Extended dual Sierpinski problem (for 78557<k<271129)

[sweety439]

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?

[philmoore]

Are there any other unresolved k values < 271129 for which you do not have a probable prime?

[henryzz]

Originally Posted by sweety439

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?

Not much use posting that without the search limits

[sweety439]

Originally Posted by philmoore

Are there any other unresolved k values < 271129 for which you do not have a probable prime?

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

[thunkii]

I have proven 2^42210+91549 as prime and uploaded the certificate to factordb (testing out new hardware).

[Jinyuan Wang]

Originally Posted by sweety439

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?

For k=79309, I checked every n < 500000 and found no primes of the the form 2^n+79309

[Alex]

Originally Posted by Jinyuan Wang

For k=79309, I checked every n < 500000 and found no primes of the the form 2^n+79309

Hello, Jinyuan Wang.

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

[ikari]

Originally Posted by Alex

Does anybody want to contribute too?
It may be called a part of Extended Dual Sierpinski problem

I like the sound of that! I tried searching for a probable prime of the form 2^n + 79309 a while ago, but found nothing (I think I searched up to n = 100000, but I don't quite remember).

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.

[gd_barnes]

Originally Posted by sweety439

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

This is a misleading list. It only lists primes/prp's for k's that remain on the "regular" 2nd Sierpinski problems, which include the Prime Sierpinski and Extended Sierpinski searches at PrimeGrid.

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 double-check 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.

[henryzz]

Originally Posted by gd_barnes

This is a misleading list. It only lists primes/prp's for k's that remain on the "regular" 2nd Sierpinski problems, which include the Prime Sierpinski and Extended Sierpinski searches at PrimeGrid.

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 double-check 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.

I feel like one of us is being brain dead(quite possibly me). Don't you need a prime for either 2^n+k or k*2^n+1 for the dual Sierpinski problem? If so starting from the remaining ks for the extended Sierpinski problem seems logical as that project has already searched the k*2^n+1 form pretty far. The dual Sierpinski problem isn't just 2^n+k. That is the representation of negative n values.
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.

[gd_barnes]

Originally Posted by henryzz

I feel like one of us is being brain dead(quite possibly me). Don't you need a prime for either 2^n+k or k*2^n+1 for the dual Sierpinski problem? If so starting from the remaining ks for the extended Sierpinski problem seems logical as that project has already searched the k*2^n+1 form pretty far. The dual Sierpinski problem isn't just 2^n+k. That is the representation of negative n values.
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.

I'm confused.

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.