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

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  • 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 1 of 6 , Mar 14, 2007
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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 2 of 6 , Mar 15, 2007
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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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