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New Constant of Primes Sum

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  • Murad AlDamen
    Hola AmiGos In this paper I will define a new constant first let S (n) is the sum of primes 2+3+4+...+p (n). Note that if I don t put the product symbol * then
    Message 1 of 1 , Jul 1, 2001
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      Hola AmiGos

      In this paper I will define a new constant first let S (n) is the sum of primes 2+3+4+...+p (n).
      Note that if I don't put the product symbol * then it will be a function example
      p ((n+1)/2) is the prime in the order (n+1)/2

      The constant will be
      S (n)/(n*p ((n+1)/2))=C (n)

      C (1) = 1
      C (3) = 1.111111...
      C (5) = 1.12
      C (7) = 1.1836734693877551020408163265306 ...
      C (9) = 1.01010101...
      C (11) = 1.11888111...
      C (13) = 1.076923...
      C (15) = 1.1508771929824561403...
      C (17) = 1.1253196930946291560102301790281 ...
      C (19) = 1.0308529945553539019963702359347 ...
      C (21) = 1.0937019969278033794162826420891 ...
      C (23) = 1.027027027...
      C (25) = 1.034146341...
      C (27) = 1.088716624...
      C (29) = 1.085840059...

      Questions
      1) Are there infinitely many p (n) with C (2*m+1)-C (2*m-1)<0?
      2) What is the C (infinite)?
      3) Can we find a relation between p (n+1)-p (n) and (p (n+1)-p (n))^2 with C (n)?
      4) What are the maximum and minimum values of C (n)?
      5) Let C (n) can be define as constant in an interval " may be it will be found at infinite" can we find p (m) if p (n) is a constant
      and m > n
      6) there is a relation between the m's and its digits and you can determaine if a number is one of the divisors of another number by it
      example
      C (21)= 1.09 3 701 99 69278033794162826420891 ...
      C (7) = 1.18 3 67346938 7755 1020408163265306 ...
      You can see that
      C (21)= 1.09 3 701 99
      C (7) = 1.18 3 67346938 7755 but wht the relation between 67346938 and 701 is?
      Also i would like to present an amazing result of above constant



      Prime-Delta Inequality

      (2*p((m+1)/2)+(2*m+3)*Delta(m+1))/(2*p(m)+(2*m+1)*Delta(m))>=((2*p(2*m+2)+Delta(2*m+2))/(2*p(2*m)+Delta(2*m))



      Sincerely
      Murad AlDamen
      Http://www.angelfire.com/de2/abbas





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