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24303Re: Prime sieving on the polynomial f(n)=n^2+1

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  • Mark
    Jul 5, 2012
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      Hello Bernhard,

      Looking at table 4a, it seems to present column c as the number of primes up to 2^n, and column d as the number of primes of the form x^2+1 up to 2^n. But the numbers can't be correct so am I misunderstanding something?

      I'm looking at the small table 5b where it seems you extrapolate the number of primes of the form x^2+1 which are between 2^n and 2^(n+1). The number of such primes is decreasing as n increases, but it seems to me it should be going up.


      You wrote in the conclusion,

      "The density of the distribution of the primes p=x^2+1 goes surely to zero.
      Supposing that the exploration of the second scenario is rigth, it could be supposed that the primes of the form x^2+1 are limited."

      Are you saying that the number of primes of the form x^2+1 appears to be finite?

      Thanks,

      Mark



      --- In primenumbers@yahoogroups.com, "bhelmes_1" <bhelmes@...> wrote:
      >
      > A beautiful day,
      >
      > There are some results for primes concerning the polynom f(n)=n^2+1
      >
      > 109.90.3.58/devalco/quadr_Sieb_x^2+1.htm
      >
      > Besides some nice algorithms how to calculate these primes,
      > there are results for n up to 2^40
      >
      > You will find some nice graphics and some calculations.
      >
      > Mathematical feedback is welcome :-)
      >
      > Greetings from the primes
      > Bernhard
      >
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