Prime Difference












3












$begingroup$


Given an integer n, output the smallest prime such that the difference between it and the next prime is at least n.



For example, if n=5, you would output 23, since the next prime is 29, and 29-23>=5.



More Input/Output Examples



1 -> 2 (3 - 2 >= 1)
2 -> 3 (5 - 3 >= 2)
3 -> 7 (11 - 7 >= 3)
4 -> 7
5 -> 23
6 -> 23
7 -> 89
8 -> 89


This is code-golf, so shortest code wins.










share|improve this question











$endgroup$

















    3












    $begingroup$


    Given an integer n, output the smallest prime such that the difference between it and the next prime is at least n.



    For example, if n=5, you would output 23, since the next prime is 29, and 29-23>=5.



    More Input/Output Examples



    1 -> 2 (3 - 2 >= 1)
    2 -> 3 (5 - 3 >= 2)
    3 -> 7 (11 - 7 >= 3)
    4 -> 7
    5 -> 23
    6 -> 23
    7 -> 89
    8 -> 89


    This is code-golf, so shortest code wins.










    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$


      Given an integer n, output the smallest prime such that the difference between it and the next prime is at least n.



      For example, if n=5, you would output 23, since the next prime is 29, and 29-23>=5.



      More Input/Output Examples



      1 -> 2 (3 - 2 >= 1)
      2 -> 3 (5 - 3 >= 2)
      3 -> 7 (11 - 7 >= 3)
      4 -> 7
      5 -> 23
      6 -> 23
      7 -> 89
      8 -> 89


      This is code-golf, so shortest code wins.










      share|improve this question











      $endgroup$




      Given an integer n, output the smallest prime such that the difference between it and the next prime is at least n.



      For example, if n=5, you would output 23, since the next prime is 29, and 29-23>=5.



      More Input/Output Examples



      1 -> 2 (3 - 2 >= 1)
      2 -> 3 (5 - 3 >= 2)
      3 -> 7 (11 - 7 >= 3)
      4 -> 7
      5 -> 23
      6 -> 23
      7 -> 89
      8 -> 89


      This is code-golf, so shortest code wins.







      code-golf number






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 2 hours ago







      Quintec

















      asked 3 hours ago









      QuintecQuintec

      1,5031722




      1,5031722






















          4 Answers
          4






          active

          oldest

          votes


















          1












          $begingroup$


          Husk, 8 bytes



          Ψḟo≥⁰≠İp


          Try it online!



          Inspired by this post in chat



          , under normal circumstances, finds the first element of a list that satisfies a predicate. However, when combined with the function Ψ, it finds the first element that satisfies a predicate with respect to its successor in the list.



          The predicate is o≥⁰≠, which asks if the absolute difference of two numbers is at least the input.



          The list is İp, the list of prime numbers






          share|improve this answer









          $endgroup$





















            0












            $begingroup$


            Husk, 9 bytes



            →←ġo<⁰-İp


            Try it online!



            This is a really interesting question allowing a range of possible approaches (and Husk is a good fit for it; I learned the language for the challenge).



            The TIO link contains a wrapper to run this function on all inputs from 1 to 10.



            Explanation



            →←ġo<⁰-İp
            İp The (infinite) list of primes
            ġ Group them, putting adjacent primes in the same group if
            - the difference between them
            <⁰ is less than the input
            o (fix for a parser ambiguity that causes this parse to be chosen)
            → Take the last element of
            ← the first group


            Grouping primes that are too close together means that the first break in the groups will be the first point at which the primes are sufficiently far apart, so we simply just need to find the prime just after the break.



            Other potential solutions



            Here's an 8-byte solution that, sadly, only works with even numbers as input (and thus isn't valid):



            -⁰LU⁰mṗN
            N On the infinite list of natural numbers
            m replace each element with
            ṗ 0 if composite, or a distinct number if prime
            U Find the longest prefix with no repeated sublist of length
            ⁰ equal to the input
            -⁰ Subtract the input from
            L the length of that prefix


            The idea is that when we have two primes that are a distance of (say) 6 apart, there'll be a sequence of five consecutive zeroes in the mṗN sequence, which contains two identical sublists of length 4 (the first four zeroes and last four zeroes), but such a repetition cannot happen earlier (because as each prime is mapped to a unique number, any length-4 substrings before the first prime gap > 4 will contain a prime number, and the substring will therefore be unique as it's the only substring which contains that number in that position). Then we just have to subtract the trailing zeroes from the length of the prefix to get our answer.



