Conjectures 'R Us; searches needed
 

Searches needed for Conjectures 'R Us
(n-limit search so far):

[B]NOTE: The searches needed in this post were last updated on 1/5/2008 and is now out of date. See the web pages for searches needed.[/B]


[B]-Sierpinski-[/B]

Base 4:
(Sieve file available to n=1M)
64494*4^n+1 (885.4K)

Base 9:
2036*9^n+1 (100K) (reserved)

Base 10:
7666*10^n+1 (195K)

Base 11:
958*11^n+1 (100K)

Base 12:
404*12^n+1 (88.5K) (reserved)

Base 16:
47 k's remaining; 38 being done by team drive #1, several unreserved
(Sieved files available for unreserved k's to n=100K)

Base 17 (all 76.5K):
(Sieve file available to n=100K)
160*17^n+1
244*17^n+1
262*17^n+1

Base 18:
122*18^n+1 (130K) (reserved)

Base 22:
1908*22^n+1 (100K)

Base 23 (all 60K; all reserved)
8*23^n+1
68*23^n+1

Base 26 (all 54K; all reserved):
32*26^n+1
65*26^n+1
155*26^n+1

Base 27 (all 25K):
342*27^n+1
398*27^n+1

Base 28 (all 5K):
k-values:
871, 1291, 1797, 2203, 2377, 3394, 4233, 4552

Base 30 (all 25K):
278*30^n+1
588*30^n+1

Base 128:
40*128^n+1 (642.8K)

Base 256:
535*256^n+1 (53.7K)
831*256^n+1 (12.5K)

New bases that can be started:
6, 19, 25, and 31


[B]-Riesel-[/B]

Base 4 (all 100K; all reserved):
9519*4^n-1
13854*4^n-1
14361*4^n-1
16734*4^n-1
19401*4^n-1
20049*4^n-1

Base 6 (most 25K; all reserved)
k-values:
1597, 9577, 17459, 21799, 29847, 33627, 35965, 36772, 37295, 40657, 43994, 48950, 51017, 57023, 58757, 29095, 77743, 78959, 79815

Base 10 (all 195K):
4421*10^n-1
7019*10^n-1
8579*10^n-1

Base 13:
(Sieve file available to n=100K)
288*13^n-1 (66K)

Base 16 (most 25K):
33 k's available; most unreserved; see web pages

Base 22 (all 100K):
3104*22^n-1
3656*22^n-1

Base 23 (all 60K; all reserved):
194*23^n-1
404*23^n-1

Base 26:
115*26^n-1 (55K) (reserved)

Base 27 (all 25K; all reserved):
258*27^n-1
706*27^n-1

Base 28 (5K, 15K, or 25K; most unreserved):
k-values:
233, 1422, 2319, 4001, 4322, 4436, 4871, 5076, 5133, 5306, 5886, 6207, 7367, 8991

Base 30 (all 25K):
k-values:
25, 225, 239, 249, 659, 774, 1024, 1580, 1642, 1873, 1936, 2293, 2538, 2916, 3253, 3256, 3719, 4372, 4897

New bases that can be started:
19, 24, 25, and 256


-- IMPORTANT NOTE REGARDING STARTING NEW BASES --
Starting new bases can be tricky and error-prone. I only suggest starting on bases that have a specific conjectured value, otherwise there is no way to know how many k's need to be searched. If there's a "?" by it, I would suggest avoiding it. Get with me first before starting any new base. Most of the bases remaining have a high conjecture and will require a very intense initial effort.

Large projects are doing searches on bases 2, 5, and 4 Sierp. We may do some coordination on base 4 Sierp with this effort.

Bases 32 and 128 Sierp cannot be proven with current technology. See the web page for an explanation.

Everyone have fun and knock out a few k's and prove a few conjectures! :smile:


Gary

Now you just need to explain step-by-step on how to use the softwares, where they are located to download, etc....

