Let’s denote by the smallest potential typical primality radius of a given positive integer .
where stands for the number of potential typical primality radii of below and is a quantity depending only on ,
where is any positive real number less than .
Hence should be taken as equal to ,
and one would thus get:
Considering the definition of the quantity in the article « Primality radius », the only possible value of such that:
Therefore one should expect the following relation to hold:
As it can be proven that:
one gets the following average value for :
for some .
This might help to establish the asymptotic Goldbach’s conjecture (every large enough even integer is the sum of two primes) and Cramer’s conjecture that says: