recently i saw on a book (Apostol Analytic Number theory if i am not wrong) the prime calculating expression [tex] \sum_{p} 10^{-p}=S [/tex](adsbygoogle = window.adsbygoogle || []).push({});

where the sum was extended to all the prime numbers, if i am right

[tex] S=0.2003000500007............. [/tex]

so knowing the value of 'S' you could get the primes, hence here is my questions if we knew an 'accelerating' process for the series above in a similar way to Euler transformation or Euler-Laurin sum formula, could we get an efficient algorithm to calculate primes?.

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# The sum over primes involving powers of 10

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