I can help with the tutorial. (this is my bookmark so that there isn't duplicate work. I'm working on it right now)

Edit: I just realized that we can use the Base-5 tutorial with a few caveats. First, the base is going to be different, hopefully people will understand the project well enough to know what to enter there. Also, after Newpgen has sieved past 2^31(a little under 2.148G) it is extremely wise to stop the sieve and continue processing with sr1sieve. To halt the sieve gracefully, which is VERY important if you want to make sure it remembers that it's past 2^31, click on the Stop button in Windows, or make the window active in Linux and press Ctrl-C. sr1sieve can be found with a Google search. Or you can simply click [url=http://www.geocities.com/g_w_reynolds/sr1sieve/]here.[/url] :) Type sr1sieve -h to get the instructions for sr1sieve after you get it. I'm pretty sure it's totally text-based.

[quote=em99010pepe;120700]Now you just need to explain step-by-step on how to use the softwares, where they are located to download, etc....[/quote]

That is in the works. A lot of info. to post.

A quick answer for experienced base 2 searching folks: Use srsieve/sr1sieve/sr2sieve for sieveing and LLR for searching just like you would for base 2. But after LLR finds a "probable prime", use PFGW to prove it prime. Note that LLR will convert bases 4, 8, 16, 32, etc. to base 2 and will prove them so no need for the PFGW step if you're searching those bases.

Alternatively you could use PFGW solely for searching but LLR is still faster even with the added PFGW step to prove the primes. For those who have PFGW but haven't used it much, here are the commands to force a deterministic proof (not a probable prime):

Sierpinski primes:
pfgw -q12345*6^7890+1 -t -f0

Riesel primes:
pfgw -q12345*6^7890-1 -tp -f0

If that doesn't work, put the equation part in quotes, i.e. -q"12345*6^7890-1". My version of PFGW doesn't take quotes but it seems that some do.

After posting a reservation thread next, I'll put some software links and instructions out there for those who have done little prime searching.


Gary

[quote=jasong;120702]I can help with the tutorial. (this is my bookmark so that there isn't duplicate work. I'm working on it right now)[/quote]


Great, Jasong; thanks! Will you have links to applicable software with instructions on how to use?


Gary

[QUOTE=gd_barnes;120704]That is in the works. A lot of info. to post.

A quick answer for experienced base 2 searching folks: Use srsieve/sr1sieve/sr2sieve for sieveing and LLR for searching just like you would for base 2. But after LLR finds a "probable prime", use PFGW to prove it prime. Note that LLR will convert bases 4, 8, 16, 32, etc. to base 2 and will prove them so no need for the PFGW step if you're searching those bases.[/QUOTE]
Last time I tried to use pfgw, it didn't work properly, if you're a Linux user, do some research before trusting pfgw. If you're using Linux and you are unable to verify that pfgw is reliable for Linux(they may have fixed it since then), then a Windows box is necessary for the pfgw step.

[quote=jasong;120708]Last time I tried to use pfgw, it didn't work properly, if you're a Linux user, do some research before trusting pfgw. If you're using Linux and you are unable to verify that pfgw is reliable for Linux(they may have fixed it since then), then a Windows box is necessary for the pfgw step.[/quote]

If PFGW does not work for Linux users, does Proth work? Proth can prove any base for -1 or +1. It is just much slower. It's actually what I used until Rogue informed me a week or so ago about the deterministic proof in PFGW.

Alternatively if people cannot prove them, I'll be glad to do the proving for them. They just need to let me know that they found a probable prime. Determining primality on a large group of moderate-sized probable primes is fast for PFGW. It's when testing large #'s of composite ones in the first place that LLR is faster.


Gary

[quote=jasong;120702]

Edit: I just realized that we can use the Base-5 tutorial with a few caveats. First, the base is going to be different, hopefully people will understand the project well enough to know what to enter there. Also, after Newpgen has sieved past 2^31(a little under 2.148G) it is extremely wise to stop the sieve and continue processing with sr1sieve. To halt the sieve gracefully, which is VERY important if you want to make sure it remembers that it's past 2^31, click on the Stop button in Windows, or make the window active in Linux and press Ctrl-C. sr1sieve can be found with a Google search. Or you can simply click [URL="http://www.geocities.com/g_w_reynolds/sr1sieve/"]here.[/URL] :) Type sr1sieve -h to get the instructions for sr1sieve after you get it. I'm pretty sure it's totally text-based.[/quote]

This is a very good start. I'll post some more formalized step-by-step instructions on the entire sieve and search process that I think works best for multiple bases sometime later tonight. My hope is to make it turnkey so that a brand new prime searcher can get started with it. I can't speak for Linux users though. If you don't mind, I'll refer them to you if needed. Thanks for your help.

