Loading ...
Sorry, an error occurred while loading the content.
 

Pi2(x) & Riemann

Expand Messages
  • Guy H Bearman
    Hello! what do folk think of this, let pi_2(x) mean the count of twin primes
    Message 1 of 1 , Oct 29, 2001
      Hello!

      what do folk think of this,

      let pi_2(x) mean the count of twin primes<=x

      c=0.6601618158... the twin prime constant,prod (p=3,inf) [1-(p-1)^-2]

      then pi_2(x)/(2c) = 1+sum(s=1,inf) (log x)^s/(s*zeta(s+1)*(s+1)!)

      logs to base e,
      which is different from Riemann's sum only in that he used s! in the
      denominator, which is a good approx. of pi(x). This approximation is
      quite good numerically.

      that's all for now

      from Guy
    Your message has been successfully submitted and would be delivered to recipients shortly.