20200517, 15:15  #2  
Nov 2016
2·3·359 Posts 
Quote:


20200517, 17:36  #3 
Random Account
Aug 2009
U.S.A.
7×191 Posts 

20200527, 04:26  #4  
Nov 2016
2·3·359 Posts 
Quote:
An interesting one is k=279, there is no known twin prime (k*2^n1 and k*2^n+1), neither known 1st kind SophieGermain prime/Cunningham chain (k*2^n1 and k*2^(n+1)1) or known 2nd kind SophieGermain prime/Cunningham chain (k*2^n+1 and k*2^(n+1)+1) Twin prime: CK=237 1st kind SophieGermain prime/Cunningham chain: CK=807 2nd kind SophieGermain prime/Cunningham chain: CK=32469 Last fiddled with by sweety439 on 20200527 at 04:30 

20200527, 15:14  #5 
Quasi Admin Thing
May 2005
3×307 Posts 
Alert regarding b=2 Twin Conjecture
There is currently work in progress, for the Twin Conjecture, for base 2, where the 9 k's are being sieved for n=1 to n=100M. Mr. Bitcoin, BOINC (YOYO) and me, is currently sieving to p=10P and hopefully farther than that. There is currently 1,129,099 pairs remaining. I expect that to be reduced to maybe as little as 700,000 or less than 700,000, once we reach p=10P. Do not redo or overtake our effort, since we are much better off, working together  compared to competing with each other
N=100M is current max and if I live to see the exhaustion of these test range, I'll sure not start up an even higher effort for larger than 100M n's 
20200706, 18:39  #6 
Quasi Admin Thing
May 2005
3·307 Posts 
Alert regarding b=2 Sophie Germain conjecture.
I have for the past four days, finally cracked the logic needed to build a Sophie Germain conjecture sieve file. The sievefile is currently sieved to p=100e9 and has 15,241,723 terms remaining for the 32 sequences. My goal is to complete sieving to p=1000e9 (1T) and then before continuing ever higher with the sieving, I'll remove the candidates that PG has factored for us. Currently remaining minimum n=67 and maximum n=99,999,979.
Due to a seperate sieve for n=100,000,001  it can be said for sure, that the 2 candidate k's that had n=100,000,000 remaining at p=10e9, no longer needed that n to be included in the sievefile, since neither n=99,999,999 and n=100,000,001 excisted for any of the 2 k's that had n=100,000,000 remaining. So the reported minimum and maximum is the actual minimum and maximum n for n=1 to n=100,000,000. DO NOT start up your own effort of Sophie Germain, fixed k variable n search, since it requires some logic to do the initial work correct  logic you may not have due to inexperiency. BOINC is not applicable for sieving Sophie Germain sievefile  due to the amount of candidates remaining  eventually the matter might be a whole different  but for now it is a manual labor and eventually I might place a call out for whilling ressources, to help push the sieve and once (if) LLR2 gets working at SRBase, the offer will be for BOINC to test the candidates ready to test. Just like with the Twin Conjecture, if I live to see the exhaustion of the testrange (n=1 to n=100M) I sure will not start up another range 
20200706, 18:52  #7  
"Mark"
Apr 2003
Between here and the
2·3^{2}·5^{2}·13 Posts 
Quote:


20200706, 19:22  #8 
Dec 2011
After milion nines:)
2·653 Posts 

20200707, 00:03  #9 
"Mark"
Apr 2003
Between here and the
2×3^{2}×5^{2}×13 Posts 

20200707, 14:45  #10  
Quasi Admin Thing
May 2005
3·307 Posts 
Quote:
What has made this extremely difficult is that we have a fixed k/variable n approach due to the conjecture stating that k=807 is the smallest conjectured k, proven to never produce a SG prime for any n. So to prove that conjecture, we in other words have to prove that k: 39, 183, 213, 219, 273, 279, 333, 351, 387, 393, 399, 417, 429, 471, 531, 543, 561, 567, 573, 591, 597, 603, 639, 681, 687, 693, 699, 723, 753, 759, 771 and 795 is in fact having a prime. We are not interested in any other k's and due to the short range of k's, sieving to optimal sieve depth for fixed n, would be a nightmare as n climbs in value. Just like with the twin conjecture, I never really found a program that could greatly outdo the use of srsieve and later on sr2sieve. There is just not (as far as I know) a really good sieve for Twins and SG primesearch, for fixed k and variable n or sequence of k's and variable n. 

20200707, 14:49  #11 
Quasi Admin Thing
May 2005
3×307 Posts 
Sieving 32 sequences using sr2sieve, for an input file containing 15,241,723 terms and sieving the range 100G to 1T, sieves in average p=420,000 per core and removes a factor every 1.75 CPU/seconds.

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