On the sum of $sum_p prime frac1p^2-1$ [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite
2












I was wondering whether there exists a closed form solution for $sum_p prime frac1p^2-1$?




summation prime-numbers zeta-functions




share|cite|improve this question











closed as off-topic by Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy Jul 30 at 0:31


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
















    up vote
    1
    down vote

    favorite
    2












    I was wondering whether there exists a closed form solution for $sum_p prime frac1p^2-1$?




    summation prime-numbers zeta-functions




    share|cite|improve this question











    closed as off-topic by Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy Jul 30 at 0:31


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy
    If this question can be reworded to fit the rules in the help center, please edit the question.














      up vote
      1
      down vote

      favorite
      2









      up vote
      1
      down vote

      favorite
      2






      2





      I was wondering whether there exists a closed form solution for $sum_p prime frac1p^2-1$?




      summation prime-numbers zeta-functions




      share|cite|improve this question











      I was wondering whether there exists a closed form solution for $sum_p prime frac1p^2-1$?





      summation prime-numbers zeta-functions





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 29 at 6:15









      Hang Wu

      658




      658




      closed as off-topic by Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy Jul 30 at 0:31


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy
      If this question can be reworded to fit the rules in the help center, please edit the question.




      closed as off-topic by Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy Jul 30 at 0:31


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Shailesh, Claude Leibovici, B. Mehta, Xander Henderson, amWhy
      If this question can be reworded to fit the rules in the help center, please edit the question.




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          1
          down vote













          Let $P$ be the prime zeta function. Then, the answer is $displaystylesum_k=1^infty,P(2k)approx 0.55168$. As far as I know, there is no simple form for any $P(k)$, where $k>1$ is a positive integer.






          share|cite|improve this answer




























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote













            Let $P$ be the prime zeta function. Then, the answer is $displaystylesum_k=1^infty,P(2k)approx 0.55168$. As far as I know, there is no simple form for any $P(k)$, where $k>1$ is a positive integer.






            share|cite|improve this answer

























              up vote
              1
              down vote













              Let $P$ be the prime zeta function. Then, the answer is $displaystylesum_k=1^infty,P(2k)approx 0.55168$. As far as I know, there is no simple form for any $P(k)$, where $k>1$ is a positive integer.






              share|cite|improve this answer























                up vote
                1
                down vote










                up vote
                1
                down vote









                Let $P$ be the prime zeta function. Then, the answer is $displaystylesum_k=1^infty,P(2k)approx 0.55168$. As far as I know, there is no simple form for any $P(k)$, where $k>1$ is a positive integer.






                share|cite|improve this answer













                Let $P$ be the prime zeta function. Then, the answer is $displaystylesum_k=1^infty,P(2k)approx 0.55168$. As far as I know, there is no simple form for any $P(k)$, where $k>1$ is a positive integer.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 29 at 6:28









                Batominovski

                22.9k22777




                22.9k22777












                    Comments

                    Post a Comment

                    Popular posts from this blog

                    What is the equation of a 3D cone with generalised tilt?

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
                    Read more

                    Color the edges and diagonals of a regular polygon

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
                    Read more

                    Relationship between determinant of matrix and determinant of adjoint?

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
                    Read more