The Counting Odd-Numbers HomePage

# An Approach to Counting Odd Numbers

## Summary & Key Findings

### Summary of the Approach :

• 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 } . { Odd Numbers } that are the product of one (1) single { odd prime number } . { Odd Numbers } that are the product of two (2) { odd prime numbers } . { Odd Numbers } that are the product of three (3) { odd prime numbers } . { Odd Numbers } that are the product of four (4) { odd prime numbers } . And so-on-and-so-forth

• so that { Category I Odd-Numbers } are always { prime numbers } .

### Key Findings :

• 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 } .

### Other Sections of the paper :

Section IIntroduction and { a-priori assumptions }
Section IINotations on { Odd-Primes }
Section IIIDefining the { Counting Categories }
Section IVCounting { odd numbers } up to [ 19,683 ]
Section VDetails on { Category II Odd-Numbers }
Section VIDetails on { Category III Odd-Numbers }
Section VIIDetails on { Category VII / VIII / IX Odd-Numbers }
Section VIIIA First Proposal for Counting { Odd Numbers }
Section IXConcluding Remarks