20201020, 12:09  #1 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
47×79 Posts 
Extended dual Sierpinski problem (for 78557<k<271129)
For the dual Sierpinski problem for 78557<k<271129, I found that 2^42210+91549 is (probable) prime, but I cannot find a (probable) prime for 2^n+79309, can someone find it?
Last fiddled with by sweety439 on 20201020 at 12:09 
20201020, 18:48  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
19×59 Posts 
Are there any other unresolved k values < 271129 for which you do not have a probable prime?

20201021, 10:25  #3 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{3}·19·41 Posts 

20201021, 15:37  #4  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
111010000001_{2} Posts 
Quote:
Code:
2^unknown+79309 2^9+79817 2^42210+91549 (PRP) 2^394+131179 2^21+152267 2^1032+156511 2^57+163187 2^1038+200749 2^44+202705 2^16+209611 2^27+222113 2^unknown+225931 2^11+227723 2^3+229673 2^38+237019 2^60+238411 

20230306, 21:22  #5 
Mar 2023
7 Posts 
I have proven 2^42210+91549 as prime and uploaded the certificate to factordb (testing out new hardware).

20230713, 06:43  #6 
Jan 2020
6_{10} Posts 

20230731, 15:37  #7  
"Alex_soldier (GIMPS)"
Aug 2020
www.Mersenne.ru
2·3·7 Posts 
PRP search: 2^n+79309
Quote:
Are you planning to continue checking further? I'm sieving the range n<10M now (currently I am at p=370M: ~193K candidates left). Next I`m planning to increase checked nmax > 500K. Does anybody want to contribute too? It may be called a part of Extended Dual Sierpinski problem 

20230801, 01:09  #8  
"Riley"
Sep 2021
Canada
2×3 Posts 
Quote:
The Dual Sierpiński Problem has been worked on extensively, but has anyone taken a stab at the Extended Dual Sierpiński Problem before? I haven't been able to find anything. I'll try looking for more k values (78557 < k < 271129) with no known (probable) primes of the form 2^n + k. If I find any, I'll make an update, and if anyone else does, I'd certainly be interested to know them. Last fiddled with by ikari on 20230801 at 02:00 

20230801, 12:37  #9  
"Gary"
May 2007
Overland Park, KS
3117_{16} Posts 
Quote:
It is no way is a complete list of the search of ALL k's for 78557<k<271129 for the extended dual Sierpinski problem, which is what the original problem was in this forum for k<78557. I'm referring to the one that was "almost" proven by finding prp's for all k<78557 of the form 2^n+k. Many years ago, I searched all k's of the form 2^n+k for 78557<k<271129 to n=25K. I showed that there were 64 k's remaining at n=25K including k=79309, 91549, and 225931 shown here. I would want to doublecheck a few things before saying for sure that the count is correct. The effort was done with a modified starting bases PFGW script from CRUS. If anyone is interested in the primes/prp's/remaining from the effort, I can post them. I have no interest in taking it further. 

20230801, 14:06  #10  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
1858_{16} Posts 
Quote:
https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number explains it fairly well. edit: After writing this post I realized that you were possibly referring to it being a misleading list for just the 2^n + k side. This is true although it may be a correct list for the dual Sierpinski problem. Last fiddled with by henryzz on 20230801 at 14:08 

20230801, 14:18  #11  
"Gary"
May 2007
Overland Park, KS
3·59·71 Posts 
Quote:
The original "five or bust" dual Sierpinski problem on this forum here, as defined by Phil Moore, had primes for all k's 2^n+k, not just ones that didn't have primes for k*2^n+1. See the project definition here: https://mersenneforum.org/showpost.p...91&postcount=1 Most of the larger primes they discovered had k's that already had primes for k*2^n+1 long before the project started. Defining a problem that allows finding either k*b^n+1 or b^n*k as a way to eliminate k's make such problems very easy and not interesting. I stand by what I said. The post that I responded to is misleading in the context of being posted in this forum. 

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