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

- 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 .

- the exact count in { Category I } , i.e. the { odd-prime-number } count ;

- counts in { Category Zero } thru { Category IX } must necessarily add up to [ 9,842 ] ,
- 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 } |
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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 |