RE: [PrimeNumbers] Re: COMMENT on A000040, A006562 and A001359 on the OEIS
- 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?
Dear Phil and primenumbers Group,
Thank you Phil for your answer.
Why the decomposition in weight*level+gap is a sieve ?
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 =
The decomposition in weight * level + gap is thus a sieve.
Applied to prime numbers, we obtain that:
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.
LLama Gratis a cualquier PC del Mundo.
Llamadas a fijos y móviles desde 1 céntimo por minuto.
[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
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) :
There is also a program in Java on the "Download" page :
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