## Sum of reciprocals of 'superprimes'

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• I don t have this value (Superprimes--by wikipedia definition--are primes of prime index, but I don t think much of the term) and it will take a while to get
Message 1 of 4 , Jul 16, 2013
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I don't have this value (Superprimes--by wikipedia definition--are primes of prime index, but I don't think much of the term) and it will take a while to get close on my machine using PARI, so if anybody wants to do this I think it's out there not computed yet. The first value over 1 (The sum is pretty close) occurs with term 148189304, the reciprocal of the 3081648379th prime (73898684653). A sharp enough estimate without actually summing is probably not hard, btw.
JGM
• ... http://math.stackexchange.com/questions/430369/what-is-the-value-of-sum-limits-i-1-infty-frac1p-p-i-where-p-i-i claims a value between 1.0444 and 1.0478.
Message 2 of 4 , Jul 16, 2013
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--- In primenumbers@yahoogroups.com, James Merickel <moralforce120@...> wrote:

> I don't have this value (Superprimes--by wikipedia
> definition--are primes of prime index, but I don't
> think much of the term) and it will take a while
> to get close on my machine

http://math.stackexchange.com/questions/430369/what-is-the-value-of-sum-limits-i-1-infty-frac1p-p-i-where-p-i-i

claims a value between 1.0444 and 1.0478.

David
• ... James did not give a refrence. As far as I can determine this result was first obtained by Richard Fischer, late in the evening of 17 October 2004.
Message 3 of 4 , Jul 19, 2013
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James Merickel <moralforce120@...> wrote:

> The first value over 1 (The sum is pretty close) occurs with term
> 148189304, the reciprocal of the 3081648379th prime (73898684653).

James did not give a refrence. As far as I can determine
this result was first obtained by Richard Fischer,
late in the evening of 17 October 2004.

>> Seit gestern spät abends kenne ich nun die Stelle,
wo die Summe 1 überschritten wird.
Dies ist bei der 148189304. prim-ten Primzahl.
n = 148189304
p(n) = 3081648359
p(p(n)) = 73898684653
Die Summe nach der Addition von 1/73898684653 lautet: 1.0000000000089
Die Extrapolationrechnung an dieser Stelle ergibt 1.043204331...
Wahrscheinlich dürfte die wahre Summe (bis n = unendlich) bis zur zweiten 4 korrekt sein, also 1.043204...
Gruss Richard <<

David
• PS: Jens confirmed and extended this result in 2005: http://tech.groups.yahoo.com/group/primenumbers/message/17241
Message 4 of 4 , Jul 19, 2013
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PS: Jens confirmed and extended this result in 2005:

> James Merickel <moralforce120@> wrote:
>
> > The first value over 1 (The sum is pretty close) occurs with term
> > 148189304, the reciprocal of the 3081648379th prime (73898684653).
>
> James did not give a refrence. As far as I can determine
> this result was first obtained by Richard Fischer,
> late in the evening of 17 October 2004.
>
>
> >> Seit gestern spät abends kenne ich nun die Stelle,
> wo die Summe 1 überschritten wird.
> Dies ist bei der 148189304. prim-ten Primzahl.
> n = 148189304
> p(n) = 3081648359
> p(p(n)) = 73898684653
> Die Summe nach der Addition von 1/73898684653 lautet: 1.0000000000089
> Die Extrapolationrechnung an dieser Stelle ergibt 1.043204331...
> Wahrscheinlich dürfte die wahre Summe (bis n = unendlich) bis zur zweiten 4 korrekt sein, also 1.043204...
> Gruss Richard <<
>
> David
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