--- In

primenumbers@yahoogroups.com, Paul Leyland <paul@...> wrote:

>

> On Mon, 2010-11-15 at 12:43 +0000, Mark wrote:

> > Yes, somewhat seriously, I had heard that the sum of the inverses of

> > the prime powers with exponent > 1 converges, while of course the sum

> > of the primes inverses does not.

>

> Given that the sum of the inverses of the integers with exponent > 1

> converges, and the primes are a proper subset of the integers, this is

> not particularly surprising.

I knew that at one time, thanks for the reminder. As

http://primes.utm.edu/infinity.shtml says, it converges to Pi^2/6.