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Old 2016-01-16, 04:41   #1
Gandolf
 
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Default Wall-Sun-Sun 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-(p|5))/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?
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Old 2016-01-21, 06:44   #2
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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.
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Old 2016-01-21, 12:36   #3
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Quote:
Originally Posted by Gandolf View Post
What is Mr. Silverman's position on the subject?
this Mr Silverman is on a ban for right now at very least.
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Old 2016-01-21, 15:06   #4
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Originally Posted by science_man_88 View Post
this Mr Silverman is on a ban for right now at very least.
Ok, thank you.
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Old 2016-01-21, 17:32   #5
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Quote:
Originally Posted by Gandolf View Post
I am curious to know the actual consensus about the existence of these primes?
On my page
https://oeis.org/wiki/User:Charles_R...special_primes
I have three references on Wall-Sun-Sun 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 2016-01-21 at 17:32
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Old 2016-01-21, 18:43   #6
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Thanks Charles, that makes it clearer now.

Do you have any idea why the conjecture appears named at OEIS as "the non-existence of Wall Sun Sun primes"?
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Old 2016-01-22, 02:50   #7
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Quote:
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Do you have any idea why the conjecture appears named at OEIS as "the non-existence of Wall Sun Sun primes"?
I don't, but I can see in the revision history that the particular entry was written by a high-school student so I would take it cum grano salis. That particular page hasn't been reviewed yet -- most of the OEIS editors focus on the sequences rather than the wiki.
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Old 2016-01-22, 03:27   #8
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Quote:
Originally Posted by CRGreathouse View Post
I don't, but I can see in the revision history that the particular entry was written by a high-school student so I would take it cum grano salis. That particular page hasn't been reviewed yet -- most of the OEIS editors focus on the sequences rather than the wiki.
Alright, the note section may indicate the reason why he named it that. Could you please read the references within it, and verify, since the name is changed now, it does not look consistent with the old reference.

http://arxiv.org/pdf/1102.1636v2.pdf

"The Wall-Sun-Sun prime conjecture is as follows,..There does not exist a prime p such that p^2 | F(p-(p|5))".
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Old 2016-01-22, 21:16   #9
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Quote:
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Alright, the note section may indicate the reason why he named it that. Could you please read the references within it, and verify, since the name is changed now, it does not look consistent with the old reference.

http://arxiv.org/pdf/1102.1636v2.pdf

"The Wall-Sun-Sun prime conjecture is as follows,..There does not exist a prime p such that p^2 | F(p-(p|5))".
The paper you cite was written, apparently, by two undergrads (sophomores, the paper says). It doesn't source the conjecture.

The Sun-Sun 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 W-S-S since the latter two do not join him.
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Old 2016-01-22, 22:54   #10
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Originally Posted by science_man_88 View Post
this Mr Silverman is on a ban for right now at very least.
Discussion on this moved to here
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Old 2016-01-23, 04:52   #11
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Discussion on this moved to here
Thanks.
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