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24306Re: Prime sieving on the polynomial f(n)=n^2+1

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  • Mark
    Jul 7, 2012
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      The message below got stuck in the ether for over a day, and surely the Higgs boson had something to do with it. Anyways, Bernhard has since clarified things for me privately and I should be better now.

      Mark


      --- In primenumbers@yahoogroups.com, "Mark" <mark.underwood@...> wrote:
      >
      >
      > 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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