The ** decomposition into weight × level + jump** is a decomposition of positive integers. The

We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the ** decomposition into weight × level + jump** of natural numbers. For natural numbers, the

For prime numbers, this decomposition led to a new classification of primes. Primes classified by *weight* follow Legendre conjecture and i conjecture that primes classified by *level* rarefy. I think this conjecture is very important for the distribution of primes. It's easy to see and prove that lesser of twin primes (*>3*) have a *weight* of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a *weight* of 3.

I am not mathematician so i decompose sequences to promote my vision of numbers. By doing this decompositions, i apply a kind of sieve on each sequences. In some way, i find composites and primes of each sequences.