Talk:Fibonacci prime

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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)


Gandalf61 - I'm glad you have a better understanding. First of all, the Fibonacci page says, "2, 3, 5, 13, 89, 233, 1597, 28657, 514229, …. It seems likely that there are infinitely many Fibonacci primes, but this has yet to be proven." Is this someone's opinion, or is there a reference?

The reference and definition of Carmichael's theorem can be thought of in explicit terms, rather than loose. "Every Fibonacci" "At least one of them" It does not state "at least x of them", where x expands at some rate. You can also look into Zsigmondy's theorem, and generalized details of the same properties. http://www.google.com/search?q=cache:h0RqXiBA72cJ:www.citebase.org/cgi-bin/fulltext%3Fformat%3Dapplication/pdf%26identifier%3Doai:arXiv.org:math/0412079+Zsigmondy+1892+&hl=en&gl=us&ct=clnk&cd=17

Details of my arguement about the infinitude, are updated frequently, and are available at the bottom(near) of this page. http://15k.us/Viswanath

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. The second link you gave, http://15k.us/Viswanath, does not seem to work - are you sure you have written it correctly ? 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)

Gandalf61 - Did you even read the first link?. Do you know what a heuristic mathematical arguement is? I've deleted the redundant filler words, until I consult with an expert for the precise definition that can be made permanent. Divineprime~~~~.

233rd Fibonacci number known to be composite??[edit]

F(7) = 13 = prime, F(13) = 233 = prime, F(233) = (if composite, what is its smallest factor??) Georgia guy 14:23, 11 July 2006 (UTC)

233 is not in the list of indices of Fibonacci primes at OEIS Sequence A001605, so F(233) is composite. Here is its factorisation, according to Ron Knott's Fibonacci pages:
F(233) = 2211236406303914545699412969744873993387956988653 = 139801 x 25047390419633 x 631484089583693149557829547141
Gandalf61 14:59, 11 July 2006 (UTC)

Error on the page[edit]

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 (talkcontribs)

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 (sequence A001605 in OEIS):

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)

All Fibonacci series[edit]

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)

Known Fibonacci Prime Section Flawed[edit]

The section listing known Fibonacci primes is erroneous and misleading. It seems to be paraphrased from the following:

"The first few proven prime Fibonacci numbers F_n are 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... (Sloane's A005478), which occur for n=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, 104911, 130021, 148091, 201107, 397379, ... (Sloane's A001605; Dubner and Keller 1999), where the Fibonacci numbers with indices 104911, 130021, 148091, 201107, 397379, 433781, 590041, 593689, 604711, 931517, 1049897, 1285607, 1636007, 1803059, 1968721, ... are probable primes (Caldwell)." [1]

Obviously 4 is neither a prime nor a Fibonacci number. It seems that the author was perhaps confused by the source. I do not know enough about the subject to correct it without leaving other errors but I want to point it out. I wish I could help more.--Rotellam1 (talk) 16:04, 9 September 2013 (UTC)

Please notice this comment from the source:
"Since F[n] divides F[mn] (cf. A001578, A086597), all terms of this sequence are primes except for a(2)=4 (=2*2 but F[2]=1). - M. F. Hasler, Dec 12 2007"
So the 4th term is a special case. — Glenn L (talk) 17:22, 9 September 2013 (UTC)
What is "erroneous and misleading" about the article saying:
"The first 33 are Fn for the n values (sequence A001605 in OEIS):
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."
It seems very clear to me that "Fn for the n values" means that the Fibonacci primes are F3, F4, F5, F7, F11, F13, F17, F23, F29, F43, F47, F83, F131, F137, F359, F431, F433, F449, F509, F569, F571, F2971, F4723, F5387, F9311, F9677, F14431, F25561, F30757, F35999, F37511, F50833, F81839
I think the list would be harder to read like that but several people have made your false "correction" of removing 4, so right after 4 I once added [1] the source comment "This prime is F_4 = 3 and should not be removed". This reduced (but didn't completely stop [2]) the false corrections, but readers don't see the comment. For each reader who makes the false correction or posts it to the talk page, there are probably many others who think we are wrong but don't do anything. The article already says: "Except for the case n = 4, all Fibonacci primes have a prime index". Do we really need to explain further that when we say "Fn for the n values", n is not the Fibonacci number but its index, and the index n = 4 gives the Fibonacci number F4 = 3, and 3 is prime although 4 is not. PrimeHunter (talk) 23:18, 9 September 2013 (UTC)

Why?[edit]

"(This implies the infinitude of primes.)" ????? — Preceding unsigned comment added by 186.140.103.166 (talk) 16:59, 15 September 2013 (UTC)

If there were only a finite number n of primes p then the n values Fp would have distinct prime factors, so each Fp would have to be one of the n primes. This is not the case. PrimeHunter (talk) 23:47, 15 September 2013 (UTC)
    • ^ Weisstein, Eric W. ""Fibonacci Prime"". MathWorld--A Wolfram Web Resource. Retrieved 9 Sept. 2013.