Riesel base 3 reservations/statuses/primes

[gd_barnes]

Originally Posted by KEP

The Riesel base 3 is tested up to k=2M and n=25k. There is a 12 remaining k's and the ranges up to 100M is in progress at once. I found that taking the k to only n=5,000 and then do sieve of the remaining k's is much more efficient (about 90% faster). Is anyony by the way knowing of a great way to sieve many different k values from n=5,001 to n=25,000? I used to use NewPGen, but it requires a great deal of manual work to prepare the sieve files. Once the sieve files is prepared Sr1sieve can be used, using a .bat file and then sieveing will be rather easy, but anyone with a great idea to speedup and reduce the amont of manual work, please consider replying to me :)

On other notice to gary: I'm not working on the base 12 k=404 (sierpinski) since it appears that my reservation did not come through, and also I feel like wanting to do more somewhere else e.g. Base 3 Riesel Conjecture :)

KEP,

4 of your k's remaining are 3 times the value of 4 other k's that you have remaining, therefore they will eventually have the same prime (with an n-value that is 1 less) because the base is 3. Therefore the following k-values can be removed from your testing:

605658
903288
1030116
1816974

Also, 2 of your k's remaining have primes already found on the top-5000 site. Therefore the following k's can be removed from your testing:

343372 (prime at n=178255)
1575148 (prime at n=70462)

So, I am showing 6 k's remaining at k=2M and n=25K for Riesel base 3 on the web pages.

Testing note: For this project, we attempt to find the lowest prime for each k-value so just because there is a prior top-5000 prime does not mean we shouldn't test it at low n-ranges up to a reasonable limit. n=25K is a reasonable limit for base 3.

Further note: The already found top-5000 primes are typically quite rare for higher k-values for any base. There are no more of them for k<10M and only 2 more of them for k<100M for riesel base 3. So you shouldn't need to concern yourself with it until k>10M.

Now, you know how I was able to get to ZERO k's remaining at k=2M for Sierp base 3. The top-5000 site helped a lot.


Gary

[KEP]

Originally Posted by gd_barnes

KEP,

4 of your k's remaining are 3 times the value of 4 other k's that you have remaining, therefore they will eventually have the same prime (with an n-value that is 1 less) because the base is 3. Therefore the following k-values can be removed from your testing:

605658
903288
1030116
1816974

Also, 2 of your k's remaining have primes already found on the top-5000 site. Therefore the following k's can be removed from your testing:

343372 (prime at n=178255)
1575148 (prime at n=70462)

Thanks for confirming the "3 times value - 1n per 3 times multiplication" theory that I got myself. In the future, I'll remove all k's that can be split to a value remaining at the k's remaining list. Actually I decided to save them, for later removal, once a prime for the prior value was found, since I did not know if they had to be primed to be 100% sure of the proof for base 3 Riesel. Now I'll submit a site for you on later terms, where all those k's that can be reduced below k=2M (or upper testing in future), since there is no reason to take them from n>2,501 to n=25,000, would that be an ok way to do this? Also how would you like the k-values not tested for prime, or removed because they are 3 times the value of a prior value?

Now thanks for your ranges and let's hope these new ideas will help bring us even further and faster towards our goal, since I think the new push will help dramatically increase speed :)

KEP

EDIT: If you can give me the values of those 2 k's below 100M k's also found by the top5000 prime pages, I would really appreciate it since I'm already in progress with the range up to 100M :)

[gd_barnes]

Originally Posted by KEP

Thanks for confirming the "3 times value - 1n per 3 times multiplication" theory that I got myself. In the future, I'll remove all k's that can be split to a value remaining at the k's remaining list. Actually I decided to save them, for later removal, once a prime for the prior value was found, since I did not know if they had to be primed to be 100% sure of the proof for base 3 Riesel. Now I'll submit a site for you on later terms, where all those k's that can be reduced below k=2M (or upper testing in future), since there is no reason to take them from n>2,501 to n=25,000, would that be an ok way to do this? Also how would you like the k-values not tested for prime, or removed because they are 3 times the value of a prior value?

Now thanks for your ranges and let's hope these new ideas will help bring us even further and faster towards our goal, since I think the new push will help dramatically increase speed :)

KEP

EDIT: If you can give me the values of those 2 k's below 100M k's also found by the top5000 prime pages, I would really appreciate it since I'm already in progress with the range up to 100M :)

KEP,

I couldn't quite tell if you were clear on this so I'll be specific about multiples of the base:

We canNOT automatically eliminate ALL k's that are k==(0 mod 3), i.e. evenly divisible by 3, for base 3.

Here is why: If k*3^n+1 has a prime at n=1 and no other known prime than 3k*3^n+1 would only have a prime at n=0 and hence would NOT be eliminated. To be eliminated n must be >= 1. Here is what I think is the best way to test to avoid a lot of manual intervention:

1. Test the base for ALL k-values (except the k's with certain mods shown on the web pages) up to some predetermined n-limit in PFGW. In my case for base 3, that limit was n=25K. In your case, it is now n=5K, although I would recommend n=10K.

