--- In

primenumbers@yahoogroups.com, "John W. Nicholson" <johnw.

nicholson@s...> wrote:

> Brun found that the sum of 1/twins is a constant. I am guessing that

> cousins and sexies sums are simular in that they have constants too.

> What I am wondering is if the 1/(sum of twins, cousins, and sexies)

is

> a constant?

If the three separate sums converge, then the sum of all three will

also converge...

> If it is a constant, at what time does the of addition of

> more terms, as to approach of the sum 1/(all primes), does the sum

> become divergent? Maybe if a constant number of primes are removed

> from the sum of pries, say every fifth prime or primeth prime?

Difficult to tell. Removing every n'th prime would still leave a

divergent sequence. Removing every prime'th prime? Would still

diverge, since it's a more dense sequence than removing every n'th

prime.

> How about instead of the twins themselves the sums of the first

primes

> prior and after the twin? Like (1/2+1/7) + (1/3+1/11) + (1/7+1/17) +

> (1/13+1/23)....

Would still converge, since pretty much identical to the prime twin

sum.

Andy