20071008, 14:34  #1 
"Jason Goatcher"
Mar 2005
5·701 Posts 
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. 
20071009, 01:27  #2 
Jun 2003
3^{2}×5^{2}×7 Posts 
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 20071009 at 01:28 
20071009, 03:00  #3  
"Jason Goatcher"
Mar 2005
5×701 Posts 
Quote:
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. 

20071009, 03:20  #4 
"Jason Goatcher"
Mar 2005
6661_{8} Posts 
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 20071009 at 03:20 
20071009, 15:41  #5 
Feb 2006
Denmark
2·5·23 Posts 
I don't plan to work more on this even Riesel project. jasong asked for a programmer to find the nontrivial 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. 
20071011, 22:16  #6 
"Jason Goatcher"
Mar 2005
DB1_{16} Posts 
17861 reserved 50K200K for n
Last fiddled with by jasong on 20071011 at 22:29 Reason: changed equals sign to dash 
20071013, 19:23  #7 
"Jason Goatcher"
Mar 2005
5·701 Posts 
17861*2^989541 is prime! Time : 23.000 sec.
23651 and 77167 reserved 
20071013, 20:34  #8 
Feb 2006
Denmark
230_{10} Posts 
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*2^552731 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. 
20071014, 01:03  #9 
Feb 2006
Denmark
11100110_{2} Posts 
srsieve to 10^11 has completed.
I ended up LLR testing to 85000 and eliminated one more: 190927*2^722891 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). 
20071014, 01:24  #10 
"Jason Goatcher"
Mar 2005
5×701 Posts 

20071014, 05:53  #11 
"Jason Goatcher"
Mar 2005
3505_{10} Posts 
17861 (17861*2^989541 is prime! Time : 23.000 sec. by jasong)
23651 reserved by jasong 77167 reserved by jasong 170467 (170467*2^552731 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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