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primes of the form p=n^2+1 and p=n^2+n+1

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  • bhelmes_1
    A peaceful day for all members of the group and especially for David, there is a small contribution for the primes of the form p(n)=n^2+1 and some algorithms
    Message 1 of 7 , Jun 17 7:14 AM
      A peaceful day for all members of the group and especially for David,

      there is a small contribution for the primes of the form p(n)=n^2+1 and some
      algorithms to calculate these primes and a result for the primes and the reducible primes
      up to n=2^40

      devalco.de I. Primes 6. quadratic sieving algorithms a) p(x)=x^2+1

      For people who like prime generators will find some nice mathematical background informations and
      different ways to impliment these algorithms.

      I tried to improve the website and there are still some improvements possible.

      It would be nice to get a little bit feedback and proposition for mathematical and algorithmical improvements.

      I plan to recalculate the primes of p(n)=n^2+n+1 up to 2^40 (see I. 6. b) which will take appr. 30 days
      and the distribution of a lot of other quadratic polynomials.

      Any suggestions which information could be useful ?
      a) number of primes for p(n)=n^2+n+1
      b) number of reducible primes p | n^2+n+1 with 1<p<n^2+n+1
      c) distribution of huge of the primes by the length of bits
      d) prime twins where p(n)=n^2+n+1 and p(n+1) are primes

      Nice greetings from the primes
      Bernhard


    • mgrogue
      For n*2^n+1, you should google for Cullen Primes. --Mark
      Message 2 of 7 , Jun 18 5:33 PM
        For n*2^n+1, you should google for Cullen Primes.

        --Mark

        ---- "bhelmes@... [primenumbers]" <primenumbers@yahoogroups.com> wrote:
        > A peaceful day for all members of the group and especially for David,
        >
        > there is a small contribution for the primes of the form p(n)=n^2+1 and some
        > algorithms to calculate these primes and a result for the primes and the reducible primes
        > up to n=2^40
        >
        > devalco.de I. Primes 6. quadratic sieving algorithms a) p(x)=x^2+1
        >
        > For people who like prime generators will find some nice mathematical background informations and
        > different ways to impliment these algorithms.
        >
        > I tried to improve the website and there are still some improvements possible.
        >
        > It would be nice to get a little bit feedback and proposition for mathematical and algorithmical improvements.
        >
        > I plan to recalculate the primes of p(n)=n^2+n+1 up to 2^40 (see I. 6. b) which will take appr. 30 days
        > and the distribution of a lot of other quadratic polynomials.
        >
        > Any suggestions which information could be useful ?
        > a) number of primes for p(n)=n^2+n+1
        > b) number of reducible primes p | n^2+n+1 with 1<p<n^2+n+1
        > c) distribution of huge of the primes by the length of bits
        > d) prime twins where p(n)=n^2+n+1 and p(n+1) are primes
        >
        > Nice greetings from the primes
        > Bernhard
        >
        >
      • djbroadhurst
        For the form n^2+1 and its associated Hardy-Littllewood constant, see http://arxiv.org/abs/0803.1456 http://arxiv.org/abs/0803.1456 David
        Message 3 of 7 , Jun 22 2:51 AM
          For the form n^2+1 and its associated Hardy-Littllewood constant, see
          http://arxiv.org/abs/0803.1456
          David


        • bhelmes_1
          Dear David, i hope you have a pleasant day, is there a list with the largest primes of the form p:=x^2+1 (or gaussian primes) and a actual list with the
          Message 4 of 7 , Jul 8, 2014
            Dear David,

            i hope you have a pleasant day,

            is there a list with the largest primes of the form p:=x^2+1 (or gaussian primes) and
            a actual list with the largest primes of the form p:=x^2+x+1 (related to eisenstein numbers)
            availible.

            It would be nice to know something more about this form of primes.

            I found The Prime Glossary: Gaussian Mersenne which is not really the same topic.

             

            I wish you a peaceful evening from Germany

            Prime numbers are very delicious for an amazing meditation


            Alles Gute

            Bernhard

          • Tom Hadley
            Bernhard, Start at www.oeis.org and enter the first few primes in the series for x^2+1 (2,5,17,37) in the search box, and it will take you to the right list.
            Message 5 of 7 , Jul 8, 2014
              Bernhard,
              Start at www.oeis.org and enter the first few primes in the series for x^2+1 (2,5,17,37) in the search box, and it will take you to the right list.
              Tom


              On Tue, Jul 8, 2014 at 10:09 AM, bhelmes@... [primenumbers] <primenumbers@yahoogroups.com> wrote:
               

              Dear David,

              i hope you have a pleasant day,

              is there a list with the largest primes of the form p:=x^2+1 (or gaussian primes) and
              a actual list with the largest primes of the form p:=x^2+x+1 (related to eisenstein numbers)
              availible.