            This doesn't work with odd inputs because the sublist of input zeroes only occurs once rather than twice, so the code ends up finding the second point at which it occurs rather than the first.






            share|improve this answer











            $endgroup$





















              0












              $begingroup$


              Perl 6, 56 bytes





              {first {$^a.$![1]-$a>=$_},.$!}
              $!={grep &is-prime,$_..*}


              Try it online!



              I feel like there's definitely some improvement to be made here, especially in regards to the $![1]. This is an anonymous code block that can be assigned to a variable, as well as a helper function assigned to $!.






              share|improve this answer









              $endgroup$





















                0












                $begingroup$


                Jelly, 8 bytes



                2Æn:+ɗ1#


                Try it online!



                How it works



                2Æn:+ɗ1#  Main link. Argument: n

                2 Set the return value to 2.
                1# Find the first k ≥ 2 such that the link to the left, called with arguments
                k and n, returns a truthy value.
                ɗ Dyadic chain:
                Æn Find the next prime p ≥ k.
                + Yield k + n.
                : Perform integer division.





                share|improve this answer









                $endgroup$













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                  4 Answers
                  4






                  active

                  oldest

                  votes








                  4 Answers
                  4






                  active

                  oldest

                  votes









                  active

                  oldest

                  votes






                  active

                  oldest

                  votes









                  1












                  $begingroup$


                  Husk, 8 bytes



                  Ψḟo≥⁰≠İp


                  Try it online!



                  Inspired by this post in chat



                  , under normal circumstances, finds the first element of a list that satisfies a predicate. However, when combined with the function Ψ, it finds the first element that satisfies a predicate with respect to its successor in the list.



                  The predicate is o≥⁰≠, which asks if the absolute difference of two numbers is at least the input.



                  The list is İp, the list of prime numbers






                  share|improve this answer









                  $endgroup$


















                    1












                    $begingroup$


                    Husk, 8 bytes



                    Ψḟo≥⁰≠İp


                    Try it online!



                    Inspired by this post in chat



                    , under normal circumstances, finds the first element of a list that satisfies a predicate. However, when combined with the function Ψ, it finds the first element that satisfies a predicate with respect to its successor in the list.



                    The predicate is o≥⁰≠, which asks if the absolute difference of two numbers is at least the input.



                    The list is İp, the list of prime numbers






                    share|improve this answer









                    $endgroup$
















                      1












                      1








                      1





                      $begingroup$


                      Husk, 8 bytes



                      Ψḟo≥⁰≠İp


                      Try it online!



                      Inspired by this post in chat



                      , under normal circumstances, finds the first element of a list that satisfies a predicate. However, when combined with the function Ψ, it finds the first element that satisfies a predicate with respect to its successor in the list.



                      The predicate is o≥⁰≠, which asks if the absolute difference of two numbers is at least the input.



                      The list is İp, the list of prime numbers






                      share|improve this answer









                      $endgroup$




                      Husk, 8 bytes



                      Ψḟo≥⁰≠İp


                      Try it online!



                      Inspired by this post in chat



                      , under normal circumstances, finds the first element of a list that satisfies a predicate. However, when combined with the function Ψ, it finds the first element that satisfies a predicate with respect to its successor in the list.



                      The predicate is o≥⁰≠, which asks if the absolute difference of two numbers is at least the input.



                      The list is İp, the list of prime numbers







                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 2 hours ago









                      H.PWizH.PWiz

                      9,95721350




                      9,95721350























                          0












                          $begingroup$


                          Husk, 9 bytes



                          →←ġo<⁰-İp


                          Try it online!



                          This is a really interesting question allowing a range of possible approaches (and Husk is a good fit for it; I learned the language for the challenge).



