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A survey on primes formulas

  1. Mar 18, 2003 #1
    a survey on primes formulas....

    let be the function a(x) defined as:

    1 Iff x is prime
    0 x is not prime

    then appliying Abel,s summation formula.it would be

    S(p)f(p)= c+I(0,Infinite)Pi(x)f´(x)

    where f(x) is a differentiable function and S(p) means summ over all the primes....Pi(x) is the usual formula of a number of primes <or = x.....¿is this formula true?.


    b)I think i have discovered a formula to summ all primes by using euler,s transformation to summ alternate series .
    in fact if you take the serie with general term:

    (-1)**n(Pi(n)-Pi(n-1))f(n) and apply Euler,s transformation you can find and approach to the summ of the series above and this series is equal to:

    S(0,Infinite)(-1)**nf(n)+S(p)f(n) .


    So you can obtain an approach to S(p)f(n).....
     
  2. jcsd
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