[ Category IV ] vs. [ Category II ]

On Prime Number Systems and Core Structural Pattern Propagations

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

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

Summary for the Section :

In this Section , we shall take a look at patterns for :
- a selected 15 [ Catgeory II Composite Numbers ]
  
  vs.
- a selected 15 [ Category IV Composite Numbers ] .

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Setting up the 15-elements Derived Patterns :

Let us now set up this table below ,

for the Natural Logarithms of the selected [ Catgeory II ] and [ Category IV ] composite numbers :

Category II			* *	Category IV
Value of [ N ]	LOG ( N )	Comment	* *	Value of [ N ]	LOG ( N )	Comment
************	************	**************	*	************	************	**************
119	4.7791	7 x 17	*	1 130 1761	16.2405	37 x 47 x 67 x 97
259	5.5568	7 x 37	*	519 2701	15.4628	17 x 47 x 67 x 97
259	5.7961	7 x 47	*	408 7871	15.2235	17 x 37 x 67 x 97
469	6.1506	7 x 67	*	286 7611	14.8690	17 x 37 x 47 x 97
629	6.4441	17 x 37	*	213 8171	14.5755	7 x 47 x 67 x 97
679	6.5206	7 x 97	*	198 0721	14.4990	17 x 37 x 47 x 97
799	6.6834	17 x 47	*	168 3241	14.3362	7 x 37 x 67 x 97
1139	7.0379	17 x 67	*	118 0781	13.9817	7 x 37 x 47 x 97
1649	7.4079	17 x 97	*	81 5591	13.6117	7 x 37 x 47 x 67
1739	7.4611	37 x 47	*	77 3381	13.5585	7 x 17 x 67 x 97
2479	7.8156	37 x 67	*	54 2521	13.2040	7 x 17 x 47 x 97
3149	8.0548	47 x 67	*	42 7091	12.9648	7 x 17 x 37 x 97
3589	8.1856	37 x 97	*	37 4731	12.8340	7 x 17 x 47 x 67
4559	8.4249	47 x 97	*	29 5001	12.5947	7 x 17 x 37 x 67
6499	8.7794	67 x 97	*	20 6941	12.2402	7 x 17 x 37 x 47

We then have this set of schematic presentations below ,

with this 1st diagram immediately following showing the Structural Pattern for the 15 [ Catgeory II Composite Numbers ] :

with this 2nd diagram below showing the Structural Pattern for the 15 [ Catgeory IV Composite Numbers ] :

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Looking at Counter-Flow and Symmetry :

Let us now bring-in this diagram below showing the [ counter-flow ] nature
- for the above 2 sets of [ 15 elements ] each .
Let us also bring-in this diagram below showing the overall [ Symmetry about a Center-Line ]
- for the combined set of [ 30 elements ] .
Again , quite straight-forward .

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

go to the last section : Section XIII - [ Category V ] vs. [Category I ] 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