. I mailed Rob on Saturday and I hope he will reply soon (meaning within a week or two).


Kosmaj

My intent was a little misconstrued here...that was to wait several days or a week to allow Rob to respond. When Cedric came right back and said he'd do n=260K to 300K, I'm thinking it's already been 9 months and there's no reportable primes in that range, so I was all for that. Obviously you agree that there's no harm in him testing that range.

But we'll have to agree to disagree on the rest of your statement, especially the definition of 'distant past'. It is my opinion that if one reserves a range and one does not report one's progress in more than 3 months, then after not responding to 2 Emails or messages, that's as good as giving up the effort. If one is too busy to complete one's prime-searching efforts, then one needs to give up at least part of those efforts. That is probably the case here.

My issue is not with the fact that there are gaps on k=243. My issue is the fact that there's been no response on progress for the k in over 9 months. There are plenty of gaps everywhere and people may or may not fill them as they are searching for reportable primes. I like to see gaps filled but don't have a big problem with them, per se, like I do with people who reserve things and then go AWOL and refuse to respond. If we had at least heard from him, even though he's searching for higher primes, then I'd be OK with letting the gaps remain until he releases the k. Like you said, everyone has different objectives.

This type of thing is a lot more noticeable at low values of k. We're trying to fill everything for k < 300. I mean if my reservations for k=19437 or k=102765 didn't get worked or their status reported for 6 months, it's doubtful that anyone would notice (but I would!). But I know it's been about 5-6 weeks on those and they are 'cued up' behind my effort on k=289 and k=775784295. k=289 is taking up my entire fastest dual-core machine right now. I hope to get another machine this week to speed things up.

Kosmaj, here's what I'd like to suggest on this if you're OK with it. Let's wait until July 15th. If you haven't heard anything from Rob by then, I'd like to start some sieving on the range of n=400K to 650K. No searching at that point, just sieving. By the end of July, if you still haven't heard anything from Rob, I'd like to post my sieved file and split it up somewhat and have people start searching on it (including myself). If we find a reportable prime, then Rob can be included in who gets credit for it.

Does that sound reasonable?


Thanks,
Gary

[VBCurtis]

There are many possible ranges to work on, even under k=300. I would prefer to wait one year since the last contact from an individual before releasing his reservation. Kosmaj is not alone in his resistance to charging ahead.

Phil Carmody has not updated k=5 in quite a while, but he is very active in the prime search community, so we give him leeway on the reservation. I'm hoping to see him update us this summer, or release it (dibs!).

Rob was active for quite a while here also-- this is not a case of a one-shot wonder who disappeared as soon as he appeared.

-Curtis