even ks and the Riesel Conjecture
 

Go [url=http://www.mersenneforum.org/showthread.php?p=115920#post115920]here[/url] 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.

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? :smile:

[QUOTE=Citrix;115967]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? :smile:[/QUOTE]
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.

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

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.

17861 reserved 50K-200K for n

17861*2^98954-1 is prime! Time : 23.000 sec.

23651 and 77167 reserved

[QUOTE=jasong;116291]17861*2^98954-1 is prime![/QUOTE]

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.

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 [url]http://hjem.get2net.dk/jka/math/evenRiesel[/url]
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 [url]http://hjem.get2net.dk/jka/[/url].

jasong has reserved 23651 and 77167 (maybe only to 200000 so far).
I reserve 173587 (note that 112391 is currently not reserved).

[QUOTE=Jens K Andersen;116302]jasong has reserved 23651 and 77167 (maybe only to 200000 so far).[/QUOTE]
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.

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.

190927*2^72289-1 is prime, written earlier.
173587*2^172609-1 is prime.
112391 reserved by me now.

112391*2^159730-1 is prime! Time : 40.493 sec.

I'm reserving 239107. All 4 remaining k's are now reserved.

update
 

17861 (17861*2^98954-1 is prime! Time : 23.000 sec. by jasong)
23651 (23651*2^237506-1 is prime! Time : 167.859 sec.) found by jasong
77167 (77167*2^153441-1 is prime! Time : 34.146 sec.) found by jasong
170467 (170467*2^55273-1 is prime. by Jens K Andersen)
173587 (173587*2^172609-1 is prime.) found by Jens K Andersen
175567 reserved by jasong
190927 (190927*2^72289-1 is prime.) found by Jens K Andersen
112391 112391 reserved by Jens K Andersen
239107 reserved by Jens K Andersen.

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

Great!
I wrote earlier that 112391*2^159730-1 is prime so we are down to 2 k's. Unfortunately one of them is the expected hardest: 239107 which has quickly growing candidates and is currently tested to 244000. I estimate less than 50% chance it has a prime below 1,000,000 digits.
175567 looks much more promising.

[QUOTE=Jens K Andersen;116351]Great!
I wrote earlier that 112391*2^159730-1 is prime so we are down to 2 k's. Unfortunately one of them is the expected hardest: 239107 which has quickly growing candidates and is currently tested to 244000. I estimate less than 50% chance it has a prime below 1,000,000 digits.
175567 looks much more promising.[/QUOTE]
Only 2 to go. That's fantastic.

I like to jump from project to project, and because I'm very impulsive, I reserved work in another project before I remembered my k. 175567*2^187425-1 is as far as I got. If anybody wants it, I'm unreserving it.

This project looks like it might be completed fairly quickly. Then, again, one or both of the remaining ks may prove to be very, very stubborn.

239107 gave no prime to 500000.
Reserving 175567 from 187425 to 500000.

If anybody decides to sieve above n=500,000 please both check here to see if anybody else has beaten you to it, and be sure to post your intentions either before you start, or at least within hours of starting.

175567 gave no prime to 500000.
175567 and 239107 have not been sieved above n=500,000.
I have stopped working on this project.
The following is a summary of the search so far.

Consider k values for which k*2^n-1 is composite for all n>0.
Odd such k are called Riesel numbers.
The goal of the Riesel problem is to find the smallest Riesel number.
The goal of our project is to prove that there is no even k below the smallest Riesel number, whatever it is. The smallest known is 509203.

The following PARI/GP script identifies odd k values which have an even multiple of form k*2^m that is a potential solution below the smallest Riesel number.
It first eliminates odd k which have no prime of form k*2^n-1 below 509203, because if any k*2^m below 509203 for such a k is a solution then k would itself be a Riesel number.
Second it eliminates k which give a prime between 509203 and k*2^1000-1.
The 61 remaining k values are printed.

