Dear math-fun, Does anyone know the value of the sum 1/p^2, taken over the primes? I expect Euler did. R.
Mathematica calls this PrimeZetaP[2] to 100 digits, its 0.4522474200410654985065433648322479341732313432398924217364189303511650273639108744489575443549068582 http://reference.wolfram.com/mathematica/ref/PrimeZetaP.html Ed Pegg Jr On Fri, Jul 19, 2013 at 2:11 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Dear math-fun, Does anyone know the value of the sum 1/p^2, taken over the primes? I expect Euler did. R.
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Many thanks, Ed & Hans. Any known connexion with gamma, pi, etc. ?? On Fri, 19 Jul 2013, Ed Pegg Jr wrote:
Mathematica calls this PrimeZetaP[2]
to 100 digits, its
0.4522474200410654985065433648322479341732313432398924217364189303511650273639108744489575443549068582
http://reference.wolfram.com/mathematica/ref/PrimeZetaP.html
Ed Pegg Jr
On Fri, Jul 19, 2013 at 2:11 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Dear math-fun, Does anyone know the value of the sum 1/p^2, taken over the primes? I expect Euler did. R.
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Doesn't seem to be. http://en.wikipedia.org/wiki/Prime_zeta_function and http://oeis.org/A085548 have more. The Applications part of http://reference.wolfram.com/mathematica/ref/PrimeZetaP.html shows a link between Mertens' constant, Euler's gamma constant, and the Prime Zeta function. On Fri, Jul 19, 2013 at 3:19 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Many thanks, Ed & Hans. Any known connexion with gamma, pi, etc. ??
On Fri, 19 Jul 2013, Ed Pegg Jr wrote:
Mathematica calls this PrimeZetaP[2]
to 100 digits, its
0.**452247420041065498506543364832**247934173231343239892421736418** 930351165027363910874448957544**3549068582
Ed Pegg Jr
On Fri, Jul 19, 2013 at 2:11 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Dear math-fun,
Does anyone know the value of the sum 1/p^2, taken over the primes? I expect Euler did. R.
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One might also expect, on similar grounds, that Euler must have known the value of the sum 1/n^3 taken over the positive integers. :-) Jim Propp On Friday, July 19, 2013, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Dear math-fun, Does anyone know the value of the sum 1/p^2, taken over the primes? I expect Euler did. R.
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participants (4)
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Ed Pegg Jr -
Hans Havermann -
James Propp -
Richard Guy