Talk:Fibonacci prime

message: Is it the lack of spaces that is making this display incorrectly?
It's missing the bottom half of the coded stuff.
Mathworld gives a different reference for the GCD rule.(Michael 1964; Honsberger 1985, pp. 131-132) Divineprime
:Divineprime - I now understand all of your statements about divisibility of Fibonacci numbers apart from the final sentence. This is where you say that Carmichael's theorem "does not seem to suggest that there are a finite number of examples where Fp is the one prime". I do not understand how you can use Carmichael's theorem to reach any conclusions about how many  Fp (with prime index) have only one primitive factor (and so are prime) or have more than one primitive factor (and so are composite). Can you give more details of your argument ? Is this last sentence your own opinion, or do you have a reference ? Gandalf61 10:47, 15 April 2006 (UTC)
replies: text: Divineprime - yes, it looks as if the statement that "it seems likely that there are infinitely many Fibonacci primes" on the Fibonacci number page is someone's unverified opinion. I have replaced it with "it is not known if there are infinitely many Fibonacci primes". I have also re-worded the final sentence in the Divisibility of Fibonacci numbers section to say that Carmichael's theorem does not tell us how many prime factors Fp will have, which is what I think you intended to say. And finally, you should end your contributions to Wikipedia discussion with four tildes, like this: ~~~~. This automatically signs your contributions with your user name and a timestamp, and makes discussions much easier to follow. Gandalf61 09:29, 20 April 2006 (UTC)
thread_title: ''Infinitely many''

message: First 2 has not been included which is both a number in the Fibonacci sequence and is a prime number.  
Second, 4 is included which is neither a prime number or a number in the Fibonacci sequence. 
Third, 7 and 11 are included which are prime numbers but are not in the Fibonacci sequence. —Preceding unsigned comment added by Agnostic 4 Now (talk • contribs) 
:I guess you refer to the text:
"It is not known if there are infinitely many Fibonacci primes. The first 33 are Fn for the n values :
:3, 4, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677, 14431, 25561, 30757, 35999, 37511, 50833, 81839."
Note that the list is not the Fibonacci primes Fn but their indices n. The corresponding Fibonacci primes Fn have up to 17103 digits for n=81839 so it would be impractical to list their decimal expansions. The page is correct. PrimeHunter (talk) 23:29, 15 May 2009 (UTC)
replies: text: To the lay person interested in this topic, it is not clear that 4 refers to the fourth Fibonacci prime rather than to the number four as a Fibonacci prime.  It would be appreciated if would be re-written to make that clear (without violating mathematical propriety. 67.209.133.209 (talk) 13:04, 25 October 2020 (UTC)
thread_title:  Error on the page 

message: Are all series considered?
0,2,2,4,6,10,26,36,62
0,3,3,6,9,15,24,39,63
divergence from convergence may be more interesting.
Mydogtrouble (talk) 21:25, 15 October 2009 (UTC)
thread_title:  All Fibonacci series 

message: This was undone  because of formal reason, but the fact is trivial. Adding the first relevant fibonacci primes (→Official OEIS list) – you can do it in Excel within one and a half minute. The result converges extreme fast to a constant number: 1.12644722767285.... — Preceding unsigned comment added by 176.5.31.69 (talk • contribs) 19:49, 21 October 2016 (UTC)
replies: text: Whether this sum is convergent depends on the behavior of the entire series (if there are infinitely many), not on the first few terms. The reciprocal of all primes diverges, so the result is not trivial at least. Of course if the pattern of large ratios between subsequent terms continues, it will converge, but adding these things to the article requires a reliable source. Gap9551 (talk) 20:08, 21 October 2016 (UTC)
replies: text: The sum must be less than the Reciprocal Fibonacci constant so it actually is trivial that it converges. But if reliable sources haven't bothered to mention it then I don't think we should either. The sum of the reciprocals of the indices of Fibonacci primes would be more interesting. I don't know whether convergence has been proved. PrimeHunter (talk) 21:04, 21 October 2016 (UTC)
replies: text: Good point, thanks. Gap9551 (talk) 17:32, 22 October 2016 (UTC)
thread_title: Reciprocal fibonacci primes

message: In that article it is conjectured to have infinitely many Fibonacci primes, so there are also Fibonacci primes above 10^10^10^100 (tetrational level) too! 2405:9800:BA31:F6:FD7E:6343:96DA:9CBD (talk) 05:44, 4 September 2021 (UTC)
thread_title:  Tetrational level