                          The TIO link contains a wrapper to run this function on all inputs from 1 to 10.



                          Explanation



                          →←ġo<⁰-İp
                          İp The (infinite) list of primes
                          ġ Group them, putting adjacent primes in the same group if
                          - the difference between them
                          <⁰ is less than the input
                          o (fix for a parser ambiguity that causes this parse to be chosen)
                          → Take the last element of
                          ← the first group


                          Grouping primes that are too close together means that the first break in the groups will be the first point at which the primes are sufficiently far apart, so we simply just need to find the prime just after the break.



                          Other potential solutions



                          Here's an 8-byte solution that, sadly, only works with even numbers as input (and thus isn't valid):



                          -⁰LU⁰mṗN
                          N On the infinite list of natural numbers
                          m replace each element with
                          ṗ 0 if composite, or a distinct number if prime
                          U Find the longest prefix with no repeated sublist of length
                          ⁰ equal to the input
                          -⁰ Subtract the input from
                          L the length of that prefix


                          The idea is that when we have two primes that are a distance of (say) 6 apart, there'll be a sequence of five consecutive zeroes in the mṗN sequence, which contains two identical sublists of length 4 (the first four zeroes and last four zeroes), but such a repetition cannot happen earlier (because as each prime is mapped to a unique number, any length-4 substrings before the first prime gap > 4 will contain a prime number, and the substring will therefore be unique as it's the only substring which contains that number in that position). Then we just have to subtract the trailing zeroes from the length of the prefix to get our answer.



                          This doesn't work with odd inputs because the sublist of input zeroes only occurs once rather than twice, so the code ends up finding the second point at which it occurs rather than the first.






                          share|improve this answer











                          $endgroup$


















                            0












                            $begingroup$


                            Husk, 9 bytes



                            →←ġo<⁰-İp


                            Try it online!



                            This is a really interesting question allowing a range of possible approaches (and Husk is a good fit for it; I learned the language for the challenge).



                            The TIO link contains a wrapper to run this function on all inputs from 1 to 10.



                            Explanation



                            →←ġo<⁰-İp
                            İp The (infinite) list of primes
                            ġ Group them, putting adjacent primes in the same group if
                            - the difference between them
                            <⁰ is less than the input
                            o (fix for a parser ambiguity that causes this parse to be chosen)
                            → Take the last element of
                            ← the first group


                            Grouping primes that are too close together means that the first break in the groups will be the first point at which the primes are sufficiently far apart, so we simply just need to find the prime just after the break.



                            Other potential solutions



                            Here's an 8-byte solution that, sadly, only works with even numbers as input (and thus isn't valid):



                            -⁰LU⁰mṗN
                            N On the infinite list of natural numbers
                            m replace each element with
                            ṗ 0 if composite, or a distinct number if prime
                            U Find the longest prefix with no repeated sublist of length
                            ⁰ equal to the input
                            -⁰ Subtract the input from
                            L the length of that prefix


                            The idea is that when we have two primes that are a distance of (say) 6 apart, there'll be a sequence of five consecutive zeroes in the mṗN sequence, which contains two identical sublists of length 4 (the first four zeroes and last four zeroes), but such a repetition cannot happen earlier (because as each prime is mapped to a unique number, any length-4 substrings before the first prime gap > 4 will contain a prime number, and the substring will therefore be unique as it's the only substring which contains that number in that position). Then we just have to subtract the trailing zeroes from the length of the prefix to get our answer.



                            This doesn't work with odd inputs because the sublist of input zeroes only occurs once rather than twice, so the code ends up finding the second point at which it occurs rather than the first.






                            share|improve this answer











                            $endgroup$
















                              0












                              0








                              0





                              $begingroup$


                              Husk, 9 bytes



                              →←ġo<⁰-İp


                              Try it online!



                              This is a really interesting question allowing a range of possible approaches (and Husk is a good fit for it; I learned the language for the challenge).



                              The TIO link contains a wrapper to run this function on all inputs from 1 to 10.