The reservations/statuses thread is now up and ready to go. Grab a few k if you're so inclined! The last time I counted, there were 65 of them and I'll be adding 60+ on Sunday. I'll also start working on brand new base 24 at that point and search it to a low level like n=5K. That should yield an additional 50-100 k's for people to search.


Gary

Base 16 Sierp complete to n=25K; 57 primes needed
 

I have completed Base 16 Sierpinski to n=25K. 57 k's are remaining that need primes. I removed all k's with higher primes found by other projects but if you found one that I missed, let me know.

You can view the k's by going through the main Sierp page or through the main reservations page. Both have links to a new page that I created for base 16 Sierp reservations. But for ease of reference, here is a direct link: [URL="http://gbarnes017.googlepages.com/Sierp-conjecture-base16-reserve.htm"]Base 16 Sierp reservations[/URL].

Come and get 'em while they're hot! Base 16 LLR's as fast as base 2 for primes of similar size, i.e. k*16^n+1 is as fast as k*2^(4n)+1.

If you have a minute, you might check some of the new links on the original pages that are pointing to the base 16 reservations page as well as the ones on the new page that point to other pages. Let me know if you find any problems.


Gary

[QUOTE=gd_barnes;120912]I have completed Base 16 Sierpinski to n=25K. 57 k's are remaining that need primes. I removed all k's with higher primes found by other projects but if you found one that I missed, let me know.

You can view the k's by going through the main Sierp page or through the main reservations page. Both have links to a new page that I created for base 16 Sierp reservations. But for ease of reference, here is a direct link: [URL="http://gbarnes017.googlepages.com/Sierp-conjecture-base16-reserve.htm"]Base 16 Sierp reservations[/URL].

Come and get 'em while they're hot! Base 16 LLR's as fast as base 2 for primes of similar size, i.e. k*16^n+1 is as fast as k*2^(4n)+1.

If you have a minute, you might check some of the new links on the original pages that are pointing to the base 16 reservations page as well as the ones on the new page that point to other pages. Let me know if you find any problems.


Gary[/QUOTE]

I hadn't realised that the partial factorisation for k=2500 also gave a trivial result for odd k. Thats interesting.

[quote=robert44444uk;120916]I hadn't realised that the partial factorisation for k=2500 also gave a trivial result for odd k. Thats interesting.[/quote]

Well...for once, it's nice to know that I found something NEW instead of something OLD. :smile: I have found this to be a very interesting excursion into the world of factoring. It's never failed to surprise me what I come up with on some of this stuff to avoid having people search barren k's. Isn't that very strange that k=2500 is the only KNOWN k (that I am aware of) for Sierp Base 16 that has algebraic factors below the conjectured Sierp k? (Math disclaimer: Don't take me 100% literally on that statement. I suppose others 'might' have algebraic factors but if they do, they most likely have a very low prime at n=1 or 2. I haven't checked for that possibility.)

I attempted to generalize it like I did for Riesel bases 12 and 29 because that is how one learns how often and it what manner these kind of factors 'repeat' so to speak. If I had a second such situation that occured, I think I could. But alas, I couldn't come up with anything and it would take too long to extend the k's searched until a second such equation was found.

Riesel base 12 was the most misleading one to generalize. I had initially assumed that the algebraic factors for 27*12^n-1 would occur for all k=m^3. Testing proved otherwise. They only occur for every k=3*m^2! :shock: While that one was the most misleading, Riesel base 28 had the most unusual 'repeating' sequence. Algebraic factors there occur only when k=m^2 AND k==(12 or 17) mod 29. :shock::shock:

Just when you think you have these things figured out, something new comes along! One thing I've concluded: If there's a larger percentage than usual of k=m^2 or k=m^3 remaining, you have to check them for algebraic factors. That should be a no-brainer but you never know. Some of them simply cannot be factored and are frequently just very low weight.


Gary

I stopped base 10 at n=195000 for the remaining four k. If someone else wants to continue, they are free to do so.

