Classification 


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. According to the numerical data, the prime numbers classified by level are rarefying (see the conjectures). 

Primes for which g(n) > sqrt(l(n)) are : 2, 3, 5, 7, 13, 19, 23, 31, 113 for n <= 5.10^7. 


Exemple : 
n 
p(n) 
g(n) 
p(n+1) 
k(n) 
L(n) 
l(n) 
76 
383 
6 
389 
13 
29 
377 
102 
557 
6 
563 
19 
29 
551 
4334 
41413 
30 
41443 
1427 
29 
41383 
6853 
68963 
30 
68993 
2377 
29 
68933 
7285 
73783 
36 
73819 
2543 
29 
73747 
9113 
94483 
30 
94513 
3257 
29 
94453 


The two first primes (p(76) and p(102)) are in zone 1 and are classified by weight, the other primes are classified by level. 

arXiv:0711.0865 : Decomposition into weight * level + jump and application to a new classification of prime numbers 
