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 F_p is the one prime". I do not understand how you can use Carmichael's theorem to reach any conclusions about how many F_p (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 F_p 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~~~~.

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

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)