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

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• Jul 5 12:29 PM
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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