? R=509203;L=1000;
? forstep(k=1,R,2,c=0;n=1;\
while(k*2^n<R,c+=isprime(k*2^n-1);n++);if(c,\
while(n<=L && !isprime(k*2^n-1),n++);\
if(n>L,print1(k", "))))
37, 337, 1589, 1721, 1807, 2257, 2317, 2683, 3775, 5857, 6869, 10021, 11887,
12401, 17861, 18089, 23651, 24161, 31453, 31841, 32257, 33373, 39817, 43151,
46411, 47653, 55687, 58331, 63367, 67001, 74857, 77167, 79601, 80771, 88115,
90907, 112391, 114367, 115451, 116257, 118447, 120457, 120997, 121061,
122017, 135787, 170467, 173467, 173587, 175567, 179677, 185347, 190357,
190927, 207397, 209737, 230407, 230827, 233221, 239107, 246787,

A prime has been found for 59 of the k values:
37*2^2553-1
337*2^11677-1
1589*2^1620-1
1721*2^1034-1
1807*2^1369-1
2257*2^1297-1
2317*2^2805-1
2683*2^2239-1
3775*2^1297-1
5857*2^4973-1
6869*2^45084-1
10021*2^1835-1
11887*2^1189-1
12401*2^26522-1
17861*2^98954-1
18089*2^1124-1
23651*2^237506-1
24161*2^8570-1
31453*2^1371-1
31841*2^1010-1
32257*2^1985-1
33373*2^5283-1
39817*2^1801-1
43151*2^23286-1
46411*2^2027-1
47653*2^1083-1
55687*2^1597-1
58331*2^1506-1
63367*2^1129-1
67001*2^9506-1
74857*2^1121-1
77167*2^153441-1
79601*2^3542-1
80771*2^9482-1
88115*2^2468-1
90907*2^4689-1
112391*2^159730-1
114367*2^1681-1
115451*2^6218-1
116257*2^1045-1
118447*2^14473-1
120457*2^1261-1
120997*2^2121-1
121061*2^2338-1
122017*2^1257-1
135787*2^7721-1
170467*2^55273-1
173467*2^6925-1
173587*2^172609-1
179677*2^2729-1
185347*2^1189-1
190357*2^15465-1
190927*2^72289-1
207397*2^5609-1
209737*2^1313-1
230407*2^1105-1
230827*2^4177-1
233221*2^1021-1
246787*2^1081-1

Used programs: PARI/GP, PrimeForm/GW, srsieve, LLR.
jasong found 17861*2^98954-1, 23651*2^237506-1, 77167*2^153441-1.
The largest found prime is 23651*2^237506-1.

Reserving k=239107 and 175567 for sieving
 

Reserving 239107 and 175567 for sieving.

I'll be sieving for n=500K-2,500K.

I'll sieve each to a billion. Then, as soon as I figure out how to combine the files, I'll use sr2sieve to sieve higher.

I'm unreserving the numbers and posting the sieve file.

[B]Edit by Max (8/30/09): Cleaned up attachment as the sieve file is now available on the [url=http://www.noprimeleftbehind.net/crus/]Conjectures 'R Us web site[/url]. (See the "Riesel Conjecture Reservations" page, under base 2.)[/B]

i inserted all k's mentioned here with their available data in the data-pages of [url]www.15k.org[/url]. the next update of these pages will be end november and then all k's are available there. so if anyone has some more infos for me (higher n values search -> more primes) i can insert them too. perhaps i push some k to higher n.

k=239107
 

reserving k=239107 for n>564k, the point jasong's sievefile starts.

[QUOTE=kar_bon;118564]reserving k=239107 for n>564k, the point jasong's sievefile starts.[/QUOTE]
Yeah, I deleted everything before that because it was tested already. Probably a bad idea, since the primality testing files probably aren't recoverable at the moment.

status
 

k=239107 is at 789k, no prime yet

reserving k=175567 from jasongs sieve file from 525k too.

end of the week the page with all info of this 'small' project is in the new update for [url]www.15k.org[/url], so hope next week they online.

to Andersen and jasong: please check than and info me if there are errors or missing informations.
karsten

info and stats
 

k=239107 tested to 794k, no prime yet
k=175567 upto 596k, no prime
searching further

the new data pages on [url]www.15k.org[/url] are available. there's also a page for the even Riesel problem here: [url]http://www.15k.org/EvenRieselProblem.htm[/url] (date is 30.11.2007 so above info not included yet).

