On Prime Number Systems and Core Structural Pattern Propagations

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

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Section XVI - [ Category III ] Patterns arising from [ 7 / 17 / 37 / 47 / 67 / 97 ]

Summary for the Section :

• In this Section , we shall take a look at the pattern for 20 selected [ Category III Composite Numbers ] .

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Setting up the 20-elements Derived Pattern :

• Let us now set up this table below
  • for the Natural Logarithms of the selected 20 [ Catgeory III Composite Numbers ] :

    Category III			* *	Category III
    Value of [ N ]	LOG ( N )	Comment		Value of [ N ]	LOG ( N )	Comment
    ************	************	**************	*	************	************	**************
    4403	8.3900	7 x 17 x 37	*	30 5453	12.6296	47 x 67 x 97
    5593	8.6293	7 x 17 x 47	*	24 0463	12.3903	37 x 67 x 97
    7973	8.9838	7 x 17 x 67	*	16 8683	12.0358	37 x 47 x 97
    1 1543	9.3538	7 x 17 x 97	*	11 6513	11.6658	37 x 47 x 67
    1 2173	9.4070	7 x 37 x 47	*	11 0483	11.6216	17 x 67 x 97
    1 7353	9.7615	7 x 37 x 67	*	7 7503	11.2581	17 x 47 x 97
    2 2043	10.0008	7 x 47 x 67	*	6 1013	11.0188	17 x 37 x 97
    2 5123	10.1315	7 x 37 x 97	*	5 3533	10.8881	17 x 47 x 67
    2 9563	10.2943	17 x 37 x 47	*	4 5493	10.7253	7 x 67 x 97
    3 1913	10.3708	7 x 47 x 97	*	4 2143	10.6488	17 x 37 x 67

  We then have this schematic presentations below for the above 20 [ Category III Composite Numbers ] :

  

• Let us now set up the Structural Frame , [ FRAME 3-C ] ,
  • for our comparison purposes in the next Section , Section XVII .

  

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Looking at the Symmetry aspect :

• Let us now bring-in this diagram below showing the Symmetric nature of the above 20 [ Category III Composite Numbers ] :

  

  And we see here again the [ Symmetry about a Center-Line ] .

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go to the next section : Section XVII - Summmarizing on [ Symmetry about a Center-Line ]

go to the last section : Section XV - [ Category IV ] vs. [ Category II ] Patterns arising from [ 7 / 17 / 37 / 47/ 67 / 97 ]

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08