On Prime Number Systems and Core Structural Pattern Propagations

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

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Section VIII - Derived Structural Patterns for [ Category III Composite Numbers ]

Summary for the Section :

• In this Section , we shall look at [ Category III Composite Numbers ] arising from the prime-numbers [ 7 / 17 / 37 / 47 ] .

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Structural Patterns for { Category III Composite Numbers } :

• Let us quickly state that :
  • there are exactly 20 distinct-and-different { Category III Composite Numbers } here ,

  

  and

  • the Geometric Mean of these 20 Composite-Numbers is roughly [ 9702.51 ] .

• Let us now quickly split the said 20 Composite-Numbers into two (2) sub-groups ,
  • [ Set A ] and [ Set Z ] respectively .

  For [ Set A ] with 16 elements ,

  • the Natural Logarithms here are then :

    	SET A
    Value of [ N ]	343	833	1813	2303
    LOG(N)	5.8377	6.7250	7.5027	7.7420
    ************	************	************	************	************
    Value of [ N ]	2023	4913	10693	13583
    LOG(N)	7.6123	8.4996	9.2773	9.5166
    ************	************	************	************	************
    Value of [ N ]	9583	2 3273	5 0693	6 4343
    LOG(N)	9.1677	10.0550	10.8335	11.0720
    ************	************	************	************	************
    Value of [ N ]	1 5463	3 7553	8 1733	10 3823
    LOG(N)	9.6462	10.5335	11.3112	11.5504
    ************	************	************	************	************

  For [ Set Z ] with 4 elements ,

  • the Natural Logarithms here are then :

    	SET Z
    Value of [ N ]	4403	5593	1 2173	2 9563
    LOG(N)	8.3900	8.6293	9.4070	10.2943
    ************	************	************	************	************

  We then have this diagram below showing the structural patterns for both [ Set A ] and [ Set Z ] :

  

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Setting up the Structural Frames :

• Let us also set up , at this point , the Structural Frames [ FRAME 3-A ] and [ FRAME 3-Z ] ,
  • for our comparisons later in Section XI ,
    • as per this set of 2 diagrams below .

  

  

  And we take special note here that :

  • { FRAME 3-Z } and { FRAME 1-A } are indeed mirror-images of one-another .

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go to the next section : Section IX - Derived Structural Patterns for [ Category IV Composite Numbers ]

go to the last section : Section VII - Derived Structural Patterns for [ Category II Composite Numbers ]

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08