status
 

k=239107 tested to 838k, no prime
k=175567 tested to 655k, no prime
searching further

[QUOTE=kar_bon;122139]k=239107 tested to 838k, no prime
k=175567 tested to 655k, no prime
searching further[/QUOTE]
How high do the n-values go? I'd be happy to start sieving those numbers if you want, just tell me the lower bound. (I've always made the upper bound 5 times as much as the lower bound when I sieve)

i took your sieved files for 175567 and 239107, both upto n=2.5M.
i sieved 175567 upto p=156G and 239107 upto p=118G.

[quote=kar_bon;122222]i took your sieved files for 175567 and 239107, both upto n=2.5M.
i sieved 175567 upto p=156G and 239107 upto p=118G.[/quote]

I have now incorporated multiples of the base into the "Conjectures 'R Us" project and web pages so this effort is now included in them.

I downloaded these sieved files and there is a link to them on one of the pages. They aren't sieved nearly far enough for testing even below n=1M, let alone above that. I can spare 2 cores for a day on a speedy sieving machine using very speedy sr1sieve on each k. Would you like me to sieve them further? I may be able to push P=750G-1T in a day on both, which probably still won't be far enough but should help you quite a bit. This is based on an estimate of P=7-9M/sec. using sr1sieve.


Gary

Suggest moving thread to conjectures project...
 

The "Conjectures 'R Us" project now incorporates k's that are multiples of the base so this thread is, in effect, a subset of the project.

Would anyone have any objection to coordinating future work on this effort through the conjectures project similar to the way bases 6-18, 22, 23, etc. threads have been moved and coordinated in the past?

If people are OK with this, I'll suggest that this thread be moved over to the project thread (which is now a sub-forum in 'Prime Search Projects') and ultimately be locked.

I haven't incorporated the even-k Sierp side yet but will request the same of that thread when I have.


Thanks,
Gary

i tested 239107 from jasong last n (564k) upto 873k now with no prime yet.

175567 tested from 525k to 655k, no prime.

i'll send you the remaining test-files for further sieving!

[quote=gd_barnes;122897]The "Conjectures 'R Us" project now incorporates k's that are multiples of the base so this thread is, in effect, a subset of the project.

Would anyone have any objection to coordinating future work on this effort through the conjectures project similar to the way bases 6-18, 22, 23, etc. threads have been moved and coordinated in the past?

If people are OK with this, I'll suggest that this thread be moved over to the project thread (which is now a sub-forum in 'Prime Search Projects') and ultimately be locked.

I haven't incorporated the even-k Sierp side yet but will request the same of that thread when I have.


Thanks,
Gary[/quote]


I have now made all site 'Conjectures 'R Us' site updates for k's that are mutliples of the base for both the Riesel and Sierp conjectures. Here, I added k=351134 and 478214 as needing primes.

After a couple of days, I'll request that this thread be moved to the "Conjectures 'R Us" prime search project to avoid duplication of effort. Since work is still remaining, if people prefer, we can leave this thread open there.


Gary

I have 4 2.4GHz cores that will slowly become free over the next 2-5 days.

If any sieving needs to be done, I have a question and a request:

Is it srsieve that's the best to one use for multiple ks with a base more than 2? The second question is, are there any particular files people would like help sieving with? A core2quad sieves pretty well, and I'd be happy to run whatever helps the project the most.

Edit: Never mind, I just noticed the new forum.

[quote=jasong;122938]I have 4 2.4GHz cores that will slowly become free over the next 2-5 days.

If any sieving needs to be done, I have a question and a request:

Is it srsieve that's the best to one use for multiple ks with a base more than 2? The second question is, are there any particular files people would like help sieving with? A core2quad sieves pretty well, and I'd be happy to run whatever helps the project the most.

Edit: Never mind, I just noticed the new forum.[/quote]

A little related info...

I am sieving the remaining two k's for Karsten (kar_bon) for this effort up to P=1T and will be done on Thurs. This still isn't enough sieving and I told him I'd have 2-6 cores available to throw at it after Sunday. For LLRing to n=1M, we probably need to sieve to at least P=4T on k=351134 (175567).