For base 31 Sierpinski number is 4562804. (331,19,7,13,37)
One thing that I have noted in generating these numbers is that as the base gets larger the sierpinski/riesel numbers get smaller and smaller and easier to generate.

[quote=rogue;120950]I stopped base 10 at n=195000 for the remaining four k. If someone else wants to continue, they are free to do so.[/quote]

Thanks for the info. Rogue.

In addition to four more base 10 k's to search, I'm "adding back" the five squared k's for Riesel base 30 that are on the web pages but where I suggested not searching them originally. More analysis convinced me that there is no combintation of numeric and algebraic factors that cover all n so they should all have a prime at some point. All are very low weight though, partly because all even n do have algebraic factors. That is in one of the equations, 25*30^n-1, where n=2*q, it factors to (5*30^q-1)*(5*30^q+1). So if you want to get up to high n-ranges quickly, these will be the ones for you. Or you can just take Rogue's k's. They're already at n=195K.

Rogue's former k's that can now be searched from n=195K:

Riesel's:
4421*10^n-1
7019*10^n-1
8579*10^n-1

Sierpinski:
7666*10^n+1

Riesel base 30 squared k's that can now be searched from n=25K in addition to the k's shown in the first post here:

25*30^n-1
225*30^n-1
1024*30^n-1
1936*30^n-1
2916*30^n-1

IMPORTANT NOTE: The sieving programs will not remove algebraic factors. After sieving to a nominal limit on squared k's such as this, you'll want to manually remove all even n's. Srsieve will show 'Warning: algebraic factors' but I don't know if any of the other sieving programs do. You can use the Excel MOD function, sorting, deleting, and resorting to accomplish this.

Personally, I like to remove them after I've run srsieve to P=500M or 1G but before I feed them to sr2sieve or sr1sieve for deeper sieving.


Gary

[quote=Citrix;120952]For base 31 Sierpinski number is 4562804. (331,19,7,13,37)
One thing that I have noted in generating these numbers is that as the base gets larger the sierpinski/riesel numbers get smaller and smaller and easier to generate.[/quote]

Oh, EXCELLENT! I had tested it to 5M and for some reason missed it so I'll show it on the page. Robert had indicated the same thing to me about the #'s getting smaller as the bases get larger. Very strange! I would have expected the opposite.

Now, your task for today is to come up with the #'s for bases 3, 7, and 15 and make sure there are no lower ones with numeric covering sets! :grin:


Gary

[QUOTE=gd_barnes;120958] Robert had indicated the same thing to me about the #'s getting smaller as the bases get larger. Very strange! I would have expected the opposite.


Gary[/QUOTE]

Why is this strange, this should be obvious? Only numbers with b^n-1 =(b-1)*prime, n small will have large Sierpinski and riesel numbers. The interesting question to ask is that can k=2 be a sierpinski or riesel number for any base:smile:

[quote=Citrix;120959]Why is this strange, this should be obvious? Only numbers with b^n-1 =(b-1)*prime, n small will have large Sierpinski and riesel numbers. The interesting question to ask is that can k=2 be a sierpinski or riesel number for any base:smile:[/quote]

D'oh! :rolleyes: :sick: Shall I ask what 2 plus 2 is now? :grin: It's funny how when someone puts something in a different light than the way you've been microfocused on it, that it becomes obvious.

That is an interesting question about k=2. Are there any conjectures about it? Have you tested it?

What software did you use to get the conjecture for Sierp Base 31?


G

[quote=Citrix;120952]For base 31 Sierpinski number is 4562804. (331,19,7,13,37)
One thing that I have noted in generating these numbers is that as the base gets larger the sierpinski/riesel numbers get smaller and smaller and easier to generate.[/quote]

OK, Citrix, I get to throw a D'oh right back at you. Shouldn't it be obvious that 4562804*31^n+1 has a trivial factor of 3. :lol: So it's not the conjecture. For base 31, you have to eliminate all k's where k==1 mod 2, 2 mod 3, and 4 mod 5. 4562804 is both == 2 mod 3 and == 4 mod 5.

This is why I had missed it in my testing to k=5M. I eliminated all k's with the above conditions before testing. I'm 99% confident that the conjecture is k>5M. But since the Riesel conjecture is 134718, I wouldn't think it would be very much higher.


