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Re: COMMENT on A000040, A006562 and A001359 on the OEIS

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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 1 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 2 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 3 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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