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Old 2007-10-08, 14:34   #1
jasong
 
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"Jason Goatcher"
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Default even ks and the Riesel Conjecture

Go here and read the first post for an introduction to the problem.

Please give the guy who actually started crunching the project(described in the linked thread) at least 36 hours to "get his ducks in a row" before reserving any ks. Even though this problem relates to even ks that don't have a known prime, reservations are to be made using the odd k, which is basically the even k with all the even factors taken out. Note that this means that the lowest n that could possibly meet the qualifications of this project, including being prime, is one more than the number of even factors in the even k. I hope that is less confusing than I think it is.
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Old 2007-10-09, 01:27   #2
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Sounds interesting. Let me know if you need any help with moderation, setting up the project etc.
Perhaps we could look at both the +1 and the -1 side?

Last fiddled with by Citrix on 2007-10-09 at 01:28
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Old 2007-10-09, 03:00   #3
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Quote:
Originally Posted by Citrix View Post
Sounds interesting. Let me know if you need any help with moderation, setting up the project etc.
Perhaps we could look at both the +1 and the -1 side?
Absolutely, on both counts. Not sure if the Sierpinski version should or shouldn't have it's own thread.

In terms of the moderation, I have to see if Jens K Andersen continues the project. Whether he does or doesn't, I really hope he PMs me info about his progress at some point. Or at least posts a detailed account.
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Old 2007-10-09, 03:20   #4
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These are the 9 k that have at least 1 even counterpart that hasn't yielded a prime below n=50,000. Note that the 50,000 number applies to the odd "counterpart" to the number, so a prime could be found within minutes of starting on the other side of 50,000.

Here are the odd k, any of them are available for reservation. I'm going to list them in a column so that Citrix can edit the entries easily, not to mention delete this sentence during the first edit. :)
-------------------------------------------------------------
tested to n=50,000(it is highly recommended that sieving be run for at least a minute or two before prime testing, even if all you have is a P4 or equivalent)

17861
23651
77167
170467
173587
175567
190927
112391
239107

Last fiddled with by jasong on 2007-10-09 at 03:20
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Old 2007-10-09, 15:41   #5
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I don't plan to work more on this even Riesel project. jasong asked for a programmer to find the non-trivial cases and that's what I did. My work to identify them is of no use in further testing them. I used slow PARI/GP and pfgw with individual trial factoring (because I know the programs well and could quickly set them up for computationally easy work). Some sieve and probably LLR should be used on exponents above 50000 in the nine remaining cases. I will leave the software choice, sieving, primality testing and organization for others who can just go ahead now without me.

One thing I could do if people want it is spend a little time documenting the identification of the 9 cases. The documentation is useless to test them above 50000 but maybe somebody would like to check that my search is correct and hasn't missed other candidates.
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Old 2007-10-11, 22:16   #6
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17861 reserved 50K-200K for n

Last fiddled with by jasong on 2007-10-11 at 22:29 Reason: changed equals sign to dash
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Old 2007-10-13, 19:23   #7
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17861*2^98954-1 is prime! Time : 23.000 sec.

23651 and 77167 reserved
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Old 2007-10-13, 20:34   #8
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Quote:
Originally Posted by jasong View Post
17861*2^98954-1 is prime!
Good!
I got free cpu time after two sudden hits on other projects. With one srsieve run I am sieving all remaining k values to 10^11 for exponents up to 500000.
And I am testing all exponents up to 80000 with LLR (started on other core before sieving reaches 10^11).
170467*2^55273-1 is prime. 7 k's left.
I expect to post LLR input files in around 5 hours. If you have sieved shorter and tested some exponents above 80000 then you can just delete them from the file.
Note: I only have one computer and run a lot of different short projects. Going back to this one doesn't mean I plan to stay for long.
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Old 2007-10-14, 01:03   #9
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srsieve to 10^11 has completed.
I ended up LLR testing to 85000 and eliminated one more:
190927*2^72289-1 is prime.
The 6 remaining k values: 23651, 77167, 173587, 175567, 112391, 239107.
6 LLR input files for exponents from 85000 to 500000 are at http://hjem.get2net.dk/jka/math/evenRiesel
The k values have different weights so the number of candidates varies a lot.
k: candidates
23651: 3295
77167: 3793
112391: 5080
173587: 2491
175567: 4392
239107: 1504

Reserve a k by posting it here. Stop testing that k if you find a prime. If you stop before 500000 without finding a prime then say how far you got.
Keep a file documenting the tests (maybe lresults.txt if you use LLR).
I'm not permanently organizing this but if nobody takes over before completing your k then you can mail the file to me using the mail link at http://hjem.get2net.dk/jka/.

jasong has reserved 23651 and 77167 (maybe only to 200000 so far).
I reserve 173587 (note that 112391 is currently not reserved).
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Old 2007-10-14, 01:24   #10
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Quote:
Originally Posted by Jens K Andersen View Post
jasong has reserved 23651 and 77167 (maybe only to 200000 so far).
I meant to reserve to 200,000, but now that you've sieved higher, I'm not sure.

I'm going to download your sieve files for those numbers and resume from where I'm at now.
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Old 2007-10-14, 05:53   #11
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17861 (17861*2^98954-1 is prime! Time : 23.000 sec. by jasong)
23651 reserved by jasong
77167 reserved by jasong
170467 (170467*2^55273-1 is prime. by Jens K Andersen)
173587 reserved by Jens K Andersen
175567 reserved by jasong
190927 open
112391 open
239107 open

testing begins at n=85,000 and continues to n=500,000.
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