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I am having difficulty finding the first eleven-digit prime number of Fibonacci..

If anyone has an answer I would greatly appreciate it. I'm mostly asking this because it's one part of a greater puzzle I am trying to solve..

David G. Stork
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CodeMonkeyAlx
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    There are no eleven-digit Fibonacci primes: https://oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$ – Noble Mushtak Dec 28 '18 at 23:07
  • @RobArthan That's not how upvotes work. If you feel that this post is a good post (i.e. that it includes things like showing genuine effort, either work or research, and some context so that you, for instance, don't have to guess whether it's a coding problem) you are free to upvote. But they do not cancel eachother out, and they're not meant to. – Arthur Dec 28 '18 at 23:16
  • @RobArthan I can see that it's one vote up and one down, rather than none. And you get 5 reputation for an upvote and lose 2 for a downvote on a question post. So no, they do not outweigh one another at all. I agree that downvoters ought to explain their reasons. But undoing votes is a moderator privilege (at least I think they can do that), and not something we should go around doing all willy nilly. Upvote if you genuinely think the post deserves it (I don't think it does). Not to undo a downvote. – Arthur Dec 28 '18 at 23:31
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    @RobArthan Also, sociopath is a very strong word. Please refrain from using the names of actual mental diagnoses on what's likely just laziness or apathy. Or possibly being a jerk. – Arthur Dec 29 '18 at 00:22
  • Alright for those who were wondering. An employer posted a puzzle to find the elusive 11 digit Fibonacci Prime. in regards to a network security job. Thing is I know the tools I just dont know the Fibonacci. So I came here seeking out some help. – CodeMonkeyAlx Dec 29 '18 at 00:49
  • @CodeMonkeyAlx So you know, it is trivial to find these posts online, and this post is already a top hit for "11 digit prime fibonacci". This employer will have a very easy time determining that you sought online help for this puzzle. – Andrew Dudzik Dec 29 '18 at 04:06
  • @RobArthan Being a sociopath and acting like a sociopath are two very different allegations. You made the former, and that's something only qualified personnel should do after serious consultation. You seem to do it based on a single button press from the other side of the internet. And personally I don't know enough about sociopathy to feel comfortable accusing someone of acting like one either. Using the word without really meaning it detracts from its actual value. "Jerk" however, is a word I feel competent enough to use, and it means exactly what you mean when you say "sociopath" here. – Arthur Dec 30 '18 at 07:26
  • @Arthur:You haven't persuaded me to use generalised abusive terms like "jerk" in this context. Please allow me to reword the original comment to which you took offence: I really hate the sociopathic practice of downvoting questions with no explanation. Apparently the Stack Exchange ethos is that anonymous downvotes are a good thing. I will continue to upvote questions that I consider to have been erroneously downvoted with no explanation. – Rob Arthan Dec 31 '18 at 02:19

2 Answers2

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Here are the Fibonacci primes:

Select[Table[Fibonacci[i], {i, 1, 200}], PrimeQ]

$\{2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437,$

$ 2971215073, 99194853094755497, 1066340417491710595814572169,$

$ 19134702400093278081449423917 \}$

David G. Stork
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It is a standard result that if the $n$-th Fibonacci number is prime, then $n$ is prime, unless $n=4$. This makes the search much easier.

The Fibonacci number $F_{47}$ has 10 digits, and the Fibonacci number $F_{59}$ has 12 digits. (this is easy to check by direct computation, or using the approximation $F_n \approx \phi^n / \sqrt{5}$.) There is only one prime between $47$ and $59$, namely $53$.

So all we have to check is whether $F_{53}$ is prime. But with a computer, it is easy to find that $953$ is a factor.

We can conclude that there are no 11-digit Fibonacci primes.

Andrew Dudzik
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