On Prime Number Systems and Core Structural Pattern Propagations

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

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Section II - The [ All-Natural Prime Number System ]

Summary for the Section :

• In this Section , we shall take a quick look at the [ All-Natural Prime Number System ] ,
  • where all [ natural numbers ] are proposed as possible [ candidates-for-primes ] .

  This is the most common [ prime number system ] in use

  • both today in contemporary mathematics and since ancient times .

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The [ All-Natural Prime Number System ] :

• In general , for the [ All-Natural Prime Number System ] :
  • all [ natural numbers ] are proposed as [ candidates-for-primes ] .

  Subsequently , each [ candidate-for-prime ] is checked , in an ascending order ,

  • as to whether-or-not it is indeed a [ composite number ] .

  And

  • IF :
    • the particular [ candidate-for-prime ] turns-out to be a [ composite number ] and therefore a [ non-prime number ] ,

    THEN :

    • that particular [ candidate-for-prime ] is knocked-off the list
      • so that only genuine [ prime numbers ] shall remain on the [ list-of-prime-numbers ] .

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The Core Mechanics for the [ All-Natural Prime Number System ] :

• For the [ All-Natural Prime Number System ] , we shall take as [ a priori ] that :
  • [ 1 ] is the [ Super-Prime ] ,

    and

  • [ 2 ] is the first-and-smallest [ prime number ] under consideration here .

• And ,
  • since [ 2 ] is the smallest [ prime number ] under consideration here within the system ,

    it then follows that :

    • [ 4 ] = 2 x 2

      is necessarily the first-and-smallest [ composite number ] under consideration within the system ,

      • for the specific purpose of knocking-off proposed [ candidates-for-primes ] as [ non-prime numbers ] .

  As such , [ candidates-for-primes ] less than [ 4 ] may now be marked-off as [ prime numbers ] ,

  • and indeed :
    • the natural numbers [ 3 ] is a [ prime number ] .

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go to the next section : Section III - The [ Modulo 30 Prime Number System ]

go to the last section : Section I - Introduction

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08