Defining the Categories

On Counting [ Candidates-for-Primes modulo 30 ] up to [ N = 1543 ]

by Frank C. Fung ( 1st published in October, 2012. )

Top Of Page

Section II - Defining the Categories for our Counting Purposes

Summary for the Section :

In this Section , we shall define the Categories of { non-zero Natural Numbers } for our counting purposes .

And the Categories here are the same as in the previous paper :
- On Counting Natural Numbers up to [ N = 1543 ]

go to Top Of Page

Defining the Categories :

We simply list-out again the categories ,

for the sake of clarity .

Category	Description
Category Zero	contains a single element - the natural number [ 1 ]
Category I	contains all [ natural numbers ] that are [ prime numbers ]
Category II	contains all [ natural numbers ] that are the product of 2 [ prime numbers ]
Category III	contains all [ natural numbers ] that are the product of 3 [ prime numbers ]
Category IV	contains all [ natural numbers ] that are the product of 4 [ prime numbers ]
Category V	contains all [ natural numbers ] that are the product of 5 [ prime numbers ]
Category VI	contains all [ natural numbers ] that are the product of 6 [ prime numbers ]
Category VII	contains all [ natural numbers ] that are the product of 7 [ prime numbers ]
Category VIII	contains all [ natural numbers ] that are the product of 8 [ prime numbers ]
Category IX	contains all [ natural numbers ] that are the product of 9 [ prime numbers ]
Category X	contains all [ natural numbers ] that are the product of 10 [ prime numbers ]
Category XI	contains all [ natural numbers ] that are the product of 11 [ prime numbers ]
and so-on-and-so-forth

( See Section II of the paper :

On Counting Natural Numbers up to [ N = 1543 ]

for full details here . )

go to Top Of Page

go to the next section : Section III - The [ Candidates-for-Primes modulo 30 ] up to [ N = 1543 ]

go to the last section : Section I - Introduction

return to the Counting via [ modulo 30 ] HomePage

original dated 2012-10-08