On Prime Number Systems and Core Structural Pattern Propagations

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

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Section XIV - [ Category V ] vs. [ Category I ] Patterns arising from [ 7 / 17 / 37 / 47 / 67 / 97 ]

Summary for the Section :

• In this Section , we shall take a look at a particular set of 6 [ Category V Composite Numbers ] ,
  • namely the 6 numbers :
    • [ 1386 5047 ] = 7 x 17 x 37 x 47 x 67
    • [ 2007 3277 ] = 7 x 17 x 37 x 47 x 97
    • [ 2861 5097 ] = 7 x 17 x 37 x 67 x 97
    • [ 3634 8907 ] = 7 x 17 x 47 x 67 x 97
    • [ 7911 2327 ] = 7 x 37 x 47 x 67 x 97
    • [ 1 9212 9937 ] = 17 x 37 x 47 x 67 x 97

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Setting up the 6-elements Derived Pattern :

• Let us now set up this table below for the Natural Logarithms of the selected six (6) [ Category V Composite Numbers ] :

  Value of [ N ]	1386 5047	2007 3277	2861 5097	3634 8907	7911 2327	1 9212 9937
  LOG ( N )	16.4449	16.8149	17.1694	17.4087	18.1864	19.0737
  ************	************	************	************	************	************	************

  We then have this schematic presentation below ,

  • showing the Structural Pattern for the above on a Logarithmic basis .

  

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Setting up the Derived Structural Frame :

• Let us now also set up the corresponding Structural Frame as shown below :

  

  And we bring back the Core Structural Frame from the last Section for a quick comparison .

  

  And we simply note here the [ counter flow ] / [ opposite flow ] mechanism in action here in the 2 diagrams above .

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Symmetry About a Center-Line :

• We then bring-in this diagram showing the [ Symmetry about a Center-Line ] for the combined 12 elements :

  

• Rather Straight-forward .

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

go to the last section : Section XIII - Identifying the Core Structural Pattern for [ 7 / 17 / 37 / 47 / 67 / 97 ]

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08