20080510, 07:45  #45 
"Gary"
May 2007
Overland Park, KS
5·7·359 Posts 
Sierp base 3 now complete to k=15M and n=25K. Continuing on to k=30M.
In the range of, k=10M15M, 16 more k's were found to be remaining in addition to the 4 k's that were effectively found by KEP on his k=110M120M search for a total of 20. This now leaves 56 k's remaining for k<15M and n=25K. The total k's remaining including the k=110M120M range to n=25K is now 119. All k's remaining are shown on the Sierp base 3 reservations page. Gary 
20080511, 07:48  #46 
Jan 2005
479 Posts 
My idea what an ideal program would do on base 3 conjecture:
1) upto the limit of remaining k's: just search for n=1 to 100, when a prime found, next k 2) Store all remaining k's in memory, and sieve from n=101 to 1000 to the optimum sievedepth. As a crude estimate it will take about 1k of memory per k, so on a 4G system we could fit in some 4M remaining k's 3) Primetest from 101 to 1000 By this time, a huge load is already eliminated, and the results which are left, can be written to disc, without storage problems. 4) if tested to n=1000, I guestimate that for each 1M candidates some 100 will remain, so for Riesel base 3, we will be left with 74M * 100 = 7,4G candidate k's Which is still a huge load, but those can again be sieved in 4M batches to n=25k Priority can be changed at all time from 1001k and 1k25k (and eventually 25k100k etc...) now... if someone has the capacity to program... 
20080511, 08:29  #47  
Quasi Admin Thing
May 2005
2·5·101 Posts 
Quote:
Now back to your idea, I actually think that attacking to 100, a range of e.g. 1 G k's would leave us about 100,000 k's according to your stats. It's a lot to sieve, but since they only has to be sieved from n 1011000 optimal sievedepth would pretty fast be reached since testing time for Base 3 at n=<1,000 is very small. So actually I like these ideas, because I was told back in the future that it always is easier and faster to sieve millions or billions of pairs at same time in stead of just 1 k at a time. Now I suggest following to be done: Sive remaining k/n pairs from n=<1,000 < n < 25,000. At n=25,000 for Riesel base 3 we would have only about 80M k's remaining. These should then be sieved to n=< 25,001 < n < 50,000. Calculations hasn't been done as to how many can be expected to be found for n between 25,001 to 50,000. And of course it can't be sieved all k's at once, especially not unless the k limit is going to be at 64 bits in stead fo 32 bits. Hope I got it all, but maybe if someone choose to try to make such a program, we should suspend any work on the base 3, base 7, base 15 and maybe the remaining base 25 conjectures since we would waste a lot of time not needed to be wasted then. Also I think it would be more worthy to try to bring down the amount of unproven conjectures and then "if such program gets coded" launch a major and combined attack on that individually hard bases. Just my thoughts. Take care! KEP 

20080512, 10:48  #48 
Quasi Admin Thing
May 2005
2×5×101 Posts 
A quick question, to whome ever feel quilified to answer it:
Why, if all odd kvalues has trivial factors of 3 for any n for Base 3, both Sierpinski and Riesel, is k=1 not the lowest conjectured k? Just came to think about it, since I thought we were looking for the lowest k unable to ever raise a prime, so anyone has an explanation? Regards KEP! 
20080513, 18:24  #49  
"Gary"
May 2007
Overland Park, KS
5×7×359 Posts 
Quote:
For base 3, odd kvalues have a trivial factor of 2, not 3. And further: Any odd base odd kvalues have a trivial factor of 2. 1*3^1+1 = 4; is not prime nor can any nvalue be prime because they all give an answer that is divisible by 2. 1*3^11 = 2; is prime so cannot be the conjecture but is not considered for the same reason as the Sierp k=1. And taking it one step further on the Sierp side, we don't consider Generallized Fermat numbers, i.e. numbers that can reduce to the form b^n+1, because for it to be prime, n must be a perfect square and so the # of possible primes is very limited and in many cases not possible to find with our current knowledge, even if one does exist. 1*3^n+1 would be a GFN. You'll see a listing of GFN's without a prime on the right side of the main conjectures pages (if it doesn't have a trivial factor like base 3 does) but those are not considered as k's remaining. Gary 

