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Old 2008-02-15, 22:36   #1
gd_barnes
 
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Default k's/n-ranges not searched for team drives

Here is a list of k's and n-ranges for 400<k<=1001 and n=260K-600K that we are partially testing or not testing at all for team drives 1, 2, and 3 that were originally reserved by VBCurtis at RPS:

Code:
          range             range          tested
k-value   included         excluded        to n=
343       500K-600K        260K-500K        600K
359       500K-600K        260K-500K        600K
361       500K-600K        260K-500K        600K
375       500K-600K        260K-500K        600K
415       (none)           260K-600K        600K
439       500K-600K        260K-500K        600K
443       500K-600K        260K-500K        1.04M
449       500K-600K        260K-500K        600K
457       500K-600K        260K-500K        600K
479       500K-600K        260K-500K        600K
505       500K-600K        260K-500K        600K

All k's and n-ranges for k<1000 will be included in future double-checking efforts.


Gary

Last fiddled with by gd_barnes on 2008-12-26 at 08:11 Reason: update testing ranges
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Old 2008-05-27, 05:58   #2
VBCurtis
 
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Steven (sjtjung) and I paused our 9 k's for a couple months at 400k, but have resumed. I expect we'll complete the 9 k's to 500k and release them by the end of June. As Gary has done with his k<100 reservations, I welcome anyone to continue the searches at 500k-up.

Note this applies to any k in 300-600 reserved to me except k=443 (edit- and 415). I have 443 to 825k now, with a sieve to 3M and no plans to release until I find a CRUS prime for base 16. It will have one or two cores assigned to it for the foreseeable future.

Edit- I forgot about k=415. I have that one sieved to 1M, but the file has been idle for a long time. I'll assign this one to a machine to catch it up to your drives tomorrow. Sorry!

(Not sure where to report my progress- this thread looks best.)
-Curtis

Last fiddled with by VBCurtis on 2008-05-27 at 06:04
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Old 2008-05-27, 06:20   #3
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Quote:
Originally Posted by VBCurtis View Post
Steven (sjtjung) and I paused our 9 k's for a couple months at 400k, but have resumed. I expect we'll complete the 9 k's to 500k and release them by the end of June. As Gary has done with his k<100 reservations, I welcome anyone to continue the searches at 500k-up.

Note this applies to any k in 300-600 reserved to me except k=443 (edit- and 415). I have 443 to 825k now, with a sieve to 3M and no plans to release until I find a CRUS prime for base 16. It will have one or two cores assigned to it for the foreseeable future.

Edit- I forgot about k=415. I have that one sieved to 1M, but the file has been idle for a long time. I'll assign this one to a machine to catch it up to your drives tomorrow. Sorry!

(Not sure where to report my progress- this thread looks best.)
-Curtis

You might be searching k=443 into the 10-million digit range before finding a base 16 prime! Finding another base 2 prime will be difficult enough...base 16 almost impossible.

Good luck and thanks for the udpate!


Gary
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Old 2008-06-01, 07:03   #4
VBCurtis
 
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I have a sieve for 415 starting at 260k. However, your pages list 415 as tested to 340k already. Since 340k is roughly the cutoff for top 5000 listing anyway, I started testing there. Is that OK? I think when I reserved it, it was only tested to 260k. I may have tested it to 340 and misplaced the results, or your double-checks may have already pushed the test limit to 340.

Let me know if I should run the 260-340 range to generate results files for your records, or if you already have them.

I agree that 443 may be stubborn for a base-16 prime. I like searching the lower-weight k's, and the idea of having a reason to test one to high n suits me. I suppose around 2M I'll have to decide whether to start another sieve from 3M up or give up.. but that won't be necessary until fall. Base 16 should merely be 1/8 as likely as base 2, right? Am I right assuming absent detailed info about specific n's that survive the sieve that half of discovered base 2 primes can be expressed as base 4? That's just saying half are even powers, half odd, right? I hope that logic can be extended to base 16. If so, I "merely" have to find 8 primes to expect 1 base 16 prime.

-Curtis
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Old 2008-06-01, 09:00   #5
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Quote:
Originally Posted by VBCurtis View Post
I have a sieve for 415 starting at 260k. However, your pages list 415 as tested to 340k already. Since 340k is roughly the cutoff for top 5000 listing anyway, I started testing there. Is that OK? I think when I reserved it, it was only tested to 260k. I may have tested it to 340 and misplaced the results, or your double-checks may have already pushed the test limit to 340.

Let me know if I should run the 260-340 range to generate results files for your records, or if you already have them.

I agree that 443 may be stubborn for a base-16 prime. I like searching the lower-weight k's, and the idea of having a reason to test one to high n suits me. I suppose around 2M I'll have to decide whether to start another sieve from 3M up or give up.. but that won't be necessary until fall. Base 16 should merely be 1/8 as likely as base 2, right? Am I right assuming absent detailed info about specific n's that survive the sieve that half of discovered base 2 primes can be expressed as base 4? That's just saying half are even powers, half odd, right? I hope that logic can be extended to base 16. If so, I "merely" have to find 8 primes to expect 1 base 16 prime.

-Curtis

Curtis,

On k=415, Karsten reflects the highest contiguous n-range that is shown as searched at Primesearch -or- the n-range that we have completed through, whichever is higher. For k=415, we aren't testing that one so he got the n=340K from the Primesearch site. There, on 1/17/2008, you showed that you completed the ranges from n=260K-340K. We're asking that people forward results files for their personal ranges if possible to help in future double checking. So if you can find those, please forward them to us. If not, it's your call as to what you do.

