## Re: Brun +

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• ... is ... If the three separate sums converge, then the sum of all three will also converge... ... Difficult to tell. Removing every n th prime would still
Message 1 of 2 , Jan 19, 2004
--- 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
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