                              Explanation



                              →←ġo<⁰-İp
                              İp The (infinite) list of primes
                              ġ Group them, putting adjacent primes in the same group if
                              - the difference between them
                              <⁰ is less than the input
                              o (fix for a parser ambiguity that causes this parse to be chosen)
                              → Take the last element of
                              ← the first group


                              Grouping primes that are too close together means that the first break in the groups will be the first point at which the primes are sufficiently far apart, so we simply just need to find the prime just after the break.



                              Other potential solutions



                              Here's an 8-byte solution that, sadly, only works with even numbers as input (and thus isn't valid):



                              -⁰LU⁰mṗN
                              N On the infinite list of natural numbers
                              m replace each element with
                              ṗ 0 if composite, or a distinct number if prime
                              U Find the longest prefix with no repeated sublist of length
                              ⁰ equal to the input
                              -⁰ Subtract the input from
                              L the length of that prefix


                              The idea is that when we have two primes that are a distance of (say) 6 apart, there'll be a sequence of five consecutive zeroes in the mṗN sequence, which contains two identical sublists of length 4 (the first four zeroes and last four zeroes), but such a repetition cannot happen earlier (because as each prime is mapped to a unique number, any length-4 substrings before the first prime gap > 4 will contain a prime number, and the substring will therefore be unique as it's the only substring which contains that number in that position). Then we just have to subtract the trailing zeroes from the length of the prefix to get our answer.



                              This doesn't work with odd inputs because the sublist of input zeroes only occurs once rather than twice, so the code ends up finding the second point at which it occurs rather than the first.






                              share|improve this answer











                              $endgroup$




                              Husk, 9 bytes



                              →←ġo<⁰-İp


                              Try it online!



                              This is a really interesting question allowing a range of possible approaches (and Husk is a good fit for it; I learned the language for the challenge).



                              The TIO link contains a wrapper to run this function on all inputs from 1 to 10.



                              Explanation



                              →←ġo<⁰-İp
                              İp The (infinite) list of primes
                              ġ Group them, putting adjacent primes in the same group if
                              - the difference between them
                              <⁰ is less than the input
                              o (fix for a parser ambiguity that causes this parse to be chosen)
                              → Take the last element of
                              ← the first group


                              Grouping primes that are too close together means that the first break in the groups will be the first point at which the primes are sufficiently far apart, so we simply just need to find the prime just after the break.



                              Other potential solutions



                              Here's an 8-byte solution that, sadly, only works with even numbers as input (and thus isn't valid):



                              -⁰LU⁰mṗN
                              N On the infinite list of natural numbers
                              m replace each element with
                              ṗ 0 if composite, or a distinct number if prime
                              U Find the longest prefix with no repeated sublist of length
                              ⁰ equal to the input
                              -⁰ Subtract the input from
                              L the length of that prefix


                              The idea is that when we have two primes that are a distance of (say) 6 apart, there'll be a sequence of five consecutive zeroes in the mṗN sequence, which contains two identical sublists of length 4 (the first four zeroes and last four zeroes), but such a repetition cannot happen earlier (because as each prime is mapped to a unique number, any length-4 substrings before the first prime gap > 4 will contain a prime number, and the substring will therefore be unique as it's the only substring which contains that number in that position). Then we just have to subtract the trailing zeroes from the length of the prefix to get our answer.



                              This doesn't work with odd inputs because the sublist of input zeroes only occurs once rather than twice, so the code ends up finding the second point at which it occurs rather than the first.







                              share|improve this answer














                              share|improve this answer



                              share|improve this answer








                              edited 2 hours ago


























                              community wiki





                              2 revs
                              ais523
























                                  0












                                  $begingroup$


                                  Perl 6, 56 bytes





                                  {first {$^a.$![1]-$a>=$_},.$!}
                                  $!={grep &is-prime,$_..*}


                                  Try it online!



                                  I feel like there's definitely some improvement to be made here, especially in regards to the $![1]. This is an anonymous code block that can be assigned to a variable, as well as a helper function assigned to $!.






