20160116, 04:41  #1 
Jan 2016
1E_{16} Posts 
WallSunSun primes
I am curious to know the actual consensus about the existence of these primes?
Do they "probably exist", or might they exist probabilistically provided that the assumption is true, ie F(p(p5))/p behaving randomly modulo p? If I understand Chris Caldwell's comment correctly then the statement should depend on the assumption. I just want to clear up any ambiguity. Does anyone know of a formula to calculate the entry point (first occurrence) of a composite factor in the Fibonacci sequence? 
20160121, 06:44  #2 
Jan 2016
1E_{16} Posts 
What is Mr. Silverman's position on the subject?
I was reading Jiri Klaska's paper, which seems to suggest a heuristic that is half of what is conjectured. Is that correct? I'm not sure if that means that WSS primes still makes sense after klaska's adjustment. 
20160121, 12:36  #3 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 
this Mr Silverman is on a ban for right now at very least.

20160121, 15:06  #4  
Jan 2016
36_{8} Posts 
Quote:


20160121, 17:32  #5  
Aug 2006
172C_{16} Posts 
Quote:
https://oeis.org/wiki/User:Charles_R...special_primes I have three references on WallSunSun primes. All agree that there should be infinitely many and that up to x you expect some multiple of log(log(x)) for large enough x. They disagree on what the multiple should be: Klaška suggests it should be 1/2, while Grell & Pend argue (more persuasively, IMO) that it should be 1. I haven't heard anyone suggest that there should be finitely many. Last fiddled with by CRGreathouse on 20160121 at 17:32 

20160122, 02:50  #7  
Aug 2006
13454_{8} Posts 
Quote:


20160122, 03:27  #8  
Jan 2016
2×3×5 Posts 
Quote:
http://arxiv.org/pdf/1102.1636v2.pdf "The WallSunSun prime conjecture is as follows,..There does not exist a prime p such that p^2  F(p(p5))". 

20160122, 21:16  #9  
Aug 2006
2^{2}×1,483 Posts 
Quote:
The SunSun paper http://matwbn.icm.edu.pl/ksiazki/aa/aa60/aa6046.pdf doesn't make this conjecture. The Williams paper http://www.sciencedirect.com/science...98122182900268 says that "Wall's problem is to find a p such that ...", and suggests the 1/p heuristic which suggests infinitely many exist. Peng http://arxiv.org/abs/1511.05645 though says that Wall conjectured (something equivalent to the nonexistence of these primes). I don't have a copy of Wall's paper at the moment, but if so then this should properly be called Wall's conjecture rather than WSS since the latter two do not join him. 

20160122, 22:54  #10  
Tribal Bullet
Oct 2004
6641_{8} Posts 
Quote:


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