:smile:
Gary

[QUOTE=gd_barnes;120965]OK, Citrix, I get to throw a D'oh right back at you. Shouldn't it be obvious that 4562804*31^n+1 has a trivial factor of 3. :lol: So it's not the conjecture. For base 31, you have to eliminate all k's where k==1 mod 2, 2 mod 3, and 4 mod 5. 4562804 is both == 2 mod 3 and == 4 mod 5.

This is why I had missed it in my testing to k=5M. I eliminated all k's with the above conditions before testing. I'm 99% confident that the conjecture is k>5M. But since the Riesel conjecture is 134718, I wouldn't think it would be very much higher.


:smile:
Gary[/QUOTE]

Good one.:blush: I did not take the factorization of 31-1 into account. Anyway using the above covering set there are no solutions up to 50 millions. Some other covering set might work, but I have not tested it.

For fixed k and variable base
We know Sierpinski and Riesel numbers for k=4.
None are known for k=3 and k=2.
I have tested these a little bit, but haven't found a candidate. Perhaps no such bases exist.
This is what I was doing some time back (not up to date).
[url]http://www.mersenneforum.org/showthread.php?t=6918[/url]
:smile:

[quote=Citrix;120974]Good one.:blush: I did not take the factorization of 31-1 into account. Anyway using the above covering set there are no solutions up to 50 millions. Some other covering set might work, but I have not tested it.

For fixed k and variable base
We know Sierpinski and Riesel numbers for k=4.
None are known for k=3 and k=2.
I have tested these a little bit, but haven't found a candidate. Perhaps no such bases exist.
This is what I was doing some time back (not up to date).
[URL]http://www.mersenneforum.org/showthread.php?t=6918[/URL]
:smile:[/quote]


Sounds like another stubborn one like b=3, 7, and 15. No surprise since it's b=2^q-1. I'll have to take it up to 10 million with all covering sets in the near future.

That thread is good and interesting info. Thanks! My intention is to have ALL conjecture type info. in the pages for this effort somewhat like Karsten has done for the RPS effort. It'll be a while but I will put it on my list of things to do to include some or all of the info. in that thread.

Note to all: I have no intention of restricting this effort in any way. If anyone has info. or has done searches on bases > 32, go ahead and forward it my way and I'll eventually get it into the web pages.


Gary

I think I will try Base 9: 2036*9^n+1 (100K - 200k)

Is that ok or have someone alredy started working on this number?

I have alredy sieved the file to 5,5G with NewPgen and have now started seiving with SR2Sieve.

[QUOTE=Citrix;120959] The interesting question to ask is that can k=2 be a sierpinski or riesel number for any base:smile:[/QUOTE]

The answer is no! k=1,2,3 are not on and it has been proven (but not published). All k exist as non trivial Riesel and Sierpinski for some base except k=2^x-1 to my belief. A few stragglers beyond k=100 are known to be super-hard to find but base values have been discovered that are not trivial, they are just very very large.

Welcome to effort
 

[quote=japelprime;121000]I think I will try Base 9: 2036*9^n+1 (100K - 200k)

Is that ok or have someone alredy started working on this number?

I have alredy sieved the file to 5,5G with NewPgen and have now started seiving with SR2Sieve.[/quote]

Thanks and welcome to the effort Japelprime!

That one is not taken. I'll reserve it for you. That's a good choice too because it would be a GREAT one to find a prime for. Not only would it make the top-5000 list if the prime is n>105200, it would prove the conjecture! :smile:

FYI, you might consider using sr1sieve instead of sr2sieve for just one equation like this. It will be over twice as fast and you don't have to mess with removing factors at the end. Sr2sieve is better for sieving 2-3 or more equations. If there are any questions about that or anything else, please let us know. I or several others can answer.


Gary

Thanks Gary.

sr2sieve is doing fine with 741kp/sec but I will see if sr1sieve is doing better.
I was not aware of that sr1sieve remove the factors.

[quote=japelprime;121021]Thanks Gary.

sr2sieve is doing fine with 741kp/sec but I will see if sr1sieve is doing better.
I was not aware of that sr1sieve remove the factors.[/quote]
It will remove the factors as long as you use the -o command line switch to specify an output file.

