On the Match-Up of Structural Patterns within Prime Number Systems

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

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Section I - Introduction

Introduction :

• This is the 4th paper in a series of six (6) papers under the 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 explain :
  • How Structural Patterns arising from [ prime numbers ] and the Derived Patterns arising therefrom
    • may be matched-up against one-another to knock-off the { non-prime numbers }
      • from the original { List of [ candidates-for-primes ] } for a { Prime Number System } .

  And we shall be using primarily the { Modulo 30 Prime Number System } for our demonstration here .

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go to the next section : Section II - A Quick Review of Unique-Factorization Combinatorics

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Original dated 2012-10-08