Category V Composite Numbers

On Prime Number Systems and Core Structural Pattern Propagations

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

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Section X - Derived Structural Patterns for [ Category V Composite Numbers ]

Summary for the Section :

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

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Structural Patterns for { Category V Composite Numbers } :

Let us quickly state that :
- there are exactly 56 distinct-and-different { Category V Composite Numbers } here ,
and
- the Geometric Mean of these 56 Composite-Numbers is roughly [ 556 5506 ] .

Let us now quickly split the said 56 Composite-Numbers into three (3) sub-groups ,

[ Set A ] , [ Set B ] and [ Set C ] respectively .

For [ Set A ] with 16 elements ,

the Natural Logarithms here are then :

	SET A
Value of [ N ]	1 6807	4 0817	8 8837	11 2847
LOG(N)	9.7296	10.6169	11.3946	11.6338
************	************	************	************	************
Value of [ N ]	58 4647	141 9857	309 0277	392 5487
LOG(N)	13.2788	14.1661	14.9438	15.1830
************	************	************	************	************
Value of [ N ]	1311 9127	3186 0737	6934 3957	8808 5567
LOG(N)	16.3896	17.2769	18.0546	18.2938
************	************	************	************	************
Value of [ N ]	3415 7767	8295 4577	1 8054 8197	2 2934 5007
LOG(N)	17.3465	18.2338	19.0115	19.2507
************	************	************	************	************

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

For [ Set B ] with 24 elements ,

the Natural Logarithms here are then :

	SET B
Value of [ N ]	9 9127	24 0737	52 3957	66 5567
LOG(N)	11.5042	12.3915	13.1692	13.4084
************	************	************	************	************
Value of [ N ]	46 9567	114 0377	248 1997	315 2807
LOG(N)	13.0596	13.9469	14.7246	14.9638
************	************	************	************	************
Value of [ N ]	74 7687	184 0097	400 4917	508 7237
LOG(N)	13.5380	14.4253	15.2030	15.4423
************	************	************	************	************
Value of [ N ]	276 9487	672 5897	1463 8717	1859 5127
LOG(N)	14.8342	15.7215	16.4992	16.7384
************	************	************	************	************
Value of [ N ]	446 8807	1085 2817	2362 0837	3000 4847
LOG(N)	15.3126	16.1999	16.9776	17.2169
************	************	************	************	************
Value of [ N ]	2116 8847	5141 0057	1 1189 2477	1 4213 3687
LOG(N)	16.8680	17.7553	18.5330	18.7723
************	************	************	************	************

We then have this diagram below showing the structural patterns for [ Set B ] :

For [ Set C ] with 16 elements ,

the Natural Logarithms here are then :

	SET C
Value of [ N ]	21 5747	27 4057	59 6477	144 8587
LOG(N)	12.2819	12.5211	13.2988	14.1861
************	************	************	************	************
Value of [ N ]	127 2467	161 6377	351 7997	854 3707
LOG(N)	14.0565	14.2957	15.0734	15.9607
************	************	************	************	************
Value of [ N ]	602 7707	765 6817	1666 4837	4047 1747
LOG(N)	15.6119	15.8511	16.6288	17.5161
************	************	************	************	************
Value of [ N ]	972 6227	1235 4937	2689 0157	6530 4667
LOG(N)	16.0903	16.3296	17.1073	17.9946
************	************	************	************	************

We then have this diagram below showing the structural patterns for [ Set C ] :

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Setting up the Structural Frames :

Let us also set up , at this point , the Structural Frames [ FRAME 5-A ] , [ FRAME 5-B ] and [ FRAME 5-C ] ,
- for our comparisons later in Section XI ,
  - as per this set of 3 diagrams below .

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go to the next section : Section XI - A Quick Comparison of the Structural Frames

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

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08