[QUOTE=Anonymous;121024]It will remove the factors as long as you use the -o command line switch to specify an output file.[/QUOTE]

Thanks Anonymous.

Here is a covering set for base 31 sierpinksi. You can try constructing the lowest such number using this set.
(13,37,7,19,331,922561,577,3637,81343,1536553,1538083,512616735577)

Base 31, Sierpinski why not just 7; 13; 19; 37; 331 with 12-cover? The solution is less than 10^7

[quote=robert44444uk;121112]Base 31, Sierpinski why not just 7; 13; 19; 37; 331 with 12-cover? The solution is less than 10^7[/quote]

You beat me to the punch Robert. I was testing this up until k=10M like I had mentioned previously when you posted this. I also was expecting the same or a similar covering set as the Riesel conjecture.

The Sierpinski conjecture for base 31 is k=6360528. The covering set is as you said.


Gary

Thread renamed
 

I have renamed this thread to 'searches needed' instead of 'primes needed' to avoid confusion with the new 'report primes here' thread.

Updates
 

I updated the searches needed for several bases and added 2 k's that need to be searched for Sierp base 256.

535*256^n+1 has already been searched to top-5000 territory (n=53.7K) so that's one that someone may want to reserve. The search limit was converted from the search limit of n=430K for 535*2^n+1 on the Prothsearch pages.


Gary

How are people searching for covering sets to conjecture Sierpinski/Riesel numbers? If someone can suggest an algorithm I would be happy to try to implement it in C/ASM.

[quote=geoff;122286]How are people searching for covering sets to conjecture Sierpinski/Riesel numbers? If someone can suggest an algorithm I would be happy to try to implement it in C/ASM.[/quote]

That would be great and it's interesting that you asked. I just run all possible k's that don't have trivial factors through srsieve for the range of n=1-10K up to P=25K; about 100000 k's at a time. Whatever the first k is that it removes from the sieve is the conjecture. I then just go to Alperton's site and figure out the covering set. This is dead-on accurate assuming that a covering set doesn't include a factor > 25K (highly unlikely I think).

It was pretty ugly but highly effective and accurate and I came up with lower conjectures that way in 3-4 cases than were previously shown in the various threads for bases 6-18, 10, 22, 23, etc. There is one exception to the 'highly effective' statement. Since srsieve only allows slightly > 100000 k's at a time, it takes quite a while to go much beyond k=2-3M, which requires all manual effort. Sierp base 31 (conjecture k>6M) took 1-2 hours of manual effort on my part to come up with and of course it's impossible for bases 3, 7, and 15, although I was able to determine that the conjectures for base 3 and base 7 had to be k>2M and k>200K respectively.

Robert and Citrix seem to know the math behind searching various covering sets and how to come up with one in the first place. I'd be curious to see it myself.


Gary

[QUOTE=gd_barnes;122289]That would be great and it's interesting that you asked. I just run all possible k's that don't have trivial factors through srsieve for the range of n=1-10K up to P=25K; about 100000 k's at a time. Whatever the first k is that it removes from the sieve is the conjecture.[/QUOTE]

That should work OK, but it is very inefficient because there are a large number of k and only a small range of n, and the algorithm used by srsieve is designed for the opposite situation.

I have found Robert's post and will think about how to automate some of [url=http://www.mersenneforum.org/showpost.php?p=95416&postcount=17]this[/url].

[quote=geoff;122340]That should work OK, but it is very inefficient because there are a large number of k and only a small range of n, and the algorithm used by srsieve is designed for the opposite situation.

I have found Robert's post and will think about how to automate some of [URL="http://www.mersenneforum.org/showpost.php?p=95416&postcount=17"]this[/URL].[/quote]


Sounds great. That's a nice piece of work by Robert but ultimately I couldn't quite understand all of it well enough to guarantee 100% accuracy in coming up with the conjectures.

About the lack of efficiency of srsieve in that scenario...that was clear but it didn't matter much with what I was running. Over 90% of the time, I just had to run one test and the total run time was generally < 5 mins. for each 100000+ k test. < 10% of conjectures are k>100000. And I wouldn't wait for it to actually save the huge file, which would take many more mins. I'd just hit Ctl-C twice, delete the file, and if no sequence was removed from the sieve, run through the next 100000+ k test.

