What is the first 11 digit prime of Fibonacci?












1












$begingroup$


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..






fibonacci-numbers







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
    $endgroup$
    – Noble Mushtak
    Dec 28 '18 at 23:07










  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:16












  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:31








  • 2




    $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 29 '18 at 0:22












  • $begingroup$
    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.
    $endgroup$
    – CodeMonkeyAlx
    Dec 29 '18 at 0:49
















1












$begingroup$


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..






fibonacci-numbers







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
    $endgroup$
    – Noble Mushtak
    Dec 28 '18 at 23:07










  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:16












  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:31








  • 2




    $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 29 '18 at 0:22












  • $begingroup$
    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.
    $endgroup$
    – CodeMonkeyAlx
    Dec 29 '18 at 0:49














1












1








1





$begingroup$


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..






fibonacci-numbers







share|cite|improve this question











$endgroup$




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..






fibonacci-numbers




fibonacci-numbers






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 28 '18 at 23:35









David G. Stork

11k41432




11k41432










asked Dec 28 '18 at 23:05









CodeMonkeyAlxCodeMonkeyAlx

1152




1152








  • 2




    $begingroup$
    There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
    $endgroup$
    – Noble Mushtak
    Dec 28 '18 at 23:07










  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:16












  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:31








  • 2




    $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 29 '18 at 0:22












  • $begingroup$
    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.
    $endgroup$
    – CodeMonkeyAlx
    Dec 29 '18 at 0:49














  • 2




    $begingroup$
    There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
    $endgroup$
    – Noble Mushtak
    Dec 28 '18 at 23:07










  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:16












  • $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 28 '18 at 23:31








  • 2




    $begingroup$
    @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.
    $endgroup$
    – Arthur
    Dec 29 '18 at 0:22












  • $begingroup$
    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.
    $endgroup$
    – CodeMonkeyAlx
    Dec 29 '18 at 0:49








2




2




$begingroup$
There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
$endgroup$
– Noble Mushtak
Dec 28 '18 at 23:07




$begingroup$
There are no eleven-digit Fibonacci primes: oeis.org/A005478 There is, however, a 10-digit Fibonacci prime: $2971215073$
$endgroup$
– Noble Mushtak
Dec 28 '18 at 23:07












$begingroup$
@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.
$endgroup$
– Arthur
Dec 28 '18 at 23:16






$begingroup$
@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.
$endgroup$
– Arthur
Dec 28 '18 at 23:16














$begingroup$
@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.
$endgroup$
– Arthur
Dec 28 '18 at 23:31






$begingroup$
@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.
$endgroup$
– Arthur
Dec 28 '18 at 23:31






2




2




$begingroup$
@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.
$endgroup$
– Arthur
Dec 29 '18 at 0:22






$begingroup$
@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.
$endgroup$
– Arthur
Dec 29 '18 at 0:22














$begingroup$
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.
$endgroup$
– CodeMonkeyAlx
Dec 29 '18 at 0:49




$begingroup$
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.
$endgroup$
– CodeMonkeyAlx
Dec 29 '18 at 0:49










2 Answers
2






active

oldest

votes


















2












$begingroup$

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.






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    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 }$






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
      $endgroup$
      – Mohammad Zuhair Khan
      Dec 28 '18 at 23:57










    • $begingroup$
      @OscarLanzi Please check the edit history.
      $endgroup$
      – Mohammad Zuhair Khan
      Dec 29 '18 at 0:10











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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$


















      2












      $begingroup$

      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.






      share|cite|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        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.






        share|cite|improve this answer









        $endgroup$



        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 29 '18 at 4:16









        SladeSlade

        25.2k12665




        25.2k12665























            1












            $begingroup$

            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 }$






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 28 '18 at 23:57










            • $begingroup$
              @OscarLanzi Please check the edit history.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 29 '18 at 0:10
















            1












            $begingroup$

            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 }$






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 28 '18 at 23:57










            • $begingroup$
              @OscarLanzi Please check the edit history.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 29 '18 at 0:10














            1












            1








            1





            $begingroup$

            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 }$






            share|cite|improve this answer











            $endgroup$



            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 }$







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Dec 29 '18 at 0:19

























            answered Dec 28 '18 at 23:18









            David G. StorkDavid G. Stork

            11k41432




            11k41432












            • $begingroup$
              OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 28 '18 at 23:57










            • $begingroup$
              @OscarLanzi Please check the edit history.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 29 '18 at 0:10


















            • $begingroup$
              OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 28 '18 at 23:57










            • $begingroup$
              @OscarLanzi Please check the edit history.
              $endgroup$
              – Mohammad Zuhair Khan
              Dec 29 '18 at 0:10
















            $begingroup$
            OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
            $endgroup$
            – Mohammad Zuhair Khan
            Dec 28 '18 at 23:57




            $begingroup$
            OP asked for an 11 digit prime number. The fact that your number ends in $5$ may suggest that you have made a mistake.
            $endgroup$
            – Mohammad Zuhair Khan
            Dec 28 '18 at 23:57












            $begingroup$
            @OscarLanzi Please check the edit history.
            $endgroup$
            – Mohammad Zuhair Khan
            Dec 29 '18 at 0:10




            $begingroup$
            @OscarLanzi Please check the edit history.
            $endgroup$
            – Mohammad Zuhair Khan
            Dec 29 '18 at 0:10


















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            Mont Emei

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            Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog...
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