Let’s denote by the smallest potential typical primality radius of a given positive integer .

Writing:

where stands for the number of potential typical primality radii of below and is a quantity depending only on ,

one gets:

and

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:

is:

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:

.