2. AFTER you finish #1 and BEFORE you begin sieving the k's remaining, it is at that point that you want to eliminate any k's that are the base times another k that is REMAINING. Or stated algebraicly, eliminate k's where k(2)=b*k(1) where k(1) is "some" k that is already remaining and k(2) is the k being checked. Note that I capitalize the word REMAINING because you don't want to automatically eliminate k's that are a multiple of the base but that are NOT the base times another k that is remaining.

You can see an example of #2 above on the web pages for your Riesel base 3. Your k=687774 is shown as the k-value with the 6th highest prime at n=12824. 687774 is divisible by 3. So the question is: Why don't we show k=687774/3=229258 with a prime of n=12825 instead since that would be a more reduced form? It's because k=229258 has a prime at n=1 and hence was immediately eliminated! This is the type of situation where we must continue testing 3*k and is why I recommend both steps 1 and 2 above.

Please excuse the overly detailed explanation if this was already intuitive to you but it's not obvious to many when they start on a new base so I figured I should offer it up here.

Here are the primes on the top-5000 site for Riesel base 3 for k=10M-100M:

19660318*3^63282-1
75030224*3^133779-1

Please go ahead and test these k's up to n=25K. If you don't find a prime to that limit, than you can eliminate them from any future sieving and I'll shown their primes on the web pages, assuming they're in the top-10 for the base.

There are no known Riesel base 3 primes shown on the top-5000 site for k=2M-10M and for k=100M-1G so that should be all you need for now.


Gary

[KEP]

@ Gary:

Thanks for your info. Sorry that I wasn't clear on my intuition, but what I meant I wanted to do, and has tried to explain on my GooglePage is exactly what you has descriped on step #1 and #2. Sorry if I caused you extra work as a lack of expression. It is obvious to me that the far easiest way to start testing a range is to use WinPFGW, but I think since a range of 1 G will leave only 40,000 candidates at n=2500 and about 5,000 candidates at n=5,000, that it will be sufficient to start sieving those candidates not going to be eliminated by lower k's remaining But again I'll decide later on, but for now it appears that the far fastes to do is to go to only n=2,500 and then sieve the remaining candidates before PRP testing useing WinPFGW, since it leaves the opportunity to stop testing k's if a prime is found.

Hope that I have not caused any confusion. But as it turns out, I have somehow given the wrong impression of what I wanted to do and in fact we were thinking to do the same However your post werent a complete waste of time, since now at least those k's remaining at sieveing below 100M will be able to be removed from the list before starting the sieve, so a little (propably non noteable) speedincrease might be a result of your effort

Thanks and again sorry if I caused you extra work and if I failed to express myself obviously and clear enough.

KEP!

[gd_barnes]

Originally Posted by KEP

@ Gary:

Thanks for your info. Sorry that I wasn't clear on my intuition, but what I meant I wanted to do, and has tried to explain on my GooglePage is exactly what you has descriped on step #1 and #2. Sorry if I caused you extra work as a lack of expression. It is obvious to me that the far easiest way to start testing a range is to use WinPFGW, but I think since a range of 1 G will leave only 40,000 candidates at n=2500 and about 5,000 candidates at n=5,000, that it will be sufficient to start sieving those candidates not going to be eliminated by lower k's remaining But again I'll decide later on, but for now it appears that the far fastes to do is to go to only n=2,500 and then sieve the remaining candidates before PRP testing useing WinPFGW, since it leaves the opportunity to stop testing k's if a prime is found.

Hope that I have not caused any confusion. But as it turns out, I have somehow given the wrong impression of what I wanted to do and in fact we were thinking to do the same However your post werent a complete waste of time, since now at least those k's remaining at sieveing below 100M will be able to be removed from the list before starting the sieve, so a little (propably non noteable) speedincrease might be a result of your effort

Thanks and again sorry if I caused you extra work and if I failed to express myself obviously and clear enough.

KEP!

No problem at all. It will also be a good reference for others in the future.

On the sieving, IMHO n=2500 is way too low to start sieving base 3. Are you taking into account all of the time needed and the extra hassle it will take you to sieve so many k's at once? The file sizes will become enourmous when sieving 40000 k's at once at such a low n-range and will be very difficult to maniptulate.

When you say you are going to sieve at n=2500, are you referring to using srsieve followed by sr2sieve? I should mention that it has a maximum # of k's that it can sieve at once. It's somewhere between 100000 and 200000 k's I think. Even though you're looking at 40000 k's, I strongly recommend using PFGW to n=10K or at least n=5K before sieving.

But if you think it will be faster, than go ahead. Just remember that it may be somewhat faster CPU-wise but there will a lot of manual intervention, i.e. determination of k's remaining, etc., when sieving so many k's. Be sure and consider your time involved also.


Gary

[gd_barnes]

Originally Posted by KEP

@ Gary: Well I has a feeling that it will be faster, but you are more experienced than I am, and with my quad (hopefully getting it tomorrow), I may consider to go to at least n=5,000. Actually the quad may be far from attacking and reenforcing the base 3 attack. At the moment I'm seriously considering to use 1 of the cores on sieveing the Base 19, actually preperation is already in progress, and currently I've begun using srsieve sieving from 10,001 to 250,000. I seriously consider running that range and reduce the amount of k's drasticly over the coming months. I know that I'm reserving loads of work at the moment, but at least this gives me a chance to contribute to something rather usefull. So hey please also sign me on this range: n>10000 > n =250000 for sierpinski base 19, all k's!

