Conjectures 

Since we have shown previously that the smallest number of each twin prime pair (except 3) has a weight equal to 3, the wellknown conjecture on the existence of an infinity of twin primes can be rewritten as : 
Conjecture 1 : The number of primes with a weight equal to 3 is infinite. 
To extend this conjecture we make this two conjectures 
Conjecture 2 : The number of primes with a weight equal to k is infinite for any k >= 3 which is not a multiple of 2. 
Conjecture 3 : The number of primes of level L is infinite for any L >= 1 which is not a multiple of 2. 

Conjecture 4 : Except for p(6) = 13, p(11) = 31, p(30) = 113, p(32) = 131 et p(154) = 887, primes which are classified by level have a weight which is itself a prime. 

The conjecture on the existence of an infinity of balanced primes can be rewritten as : 
Conjecture 5 : The number of primes of level (1; 1) is infinite. 
That we can easily generalize by : 
Conjecture 6 : The number of primes of level (1; i) is infinite for any i >= 1. 

Conjecture 7 : If the jump g(n) is not a multiple of 6 then l(n) is a multiple of 3. 
Conjecture 8 : If l(n) is not a multiple of 3 then jump the g(n) is a multiple of 6. 

Knowing that the primes are rarefying among the natural numbers and according to the numerical data, we make the following conjecture : 
Conjecture 9 : The prime numbers classified by level are rarefying among the primes. 