20080513, 20:21  #50  
Quasi Admin Thing
May 2005
2·5·101 Posts 
Quote:
Base 19 sierpinski is at n=10444 and a total of 30 primes has been found and 22 made public for now. Base 12 sierpinski is at n=119646 and a total of 531 tests has been conducted, no primes yet Base 27 riesel. I'm actually considering releasing the 2 portions of sieved files aswell as the commandline.txt for rogue or other interested, since I'm in way over my head and really would like to focus fully on bringing down the sierpinski base 19 adn hopefully prove it, plus the time before I'm going to work further on the Base 27 Riesel range may be months in to the future, so I concluded that it would be most reasonable and fair to attach what work I've done on the range and release it to other more resourcesfull people. So attached is following file: Combo.zip which contains following files: Base27_1.zip contains the first of 2 sieve portions for base 27 riesel. Base27_2.zip contains the last of 2 sieve portions for base 27 riesel. A total of around 15,530 candidates remain below n 1M. Thanks and good luck to whoever takes this range and continues it. Regards KEP! Last fiddled with by KEP on 20080513 at 20:27 

20080519, 07:12  #51  
"Gary"
May 2007
Overland Park, KS
5×7×359 Posts 
Quote:
KEP, Thanks for releasing your sieved files here. One question: What ranges have you sieved? It looks like in one file you've sieved fully to 5195043419339, i.e. 5.195T. In the other file, it shows 14140965245863, i.e. 14.141T but it has more k's remaining. If you can clarify the ranges sieved, then we'll known what we need to sieve to complete the task. Thanks, Gary 

20080519, 08:58  #52 
"Gary"
May 2007
Overland Park, KS
5×7×359 Posts 

20080521, 10:10  #53 
Jan 2005
479_{10} Posts 

20080521, 22:08  #54 
Jan 2005
111011111_{2} Posts 
These are the sequences which have no primes upto 25k:
Code:
100143534*3^n+1 100190284*3^n+1 100193792*3^n+1 100670062*3^n+1 100852424*3^n+1 100999194*3^n+1 101186136*3^n+1 101311318*3^n+1 101315816*3^n+1 101349544*3^n+1 101619814*3^n+1 101818118*3^n+1 102014072*3^n+1 102046676*3^n+1 102127076*3^n+1 102159132*3^n+1 102281274*3^n+1 102531558*3^n+1 102746214*3^n+1 102857408*3^n+1 102862036*3^n+1 103152904*3^n+1 103267408*3^n+1 103270912*3^n+1 103321514*3^n+1 103323622*3^n+1 103396498*3^n+1 103950370*3^n+1 104168308*3^n+1 104618212*3^n+1 104882964*3^n+1 104927976*3^n+1 105070822*3^n+1 105080544*3^n+1 105207608*3^n+1 105492768*3^n+1 106047226*3^n+1 106065522*3^n+1 106148886*3^n+1 106337178*3^n+1 106349294*3^n+1 106430128*3^n+1 106463062*3^n+1 106634644*3^n+1 106646518*3^n+1 106743948*3^n+1 106967156*3^n+1 107217094*3^n+1 107248756*3^n+1 107463828*3^n+1 107468612*3^n+1 107617826*3^n+1 107778904*3^n+1 108009836*3^n+1 108143806*3^n+1 108232966*3^n+1 108326796*3^n+1 108410678*3^n+1 108520572*3^n+1 108532532*3^n+1 108609752*3^n+1 108638384*3^n+1 108776886*3^n+1 108790434*3^n+1 109042244*3^n+1 109116134*3^n+1 109384864*3^n+1 109486222*3^n+1 109668712*3^n+1 109832148*3^n+1 109842394*3^n+1 109908926*3^n+1 Last fiddled with by gd_barnes on 20080522 at 03:42 Reason: changed remaining k's to be within 'code' vs. 'quote' 
20080523, 07:26  #55  
"Gary"
May 2007
Overland Park, KS
5·7·359 Posts 
Quote:
Code:
kvalue reduces to 101186136 11242904 102281274 11364586 102746214 11416246 104927976 11658664 105080544 3891872 106065522 11785058 106337178 3938414 108790434 12087826 109832148 12203572 Code:
kvalue reduces to 100143534 33381178 100999194 33666398 102531558 34177186 104882964 34960988 105492768 35164256 106148886 35382962 106743948 35581316 107463828 35821276 108326796 36108932 108520572 36173524 108776886 36258962 Gary 

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