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Re: [PrimeNumbers] Re: COMMENT on A000040, A006562 and A001359 on the OEIS

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  • Phil Carmody
    ... I personally found next to nothing interesting in your post. If I were an editor of OEIS, I d have had serious reservations about your submissions. ... No
    Message 1 of 6 , Mar 12 5:54 AM
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      --- reismann@... wrote:
      > Your silence is deafening.

      I personally found next to nothing interesting in your post. If I were an
      editor of OEIS, I'd have had serious reservations about your submissions.

      > The decomposition prime(n)=weight*level+gap is a sieve.

      No it is not.

      > If we apply it to the
      > natural numbers, we obtain that:
      > http://reismann.free.fr/Graph_Entiers_1000000-R.html
      > It is a beautiful representation of the sieve of Eratosthene.

      No it is not.

      Phil

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    • reismann@free.fr
      Dear Phil and primenumbers Group, Thank you Phil for your answer. Why the decomposition in weight*level+gap is a sieve ?
      Message 2 of 6 , Mar 13 2:48 AM
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        Dear Phil and primenumbers Group,

        Thank you Phil for your answer.

        Why the decomposition in weight*level+gap is a sieve ?

        http://reismann.free.fr/img/sieveNb.jpg
        This graph is the representation of the decomposition of the natural numbers in
        weight * level (or weight * level + gap with gap = 0, the weight is the smallest
        divisor of n). The sets 1, 2, 3 etc... are exactly those whom we obtain by
        making a sieve of Eratosthene on the paper.
        This graph is also the representation of the decomposition of the natural
        numbers in weight * level + gap (with gap = 1, the weight is the smallest
        divisor of n-1). In that case the odd numbers have a weight of 2 (ex: 3 =
        2*1+1).
        The decomposition in weight * level + gap is thus a sieve.

        Applied to prime numbers, we obtain that:
        http://reismann.free.fr/classement.php

        The main differences:
        - for the natural numbers :
        * the weights are prime numbers
        * in the zone weight>level, We have only the numbers of level 1
        - for prime numbers:
        * the weights are odd
        * in the zone weight>level (zone 2), we have several levels (and a limit
        level, very important for the new algo).

        The decomposition in weight * level + gap is a sieve but by factorizing n-gap or
        prime(n)-gap(n). There are "multiples" and "waves" in prime numbers as there is
        among the natural numbers.

        Best,

        Rémi
      • Robin Garcia
        So,we must know p(n+1) to know p(n) and its unique decomposition. Est-ce que vous pensez que cette double et nécessaire connaissance, apportera vraiment un
        Message 3 of 6 , Mar 14 7:34 PM
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          So,we must know p(n+1) to know p(n) and its unique decomposition.

          Est-ce que vous pensez que cette double et nécessaire connaissance, apportera vraiment un air nouveau à notre connaissance des nombres premiers?

          Je ne dis pas que votre travail ne soit pas intéressant, mais je ne vois pas d´algorithmes utilisables.En avez vous?


          reismann@... escribió:
          Dear Phil and primenumbers Group,

          Thank you Phil for your answer.

          Why the decomposition in weight*level+gap is a sieve ?

          http://reismann.free.fr/img/sieveNb.jpg
          This graph is the representation of the decomposition of the natural numbers in
          weight * level (or weight * level + gap with gap = 0, the weight is the smallest
          divisor of n). The sets 1, 2, 3 etc... are exactly those whom we obtain by
          making a sieve of Eratosthene on the paper.
          This graph is also the representation of the decomposition of the natural
          numbers in weight * level + gap (with gap = 1, the weight is the smallest
          divisor of n-1). In that case the odd numbers have a weight of 2 (ex: 3 =
          2*1+1).
          The decomposition in weight * level + gap is thus a sieve.

          Applied to prime numbers, we obtain that:
          http://reismann.free.fr/classement.php

          The main differences:
          - for the natural numbers :
          * the weights are prime numbers
          * in the zone weight>level, We have only the numbers of level 1
          - for prime numbers:
          * the weights are odd
          * in the zone weight>level (zone 2), we have several levels (and a limit
          level, very important for the new algo).

          The decomposition in weight * level + gap is a sieve but by factorizing n-gap or
          prime(n)-gap(n). There are "multiples" and "waves" in prime numbers as there is
          among the natural numbers.

          Best,

          Rémi






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        • reismann@free.fr
          Dear Robin and primenumbers group, Yes it is necessary to know p(n+1) to have the decomposition. I do not propose magic formula. The magic formula would be to
          Message 4 of 6 , Mar 15 2:12 AM
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            Dear Robin and primenumbers group,

            Yes it is necessary to know p(n+1) to have the decomposition. I do not propose
            magic formula. The magic formula would be to have the decomposition without
            knowing p(n+1)...

            Will my vision of prime numbers bring answers to the big questions of the theory
            of the numbers?
            I do not know, I am not sure.
            But to what is of use a classification ? It serves for having a common language.
            It is surprising that in approximately 2500 years nobody did not find the
            sequence of the weights. No?

            >Have you a useful algorithm?
            With my friends Fabien we worked on a program giving the decompostion of prime
            numbers (in assembly for Windows) :
            http://reismann.free.fr/download/class_asm.zip
            There is also a program in Java on the "Download" page :
            http://reismann.free.fr/telechargements.php
            It is a "naive" algorithm. We work at present on a new algorithm closer to the
            sieve of Eratosthène.

            Thank you for your answer Robin

            Best,

            Rémi
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