Thanks, and after sometime I think 2-3 month from now, this quad may be shipped to base 3 conjecture and to work with that one only, so we can consider this enrolement as praxis for the future and bigger battle it will enlist in

KEP!

It's more about manual intervention and messing with large files than anything. CPU-wise, n=2500 or 5000 may be slightly faster than 10000 or 25000 (although I doubt it on n=2500). It's just a matter of how much time you have to mess with the manipulation of large files and a large # of k's.

I'm all about results. Feel free to test it however you like. As long as it's done and not taking an extreme period of time, it makes little difference to me how you go about it.


Gary

[KEP]

Everyone, due to lack of interest and lack of possibilities of involveing myself, I've decided to release the entire Base 3 Riesel for k>100M to anyone interested in conducting work on those billions of k's remaining. This may actually be lower in the future who knows, but for now I'm signing out, and you will occationally see me check back, once I have work to add for the Base 19 Sierpinski. It's been a pleasure to be here, and I really look forward to get online every week and see what changes has been made.

Maybe in the future, given the fact that I'm a twin, I may give the Twin Prime Search, Gary is also coordinating a try, but for now I'm signing out. Thanks for all your kindness, and hope to see you some day when I can get more involved and sit behind a permanent internet connection more than 0-2 days a week

So anyone up for using NewPGen to remove lots of candidates and remove all the k's from k>100M up to n=25,000?

Take care!

KEP!

[KEP]

@Everyone: Thanks to Michafs script, I have gained the will to continue with this project. However for starters with, I'll only run it on 1 core and then on 2 cores and in 6 months on 6 cores. But unless anything else is noted, please reserve the entire base 3 riesel for me Gary. Now I just hope that it can be reduced even more, and that the sierpinskis can be equaly reduced, so we can just start dreaming about the bases being in the hundreds, maybe even dream so big that we can get to a point where we outrun the WinPFGW software, when it comes to the base limits which is unfortunantly at base 255 at the moment

Regards

Kenneth!

[gd_barnes]

Originally Posted by KEP

@Everyone: Thanks to Michafs script, I have gained the will to continue with this project. However for starters with, I'll only run it on 1 core and then on 2 cores and in 6 months on 6 cores. But unless anything else is noted, please reserve the entire base 3 riesel for me Gary. Now I just hope that it can be reduced even more, and that the sierpinskis can be equaly reduced, so we can just start dreaming about the bases being in the hundreds, maybe even dream so big that we can get to a point where we outrun the WinPFGW software, when it comes to the base limits which is unfortunantly at base 255 at the moment

Regards

Kenneth!

OK, I'll reserve all of Riesel base 3 for you Kenneth. I'm making an exception here. I usually recommend that no one bite off too big of an effort at once but in this case, coordinating amongst many people when just starting this particular base is quite difficult, as you saw with the Sierp side that still has a huge testing gap. When it comes to k-values remaining, frequently k's come up that can be reduced to k-values that others may be searching.

That said, once you get past about k=100M or so and all of the k-ranges below that have been searched, it shouldn't be an issue for several people to work on it at once. The key is that the range be kept within a multiplier-of-3 range so that k's that can be reduced are reduced to k-value ranges that have ALREADY been searched. That is, if we are at k=100M, we should limit the entire reservations of everyone to k=100M-300M. If we're at k=300M, then the limit would be k=300M-900M, etc. on up to where there is no limit once we're up to the conjecture divided by 3.

The confusion came in when people were searching k=100M-120M when the lower limit had only been searched to k=~15M resulting in reduced k-values in the k=33.3M-40M range, which had not been searched yet. This looks very strange and is kind of confusing to anyone new who comes along.


Gary

[KEP]

@Gary:

About your important 'or', I'm currently running the range 100-110M k, with Michafs script, to n<=5,000. Once they are verified, as the only k's remaining, I was considering to remove all k's that is divisable with the base, which in my case means that they can be k mod 3=0, but if this is not acceptabel (and if it involves to much manual work, though I think a spread sheat should be able to do the work for me pretty fast) I of course not will do it, so if I can get your oppinion on this it would really be appreciated.

Regards

Kenneth

Ps. It may be 14 days to 3 weeks before you really hears back anything from the further work done on the riesel base 3, due to working situations and the fact that I've stucked my Quad with other work for now. Also I have to finish wrapping the base 19 sierpinski to optimal sieve depth, before finally having 1 core availeable (hopefully in one weeks time). But in 3 weeks I may throw in the entire 6 cores. If that doesn't happen, I'll get back to you and we can then decide on how to proceed in the future run (simply to make sure we get somewhere and brings down this conjecture)

[michaf]

Missing out one or two with known primes isn't too bad; it's only a fraction of the total work to be done.
However, if it can be avoided, the better it is :)