What is this product?

[MARTIN FULLER]

Perhaps 0.559865616932... although that value is not
in Plouffe's Inverter.

My estimate comes from
SUM(prime p; 1/p^2) = A085548, and
SUM(prime p; log(1-1/p)/p) + SUM(prime p; 1/p^2) =
  -0.127811073773...

which was based on a PARI calculation on the first
2^20 primes with 1000 digit precision.  The change
from 2^19 to 2^20 primes was -5E-14 and the
convergence appeared to be quadratic.

--- David Wilson <davidwwilson at comcast.net> wrote:

> What is PROD(prime p; ((p-1)/p)^(1/p))?  Is it 0 or
> positive?
> 
> It might be interpreted as the expected value of
> phi(n)/n for very large n.