On Prime Number Systems and Core Structural Pattern Propagations

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

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Section I - Introduction

Introduction :

• This is the 1st paper in a series of six (6) papers under umbrella of the Title Paper :
  • An Approach to the Structural Integrity of Prime Number Systems

    with the 6 papers here being :

    1st paper	* *	On Prime Number Systems and Core Structural Pattern Propagations
    2nd paper	* *	On Counting Natural Numbers up to [ N = 1543 ]
    3rd paper	* *	On Counting [ Candidates-for-Primes modulo 30 ] up to [ N = 1543 ]
    4th paper	* *	On Unique-Factorization Combinatorics via the Pascal Triangle
    5th paper	* *	On the Match-Up of Structural Patterns within Prime Number Systems
    6th paper	* *	On the Unique-Factorization Equation within each Prime Number System
    **********	*	********************************************************

  And in this paper , we shall attempt to do the following :

  • explain what exactly do we mean by the term [ Prime Number Systems ] ;

    and

  • take a brief look as to how [ core prime-number distribution patterns ] may propagate into :
    • [ Category II Composite Numbers ] that are the product of 2 prime-numbers ,

    • [ Category III Composite Numbers ] that are the product of 3 prime-numbers ,

    • [ Category IV Composite Numbers ] that are the product of 4 prime-numbers ,

      and so-on-and-so-forth .

  This a necessary preliminary step to properly set the stage for the remaining 5 papers to follow .

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go to the next section : Section II - The All-Natural Prime Number System

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Original dated 2012-10-08