# Decomposition into weight × level + jump of prime numbers commented - classification of prime numbers

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2 trivialities:
• lesser of twin primes (except 3) have a weight of 3.
• by definition primes classified by weight (A162175) follow Legendre's conjecture and Andrica's conjecture.
One conjecture:
• primes classified by level (A162174) are rarefying among prime numbers.

2, 3 and 7 are not classfied.

Zone 1: primes for which k(n) ≤ L(n) or primes classified by weight. We have the following relation:

• g(n) + 1 ≤ k(n) ≤ sqrt(l(n)) ≤ L(n) ≤ l(n) / 3
For the first 50 000 000, 82,89 % of prime numbers are classified by weight.

Zone 2: primes for which k(n) > L(n) or primes classified by level. We have the following relations:

• L(n) < sqrt(l(n)) < k(n) ≤ l(n)
• L(n) + 2 ≤ g(n) + 1 ≤ k(n) ≤ l(n)
For the first 50 000 000, 17,11 % of prime numbers are classified by level.

Definitions of the decomposition into weight × level + jump on the OeisWiki.
OEIS sequences submitted and/or edited.
arXiv:0711.0865 [math.NT]: Decomposition into weight * level + jump and application to a new classification of primes.