Reference best sieving software:
For 1 or 2 k's, use 1 or 2 instances of sr1sieve. (sr1sieve is over twice as fast as anything else for a single k)
For 3 to ~50-100 k's, use sr2sieve.
For ~50-100 k's or more, use srsieve.

For a small # of k's, srsieve is about the slowest software that you can use. Use sr1sieve or sr2sieve instead. (You'll have to get it started with srsieve and then switch over.) I'm getting P=6M and P=9M/second using sr1sieve on the files that you left posted here and that's on a Dell core duo, which is my fastest siever. You'd probably get faster on your quad.

I think the same applies to all bases.

As for helping sieve, you could help with team drive #1 in Conjectures 'R Us running sr2sieve beginning on Saturday. I have a couple of large factor gaps that I need to fill going up to P=1T but I'll have them filled by Saturday. We need to go to about P=1.5T, which I'm thinking will take about 10-12 CPU days on a core 2 duo; perhaps less on your quad.

If you're interested in sieving a portion of P=1T-1.5T (perhaps P=1T-1.2T) on the drive, let me know. We're sieving the range of n=100K-200K base 16 so they're all top-5000 candidates.

Thanks for the offer.


Gary

[QUOTE=gd_barnes;122953]A little related info...

I am sieving the remaining two k's for Karsten (kar_bon) for this effort up to P=1T and will be done on Thurs. This still isn't enough sieving and I told him I'd have 2-6 cores available to throw at it after Sunday. For LLRing to n=1M, we probably need to sieve to at least P=4T on k=351134 (175567).

Reference best sieving software:
For 1 or 2 k's, use 1 or 2 instances of sr1sieve. (sr1sieve is over twice as fast as anything else for a single k)
For 3 to ~50-100 k's, use sr2sieve.
For ~50-100 k's or more, use srsieve.

For a small # of k's, srsieve is about the slowest software that you can use. Use sr1sieve or sr2sieve instead. (You'll have to get it started with srsieve and then switch over.) I'm getting P=6M and P=9M/second using sr1sieve on the files that you left posted here and that's on a Dell core duo, which is my fastest siever. You'd probably get faster on your quad.

I think the same applies to all bases.

As for helping sieve, you could help with team drive #1 in Conjectures 'R Us running sr2sieve beginning on Saturday. I have a couple of large factor gaps that I need to fill going up to P=1T but I'll have them filled by Saturday. We need to go to about P=1.5T, which I'm thinking will take about 10-12 CPU days on a core 2 duo; perhaps less on your quad.

If you're interested in sieving a portion of P=1T-1.5T (perhaps P=1T-1.2T) on the drive, let me know. We're sieving the range of n=100K-200K base 16 so they're all top-5000 candidates.

Thanks for the offer.


Gary[/QUOTE]
I have a couple days of sieving to do for a friend, and then ~850G for Riesel Sieve, then everything will be freed up for your(our?) project.

Looking forward to it. :)

[quote=kar_bon;122898]i tested 239107 from jasong last n (564k) upto 873k now with no prime yet.

175567 tested from 525k to 655k, no prime.

i'll send you the remaining test-files for further sieving![/quote]


Karsten,

I have sieved k=351134 to P=5T and k=478214 to P=2.5T for the Riesel base 2 conjectures for even k's. This should be sufficient for LLRing well past n=1M now on both because k=478214 is so much lower weight. I'll do some calculations later on and let you know about how far to LLR them before sieving should be needed again.

The files are in their normal links on the Riesel conjectures reservation page.

Sieving removed 10-15% of the candidates in both files. You should get a significant time savings now.


Gary

that's great. i'll continue llr-test by now.

perhaps the 2 missing primes to prove this conjecture are just around the corner!

status
 

k=175567 at n=691k

k=239107 at n=918k

no new prime yet

Status
 

Riesel base 2 even:
14361, 19401 and 20049 at n=379k

Riesel base 2 odd:
all 12k's at n=301k (includes doublechecking of Jean's k's)