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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