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