                                  share|improve this answer









                                  $endgroup$


















                                    0












                                    $begingroup$


                                    Perl 6, 56 bytes





                                    {first {$^a.$![1]-$a>=$_},.$!}
                                    $!={grep &is-prime,$_..*}


                                    Try it online!



                                    I feel like there's definitely some improvement to be made here, especially in regards to the $![1]. This is an anonymous code block that can be assigned to a variable, as well as a helper function assigned to $!.






                                    share|improve this answer









                                    $endgroup$
















                                      0












                                      0








                                      0





                                      $begingroup$


                                      Perl 6, 56 bytes





                                      {first {$^a.$![1]-$a>=$_},.$!}
                                      $!={grep &is-prime,$_..*}


                                      Try it online!



                                      I feel like there's definitely some improvement to be made here, especially in regards to the $![1]. This is an anonymous code block that can be assigned to a variable, as well as a helper function assigned to $!.






                                      share|improve this answer









                                      $endgroup$




                                      Perl 6, 56 bytes





                                      {first {$^a.$![1]-$a>=$_},.$!}
                                      $!={grep &is-prime,$_..*}


                                      Try it online!



                                      I feel like there's definitely some improvement to be made here, especially in regards to the $![1]. This is an anonymous code block that can be assigned to a variable, as well as a helper function assigned to $!.







                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered 2 hours ago









                                      Jo KingJo King

                                      21.4k248110




                                      21.4k248110























                                          0












                                          $begingroup$


                                          Jelly, 8 bytes



                                          2Æn:+ɗ1#


                                          Try it online!



                                          How it works



                                          2Æn:+ɗ1#  Main link. Argument: n

                                          2 Set the return value to 2.
                                          1# Find the first k ≥ 2 such that the link to the left, called with arguments
                                          k and n, returns a truthy value.
                                          ɗ Dyadic chain:
                                          Æn Find the next prime p ≥ k.
                                          + Yield k + n.
                                          : Perform integer division.





                                          share|improve this answer









                                          $endgroup$


















                                            0












                                            $begingroup$


                                            Jelly, 8 bytes



                                            2Æn:+ɗ1#


                                            Try it online!



                                            How it works



                                            2Æn:+ɗ1#  Main link. Argument: n

                                            2 Set the return value to 2.
                                            1# Find the first k ≥ 2 such that the link to the left, called with arguments
                                            k and n, returns a truthy value.
                                            ɗ Dyadic chain:
                                            Æn Find the next prime p ≥ k.
                                            + Yield k + n.
                                            : Perform integer division.





                                            share|improve this answer









                                            $endgroup$
















                                              0












                                              0








                                              0





                                              $begingroup$


                                              Jelly, 8 bytes



                                              2Æn:+ɗ1#


                                              Try it online!



                                              How it works



                                              2Æn:+ɗ1#  Main link. Argument: n

                                              2 Set the return value to 2.
                                              1# Find the first k ≥ 2 such that the link to the left, called with arguments
                                              k and n, returns a truthy value.
                                              ɗ Dyadic chain:
                                              Æn Find the next prime p ≥ k.
                                              + Yield k + n.
                                              : Perform integer division.





                                              share|improve this answer









                                              $endgroup$




                                              Jelly, 8 bytes



                                              2Æn:+ɗ1#


                                              Try it online!



                                              How it works



                                              2Æn:+ɗ1#  Main link. Argument: n

                                              2 Set the return value to 2.
                                              1# Find the first k ≥ 2 such that the link to the left, called with arguments
                                              k and n, returns a truthy value.
                                              ɗ Dyadic chain:
                                              Æn Find the next prime p ≥ k.
                                              + Yield k + n.
                                              : Perform integer division.






                                              share|improve this answer












                                              share|improve this answer



                                              share|improve this answer










                                              answered 2 hours ago









                                              DennisDennis

                                              187k32297737




                                              187k32297737






























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                                                    Explanations of your answer make it more interesting to read and are very much encouraged.


                                                  • …Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.



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                                                  • …Please make sure to answer the question and provide sufficient detail.


                                                  • …Avoid asking for help, clarification or responding to other answers (use comments instead).





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