On k=443, no, it's not as bad as you think for base 16. 1 out of every FOUR base 2 primes should be a base 16 prime, i.e. 2^4 = 16^1, 2^8 = 16^2, etc.

That said, as you probably know, that doesn't mean that the respective weights for base 2 where n==(0 mod 4), n==(2 mod 4), etc. are equal in the long run. Just like there can be 10% even n-value and 90% odd n-value primes for a base 2 k-value, resulting in only 10% as many total base 4 primes as there are total base 2 primes, there can be an extremely uneven distribution of the various modulos for base 16 primes vs. base 2 primes due to unusual distributions of factors, which is clearly the case here. So, no, just because every 4th n-value makes a base 2 prime a base 16 prime doesn't mean that 1 out of every 4 base 2 primes should be a base 16 prime. It may be more like 1 in 20 or 1 in 100 in the long run!! That is why I think you may be searching into 10M-digit range for a base 16 prime. Other powers-of-2 bases k-values have widely varying weights just like base 2 and they can be very much unrelated to the weight of the base 2 k-value. It all depends on how the distribution of the factors plays out.

Here, since the k is not divisible by 3, all of the base 2 primes must even n-values. But what is unusual is that they are all n==(2 mod 4), which of course means that while they are all base 4 primes, NONE of them are base 16 primes where n must be divisible by 4. This tells me that while k=443 base 2 and base 4 are very low weight, k=443 base 16 is FAR less than half the weight of base 4. This happens for the same reason that you can get 90% even n-value and 10% odd n-value primes on some base 2 k's even though the k is divisible by 3.

But one thing you may not have noticed way back in one of the CRUS forum threads is that I alluded to the fact that k=7088 is remaining for Riesel base 256 and that converts to k=443 base 2. As you thought for base 16, THAT is the one that will occur only 1 out of every 8 n-values! (1 out of every 4 EVEN n-values in this case.)

The bottom line is that to knock out base 16, your prime would need to be n==(0 mod 4) and to knock out base 256, it would need to be n==(4 mod 8).

Good luck on that base 256 prime! I would be amazed if we found one in our lifetime!


Gary

Last fiddled with by gd_barnes on 2008-06-14 at 01:05
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Old 2008-07-04, 08:16   #6
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415 was completed in a few days to 410k, followed by a nasty crash on that machine rendering it useless. 410 to 500 should run in July when another machine opens up, sooner if our IT

I located the results file for 260-340, and plan to send it when I complete to 500k.

The machine running 443 also crashed terribly, and I just put that file on a new machine at 825k. A month's work was lost in the crash, roughly. These two were public machines used by undergrads in my dept, and fell victim to viral maladies. The results I do have are legit- these weren't hardware-related crashes, just impetuous undergrads.
Edit: The other 9 k's are complete to roughly 400k, running on one core with a second to be added shortly. I estimate 4 to 8 weeks for completion. These were set aside for a large attack on k=5 and 31 for a few months.

-Curtis

Last fiddled with by VBCurtis on 2008-07-04 at 08:19 Reason: forgot the other 9 k's
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Old 2008-07-20, 08:28   #7
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415 is active now, complete to 430k. I should be at 500k by the end of July.
The other k's reserved to me are complete to 440k, active on one core at the moment. Steven (sjtjung) is finishing that drive, and will put a second machine on it to get our effort done within 4-5 weeks.

Sorry for the delays.
-Curtis
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Old 2008-07-20, 09:55   #8
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Quote:
Originally Posted by VBCurtis View Post
415 is active now, complete to 430k. I should be at 500k by the end of July.
The other k's reserved to me are complete to 440k, active on one core at the moment. Steven (sjtjung) is finishing that drive, and will put a second machine on it to get our effort done within 4-5 weeks.

Sorry for the delays.
-Curtis
Thanks for the update. A couple of questions:

First; we have you reserved for k=415 up to n=600K. Is it still your intent to take it that far? If not, we'll do a "side-effort" search for n=500K-600K since we're already nearing n=510K on all k's.

Second; can you check your results files and see if you've missed reporting any top-5000 or smaller primes? The only one with top-5000 primes is k=479 and k=457 had a non-top 5000 prime. It seems very unusual that only 2 of 11 k's would have any primes for the wide range of n=260K to 430K or 440K even considering that a majority are low-weights in your search. Perhaps you've reported them at RPS or elsewhere. I haven't seen in any additional primes reported here or at the Primesearch site.

I mention this because we have already found 2 primes for k=375 for n=500K-~530K.


Thanks,
Gary

Last fiddled with by gd_barnes on 2008-07-24 at 07:19
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Old 2008-07-24, 07:11   #9
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Karsten,

The n-ranges complete on Curtis's reserved k's should only reflect what he has completed in his mini-drive shown in the first post of this thread.

On rieselprime.org, you are showing them completed as far as our drives have completed most of the k's.

Technically, for the k's he is only searching to n=500K, there is a gap from his search limit up to n=500K. For n>500K, we are including them in our searches. k=375 is the best example where we have found 2 new primes for n>500K but have not searched n<=500K.


Gary
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Old 2008-07-24, 12:59   #10
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ok, corrected!

PS:
not yet. got no connection to the server! perhaps tomorrow!

Last fiddled with by kar_bon on 2008-07-24 at 14:30 Reason: PS
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Old 2008-07-24, 14:33   #11
VBCurtis
 
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Gary-
I have 415 sieved to 1M, and plan to take it that far.

I have no reason to think there are any unreported primes- what incentive would I have to not report something? I've never had LLR fail to print a found prime to primes.txt, but you'll get the results files when my mini-drive is done anyway, and can look them over and continue to be surprised.
-Curtis
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