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Re: [PrimeNumbers] question on straigh forward calculation of prime numbers

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  • Maximilian Hasler
    ... Did you google ? There are explicit formulae for prime(n) but they are inefficient to compute. For example, on
    Message 1 of 2 , Mar 7, 2013
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      On Thu, Mar 7, 2013 at 10:55 AM, viva8698 <vaseghisam@...> wrote:
      > Hi,
      >
      > I have a question where I need a very very reliable answer:
      >
      > Does there exist any function in the world to which I can input the first 6 prime numbers and by finding its zeros I could just get the next 12768 prime numbers - and so forth?

      Did you google ?
      There are explicit formulae for prime(n)
      but they are inefficient to compute.
      For example, on http://en.wikipedia.org/wiki/Formula_for_primes
      you find
      p_n = 1 + \sum_{k=1}^{2(\lfloor n \ln(n)\rfloor+1)} \left(1 -
      \left\lfloor{\pi(k) \over n} \right\rfloor\right)
      with
      \pi(k) := k - 1 + \sum_{j=1}^k \left\lfloor {2 \over j} \left(1 +
      \sum_{s=1}^{\left\lfloor\sqrt{j}\right\rfloor} \left(\left\lfloor{ j-1
      \over s}\right\rfloor - \left\lfloor{j \over s}\right\rfloor\right)
      \right)\right\rfloor

      Now these aren't directly given as "roots of polynomials"
      even though that could probably be done ;

      OTOH I don't understand really well your "and so forth" - can you give
      an example for any other sequence of numbers, to see how that should
      work ?

      Maximilian


      >
      > I am indeed talkig about a straight forward calculation and not a sieving etc.
      >
      > I would be deeply thankful for your help.
      >
      > Thanks in advance
      > -Sam
      >
      >
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