The Counting Odd-Numbers HomePage

An Approach to Counting Odd Numbers

Summary & Key Findings

Our { a-priori assumptions } here are as follows :
- [ 1 ] is not considered a { prime number } ,
- [ 2 ] is the one-and-only { even prime number } ,
- [ 3 ] is the first { odd prime number } , and
- all subsequent { prime numbers } are { odd numbers } .

The { counting categories } are set-up as follows :

Category Zero	contains a single member , the { odd number } [ 1 ] , which is not a { prime number } .
Category I	{ Odd Numbers } that are the product of one (1) single { odd prime number } .
Category II	{ Odd Numbers } that are the product of two (2) { odd prime numbers } .
Category III	{ Odd Numbers } that are the product of three (3) { odd prime numbers } .
Category IV	{ Odd Numbers } that are the product of four (4) { odd prime numbers } .
And so-on-and-so-forth

In counting { odd numbers } up to [ 3^9 ] , or [ 19,683 ] ,
- it is absolutely not necessary to involve { Category X } , { Category XI } or higher-categories { odd numbers } .
In counting { odd numbers } up to [ 3^9 ] , or [ 19,683 ] ,
- counts in { Category Zero } thru { Category IX } must necessarily add up to [ 9,842 ] ,
  - with [ 9,842 ] being the count of { all odd numbers } from [ 1 ] thru [ 19,683 ] .
Since the count in { Category Zero } is constant at [ 1 member ] ,
- knowing the exact counts for { Category II } thru { Category IX } will always yield :
  - the exact count in { Category I } , i.e. the { odd-prime-number } count ;
    
    via a subtraction procedure .
Our first proposal here is therefore to do a full count of all { categories of odd-numbers } ,
- in lieu of just the { Category I Odd-Numbers } count , i.e. the { odd-prime-numbers } count .
This might possibly , in the longe-run , contribute to a better understanding of { prime numbers } .

Section I	Introduction and { a-priori assumptions }
Section II	Notations on { Odd-Primes }
Section III	Defining the { Counting Categories }
Section IV	Counting { odd numbers } up to [ 19,683 ]
Section V	Details on { Category II Odd-Numbers }
Section VI	Details on { Category III Odd-Numbers }
Section VII	Details on { Category VII / VIII / IX Odd-Numbers }
Section VIII	A First Proposal for Counting { Odd Numbers }
Section IX	Concluding Remarks