              It would be nice to know something more about this form of primes.

              I found The Prime Glossary: Gaussian Mersenne which is not really the same topic.

              The Prime Glossary: Gaussian Mersenne
              Welcome to the Prime Glossary: a collection of definitions, information and facts all related to prime numbers. This pages contains the entry titled 'Gaussi...
              Preview by Yahoo

               

              I wish you a peaceful evening from Germany

              Prime numbers are very delicious for an amazing meditation


              Alles Gute

              Bernhard


            • bhelmes_1
              A peaceful evening for all members of the group,If someone is pleased by prime genarator algorithm concerning quadratic irreducible polynomialsthen he will
              Message 6 of 7 , Aug 18, 2014
                A peaceful evening for all members of the group,If someone is pleased by prime genarator algorithm concerning quadratic irreducible polynomialsthen he will find some nice descriptions about several algorithms and some resultsconcerning the cyclic polynomial f(n)=n²+1 and f(n)=n²+n+1 up to n=10^12I tried to describe the mathematical background and the algorithms so good as possible for me.Feedback or improvements are welcome.As far as i see there are something about 300 different polynomials which are usefull for prime generators.These polynomials have surely a relationship to the quadratic binary forms.It would be nice to get some more informations whether there is a geometrical explication in this contextor a deeper mathematical explication concerning the different kinds of multiplication structure of these groups.I limit the search for suitable polynomials only to prime generating functions for a kind of algorithms,which might be arbitrary as David mentioned.I am very interesting if someone will find faster algorithms maybe in the complex field which is still an open question.If someone is pleased by the thougt to calculate one or more sequences and has 4 weeks computer time free,help is very welcome.Description and results underDevalco - Einiges über Primzahlen

                 

                I. Primes 6. quadratic sieving algorithms a) and b) especiallyNice greetings from the primesBernhard
              • amel dalluge
                i have been hoping that we as a group could formulate a concrete solution to all primes using the waves i prior shared. because of the precision its just a
                Message 7 of 7 , Aug 19, 2014
                  i have been hoping that we as a group could formulate a concrete solution to all primes using the waves i prior shared. because of the precision its just a matter of doing the work. i am uneducated so it was a dream to work with the greatest minds on the subject but, you all seem reluctant and would rather get lost in guesses rather than fact.
                  all primes end with a one, three, seven or nine. these make four perfectly logical waves. breaking it down further, a person could take each of the four matching parts of the waves and make four new wave that only produce ending of one, three, seven or nine.
                  to demonstarate the true simplicity of primes and a concrete formula i will use the endings of one. in each wave there is four equations that can proude an ending of one; one times one, three times seven, seven times three, nine times nine.
                  these grow at a ratio of ten plus the multiplied. one wave in the group will grow at a ratio of ten plus the multiplier and will be your core wave with the other waves centering around it (ex; one times one become eleven times one and eleven times eleven).
                  using scientific notation one can determine how far out they want to go. i am uneducated and so i tried to put such strictly with endings of one in a tangible term some of you more knowledgable minds may be able to grasp to further distill or correct:
                  [1+(10)(infinity)][1+(10)(inf)]
                  =
                  1+[(10)(inf)+(100)(inf)][1+(10)(inf)];
                  [3+(10)(inf)][7]
                  =
                  21+[(30)(inf)+(100)(inf)];
                  [7+(10)(infi)][3]
                  =
                  21+[(70)(inf)+(100)(inf)];
                  [9+(10)(inf)][9]
                  =
                  81+[(90)(inf)+(100)(inf)].
                  this is just the formula for endings of one but, as can be apparent after the equals is the symetry of the growth. this makes a ratio of potential growth that is concrete. to illustrate, the product increases by ten times the multiplied, when the multiplied increases by ten the product increases by ten times the multiplier and the new product formula becomes an increase of a hundred to the original product increase of ten (110).
                  as i said, i'm uneducated and, it was my dream to work with this group and all the great minds to put prime numbers down once and for all. if any of you more knowledgable truly had sense you would realize your glory is superficial as an uneducated nobody is taking your cup of tea (glory) because you refuse to believe the impossible is possible when different walks of life combine their talents with an ambition to succeed.
                  all i want is success of a quest that no group has been able to accomplish and i'm trying my most to provide the concept of how to you minds who are clever enough to dare the impossible
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