What we really need a program for at this point are bases 3, 7, and 15 only that I am aware of, although I've only tested all bases up to base 33 plus bases 64, 128, and 256. But it would certainly speed up things when and if we extend to larger bases in the future.


Gary

Liskovets-Gallot numbers are beautiful for us!
 

Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

[url]http://www.mersenneforum.org/showthread.php?t=9830#2[/url]

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean

i read about your post but no time yet to work with.
it's quite an interesting conjecture to prove and i'm interested in the Riesel odd/even side of this problem. it's worth another extra data page for the RPS site.
will do this for the Riesel power-2 bases for CRUS too next time.
i think i take some searching on 9519, 14361, 19401 and 20049. which ranges you searched yet? any findings?
karsten

[quote=Jean Penné;122567]Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

[URL]http://www.mersenneforum.org/showthread.php?t=9830#2[/URL]

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean[/quote]

Oh yes, I saw it. I had to think about it before responding and then promptly forgot to respond! :rolleyes:

I would be in favor of doing the even conjecture on both sides because it is subset of this project! The even Sierp conjecture is a subset of your Sierp base 4 project. In other words, as stated before, I'll be glad to help coordinate sieving and searching Sierp base 4. But I/we can make k=23451 and 60849 our first priority.

The same applies to Riesel base 4. We (you, in this case because you're searching them) can make k=9519, 14361, 19401 and 20049 a higher priority for Riesel base 4 than the other k's.

Finding a prime for these 6 k's wouldn't prove our conjectures but it would help out a lot and of course it would prove the 'Gallot conjectures'.

I think the odd conjectures would be somewhat outside of the scope of this project so I wouldn't be inclinded to coordinate a search on it (I'm so busy I can't hardly see straight with what we have!). But if you want to create a thread within this project, keep track of everything, and ask people if they'd like to help with sieving/searches, that's fine with me.

I didn't know if you wanted my opinion on doing searches on them or what I thought about the conjectures themselves. I think they were a BRILLIANT piece of work when they came out in 2001. Not so much in today's day and age when they can be easily computed. The even conjectures are just a subset/variation of our current base 4 conjectures and the odd conjectures would be kind of like a base 3.5 or 4.5 conjecture or something similar and could be easily computed by tweaking some of today's software that searches for covering sets.


Gary

I moved some status/reservation posts for Riesel base 4 to that thread.

[quote=Jean Penné;122567]Hi,

I would be happy to know your opinion about what I posted the 08 Jan 08 :

[URL]http://www.mersenneforum.org/showthread.php?t=9830#2[/URL]

(but perhaps it was misplaced, thus not seen...)

Regards,
Jean[/quote]

Jean,

I just had a small PM exchange with Karsten. Even though it isn't exactly what our project is doing, I think the base 2 odd/even cojectures would be an excellent sub-project for it so that is what we will do.

Karsten has a small web page already set up for it that I think he has now sent you. In a few days or when Karsten feels his web page is ready, I'll add it as a link from some of the current conjectures web pages as well as add its description as a sub-project in our project description.

As I told Karsten, one or both of you are free to create a new thread in this forum to coordinate searches for this if you desire.

Thanks for bringing up this interesting piece of work! The odd conjectures are the most interesting since they are unexplored territory whereas the even conjectures are just subsets of our current base 4 conjectures.

If you really want to take this to the maximum, you could come up with conjectures for k's that only have primes for n==0mod3, 1 mod3, 0mod5, 1mod5, etc., etc. I don't know if that's mathematically reasonable to pursue but it might be interesting to find out.


Gary

Considering that we now have all of this thread's info on the stats pages, should this thread be un-stickied and locked?

[quote=Anonymous;123161]Considering that we now have all of this thread's info on the stats pages, should this thread be un-stickied and locked?[/quote]


Yeah, that's one of about 25 things on my task list for this weekend! Actually my task was to update the first page here but it's becoming a duplicate maintenance nuisance. There may be some use for the thread in the future so I'll just unsticky it and put a date on the first page that shows when it was applicable.

Good suggestion.


G