20080504, 21:49  #12  
"Gary"
May 2007
Overland Park, KS
11,839 Posts 
Quote:
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 nvalue that is 1 less) because the base is 3. Therefore the following kvalues can be removed from your testing: 605658 903288 1030116 1816974 Also, 2 of your k's remaining have primes already found on the top5000 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 kvalue so just because there is a prior top5000 prime does not mean we shouldn't test it at low nranges up to a reasonable limit. n=25K is a reasonable limit for base 3. Further note: The already found top5000 primes are typically quite rare for higher kvalues 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 top5000 site helped a lot. Gary 

20080505, 06:38  #13  
Quasi Admin Thing
May 2005
1111010110_{2} Posts 
Quote:
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 :) Last fiddled with by KEP on 20080505 at 06:41 

20080505, 19:26  #14  
"Gary"
May 2007
Overland Park, KS
11,839 Posts 
Quote:
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 kvalues (except the k's with certain mods shown on the web pages) up to some predetermined nlimit 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 kvalue 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 top5000 site for Riesel base 3 for k=10M100M: 19660318*3^632821 75030224*3^1337791 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 top10 for the base. There are no known Riesel base 3 primes shown on the top5000 site for k=2M10M and for k=100M1G so that should be all you need for now. Gary 

20080505, 20:19  #15 
Quasi Admin Thing
May 2005
2·491 Posts 
@ 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! 
20080505, 20:34  #16  
"Gary"
May 2007
Overland Park, KS
11,839 Posts 
Quote:
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 nrange 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 CPUwise 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 

20080505, 21:27  #17  
"Gary"
May 2007
Overland Park, KS
11,839 Posts 
Quote:
It's more about manual intervention and messing with large files than anything. CPUwise, 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 

20080523, 15:40  #18 
Quasi Admin Thing
May 2005
2×491 Posts 
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 02 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! 
20080524, 20:02  #19 
Quasi Admin Thing
May 2005
2·491 Posts 
@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! 
20080525, 01:16  #20  
"Gary"
May 2007
Overland Park, KS
11,839 Posts 
Quote:
That said, once you get past about k=100M or so and all of the kranges 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 multiplierof3 range so that k's that can be reduced are reduced to kvalue ranges that have ALREADY been searched. That is, if we are at k=100M, we should limit the entire reservations of everyone to k=100M300M. If we're at k=300M, then the limit would be k=300M900M, 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=100M120M when the lower limit had only been searched to k=~15M resulting in reduced kvalues in the k=33.3M40M range, which had not been searched yet. This looks very strange and is kind of confusing to anyone new who comes along. Gary Last fiddled with by gd_barnes on 20080525 at 01:27 

20080525, 07:24  #21 
Quasi Admin Thing
May 2005
3D6_{16} Posts 
@Gary:
About your important 'or', I'm currently running the range 100110M 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) Last fiddled with by KEP on 20080525 at 07:27 Reason: Forgot a ps 
20080525, 07:31  #22 
Jan 2005
479 Posts 
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 :) 
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