- --- 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

No it is not.

> natural numbers, we obtain that:

> http://reismann.free.fr/Graph_Entiers_1000000-R.html

> It is a beautiful representation of the sieve of Eratosthene.

Phil

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http://farechase.yahoo.com/promo-generic-14795097 - 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 - 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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[Non-text portions of this message have been removed] - 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