Rémi Eismann
@decompwlj
Followers
718
Following
210K
Statuses
11K
I have invented the decomposition into weight × level + jump, an extension to the fundamental theorem of arithmetic and a new way to see the numbers. #decompwlj
France
Joined December 2013
#decompwlj OEISWiki (en) ➡️ Wikiversité (fr) ➡️ arXiv [math.NT] ➡️ 1000 seq decomposed but my data have not been verified (dump, img and csv zipped) ➡️
1
2
51
Decomposition into weight × level + jump of prime numbers in 3D, threejs - webGL (#decompwlj) ⬇️
0
0
3
The decomposition into weight × level + jump (#decompwlj) of natural numbers is the fundamental theorem of arithmetic; applied to prime numbers, it leads to a new classification of primes.
0
0
2
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers (#decompwlj)
0
0
2
Decomposition into weight × level + jump (#decompwlj) ➡️ It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3 /2×a(n) and we have the unique decomposition a(n)=weight × level + jump. 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 weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1). 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 these decompositions, i apply a kind of sieve on each sequences.
0
0
3
Decomposition into weight × level + jump of natural numbers and prime numbers: 3D graph, threejs - webGL (log(weight), log(level), log(jump)) #decompwlj
0
0
2
My data have not been verified but my work is highly reproducible. - Downloads (img, csv, dump) ➡️ - Algorithms ➡️ #decompwlj
0
0
2
One day, one decomposition A179888: Starting with a(1)=2: if m is a term then also 4*m+1 and 4*m+2 3D graph, threejs - webGL ➡️ 2D graph, first 500 terms ➡️ #decompwlj
0
0
2
RT @decompwlj: Decomposition into weight × level + jump of prime numbers in 3D (threejs - webGL) (#decompwlj) ⬇️
0
1
0
RT @decompwlj: The decomposition into weight × level + jump (#decompwlj) of natural numbers is the fundamental theorem of arithmetic; appli…
0
1
0
RT @decompwlj: My first, favorite and most important sequence, the weights of prime numbers, A117078. We see prime numbers classified by le…
0
1
0
RT @decompwlj: Decomposition into weight × level + jump of prime numbers: - a new classification of primes; - in 3D (threejs - webGL). #dec…
0
1
0
RT @decompwlj: One day, one decomposition A179336: Primes containing at least one prime digit in base 10 3D graph, threejs - webGL ➡️ http…
0
1
0
Decomposition into weight × level + jump of prime numbers in 3D (threejs - webGL) (#decompwlj) ⬇️
0
1
5
The decomposition into weight × level + jump (#decompwlj) of natural numbers is the fundamental theorem of arithmetic; applied to prime numbers, it leads to a new classification of primes.
0
1
5
My first, favorite and most important sequence, the weights of prime numbers, A117078. We see prime numbers classified by level and by weight on the graph. #decompwlj
0
1
5
Decomposition into weight × level + jump, an extension of the fundamental theorem of arithmetic and a new way to see the numbers: - OEISWiki ?? - arXiv:0711.0865 [math.NT] ?? #decompwlj
0
0
4
Decomposition into weight × level + jump (#decompwlj) ➡️ It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3 /2×a(n) and we have the unique decomposition a(n)=weight × level + jump. 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 weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1). 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 these decompositions, i apply a kind of sieve on each sequences.
0
0
4
Decomposition into weight × level + jump of prime numbers: - a new classification of primes; - in 3D (threejs - webGL). #decompwlj
0
1
6
My data have not been verified but my work is highly reproducible. - Downloads ➡️ - Algorithms ➡️ #decompwlj
0
0
4