20230801, 15:11  #12  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
14104_{8} Posts 
Quote:
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. 

20230801, 15:21  #13  
"Gary"
May 2007
Overland Park, KS
2^{8}·7^{2} Posts 
Quote:
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. Last fiddled with by gd_barnes on 20230801 at 15:29 

20230812, 20:23  #14 
"Alex_soldier (GIMPS)"
Aug 2020
www.Mersenne.ru
2·3·7 Posts 
A map of Sierpinski problems :)
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  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)  I hope I didn't miss anything 
20230815, 15:36  #15 
"Alexander"
Nov 2008
The Alamo City
3^{2}·113 Posts 
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) Last fiddled with by Happy5214 on 20230815 at 15:36 Reason: Syntax typo 
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