11/16/2014, 07:40 PM

To estimate A(M) I use the following

Tommy's density estimate

***

Let f(n) be a strictly increasing integer function such that f(n)-f(n-1) is also a strictly increasing integer function.

Then to represent a positive density of primes between 2 and M

we need to take T_f(M) elements of f(n).

T_f(M) is about ln(M)/ln(f^[-1](M)).

This is an upper estimate.

***

In this case to represent a positive density of primes between 2 and M we then need about

ln(M)/ln^[3/2](M) 2S numbers.

This is a brute upper estimate.

A(M) is estimated as sqrt( ln(M)/ln^[3/2](M) ).

Improvement should be possible.

regards

tommy1729

Tommy's density estimate

***

Let f(n) be a strictly increasing integer function such that f(n)-f(n-1) is also a strictly increasing integer function.

Then to represent a positive density of primes between 2 and M

we need to take T_f(M) elements of f(n).

T_f(M) is about ln(M)/ln(f^[-1](M)).

This is an upper estimate.

***

In this case to represent a positive density of primes between 2 and M we then need about

ln(M)/ln^[3/2](M) 2S numbers.

This is a brute upper estimate.

A(M) is estimated as sqrt( ln(M)/ln^[3/2](M) ).

Improvement should be possible.

regards

tommy1729