Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[2014] Representations by 2sinh^[0.5]
#2
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
Reply


Messages In This Thread
RE: [2014] Representations by 2sinh^[0.5] - by tommy1729 - 11/16/2014, 07:40 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  tommy's simple solution ln^[n](2sinh^[n+x](z)) tommy1729 1 2,168 01/17/2017, 07:21 AM
Last Post: sheldonison
  2sinh^[r](z) = 0 ?? tommy1729 0 1,177 02/23/2016, 11:13 PM
Last Post: tommy1729
  [2014] Beyond Gamma and Barnes-G tommy1729 1 2,077 12/28/2014, 05:48 PM
Last Post: MphLee
  [2014] Uniqueness of periodic superfunction tommy1729 0 1,730 11/09/2014, 10:20 PM
Last Post: tommy1729
  [2014] The angle fractal. tommy1729 1 1,997 10/19/2014, 03:15 PM
Last Post: tommy1729
  [2014] " statistical dynamics " tommy1729 0 1,538 08/31/2014, 11:53 PM
Last Post: tommy1729
  [2014] exp^[s](z) = z tommy1729 0 1,414 08/26/2014, 07:45 PM
Last Post: tommy1729
  [2014] composition of 3 functions. tommy1729 0 1,610 08/25/2014, 12:08 AM
Last Post: tommy1729
  [2014] combining some recent ideas. tommy1729 0 1,513 08/19/2014, 12:25 PM
Last Post: tommy1729
  [2014] Inconsistant equation ? tommy1729 0 1,609 07/27/2014, 02:38 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)