On Prime Number Systems and Core Structural Pattern Propagations

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

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Section XI - A Quick Comparison of the Structural Frames

Summary for the Section :

• In this Section , we shall do a quick comparison of the Structural Frames ,
  • developed previously in Section VI thru Section X .

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Comparing [ Type A ] Structural Frames :

• Let us now bring back the Structural Frames [ FRAME 1-A / 2-A / 3-A / 4-A / 5-A / 5-C ] for a quick comparison :

  

  • We see here that the above six (6) Structural Frames are indeed similar-in-shape ,
    • and the [ ratios of the gap sizes ] within each Structural Frame is maintained throughout .

  And in particular :

  • [ FRAME 2-A ] is twice the size of [ FRAME 1-A ] ;

  • [ FRAME 3-A ] is also twice the size of [ FRAME 1-A ] ;

  • [ FRAME 4-A ] is three-times the size of [ FRAME 1-A ] ;

  • [ FRAME 5-A ] is four-times the size of [ FRAME 1-A ] ;

    but :

  • [ FRAME 5-C ] is only twice the size of [ FRAME 1-A ] ,
    • and therefore the same size as [ FRAME 2-A ] and [ FRAME 3-A ] .

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Comparing [ Type B ] Structural Frames :

• Let us now bring back the Structural Frames [ FRAME 2-B / 4-B / 5-B ] for a quick comparison :

  

  • We see here that the above three (3) Structural Frames are indeed similar-in-shape ,
    • and the [ ratios of the gap sizes ] within each Structural Frame is maintained throughout .

  And in particular :

  • both [ FRAME 4-B ] and [ FRAME 5-B ] are twice the size of [ FRAME 2-B ] .

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go to the next section : Section XII - The Range for each Category of Composite Numbers

go to the last section : Section X - Derived Structural Patterns for { Category V Composite Numbers }

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08