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

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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
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:

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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• 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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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) :