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

[henryzz]

Originally Posted by gd_barnes

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.

Looks like I have been fooled by the name "dual". Yes, this is definitely very misleading.

I am not sure that the joint conjectures are quite as easy as you make out. 28433 was part of both 5 and 17 or bust and 19249 was part of 17 and didn't quite make 5 (8th largest dual prp). I assume that being low weight for k*b^n+1 extends to being low weight for b^n+k.

[gd_barnes]

Originally Posted by henryzz

Looks like I have been fooled by the name "dual". Yes, this is definitely very misleading.

I am not sure that the joint conjectures are quite as easy as you make out. 28433 was part of both 5 and 17 or bust and 19249 was part of 17 and didn't quite make 5 (8th largest dual prp). I assume that being low weight for k*b^n+1 extends to being low weight for b^n+k.

Yeah, there is always a difficult 1-2-3 remaining. But that's about it. It would be like searching a base with conjecture < 1000 at CRUS. If you didn't prove it, there's a good chance it would have just a few k's remaining. The 2 k's remaining here would be like one of those.

I do agree that the "dual" definition likely means find a prime for either form to eliminate a k as shown on Wiki. It's just not the way it was set up here, which is why I didn't understand the post by Sweety earlier in this thread after Phil asked him if he knew of other k's without a prime. I felt like the response was not what was asked for but only Phil could answer that.

I checked my records further. I actually searched all 78557 < k < 271129 to n=100K back in 2010. 45 k's remain without a prime/prp.

[Alex]

Ikari, very well!

I think it`s time to make a map of Sierpinski problems

1) n > 0 and 2 < k < 78557 (Sierpinski problem: k*2^n+1)
ProthSearch, Seventeen or Bust, PrimeGrid

1a) n > 0 and 1 < k < 159986 (Sierpinski problem base 5: k*5^n+1)
Forum, PrimeGrid

2) n < 0 and 2 < k < 78557 (Dual Sierpinski problem: 2^|n|+k)
The dual Sierpinski problem search, Five or Bust

1+2) n > 0 and 2 < k < 78557 (Mixed Sierpinski problem: k*2^n+1 and 2^n+k)
EMIS - pdf

3) n > 0 and 78557 < k < 271129 (Extended Sierpinski problem: k*2^n+1)
PSP, PrimeGrid ESP, PrimeGrid PSP

4) n < 0 and 78557 < k < 271129 (officially unnamed, but may be called "Extended Dual Sierpinski problem")
(Riesel primes are not officially named either, but in many projects they are called that way)
We are here

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5) n > 1000 and 2 < k < 78557 (2nd Sierpinski problem: k*2^n+1)
(I have seen it somewere - may be in PrimeWiki - searching for the 2nd prime for k with only one n less than 1000)

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I hope I didn't miss anything

[Happy5214]

In addition to all of CRUS's Sierpinski conjectures for b ≤ 1030 (excluding b=2 and 5), PrimeGrid has done these in the past:

New Sierpinski Problem (SNoB): 2^n > k, 2 < k < 78557
PrimeGrid forums - Stream's GFN server

Extra SNoB: 2^n > k, 78557 < k < 271129
(same links)

Mega SNoB: 2^n > k, 271129 < k < 1048576
(same links)