On Counting Natural Numbers up to [ N = 1543 ]

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

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Section IV - The Powers-of-[ 2 ] in relation to [ N ]

Summary for the Section :

• In this Section , we shall take a look at the { powers-of-[ 2 ] } in relation to [ N ] ,
  • with [ N ] being the natural number [ 1543 ] .

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Listing-out the Powers-of-[ 2 ] :

• We then have this table below for the { powers-of-[ 2 ] } in relation to [ N = 1543 ] :

  Powers of [ 2 ]		* * *	[ 1543 ] divided by [ X ]	* * *	Next Prime Number smaller than [ Z ]		* * *	Next Prime Number larger than [ Z ]
  Description	Value				Value of Prime Number	Rank of Prime Number		Value of Prime Number	Rank of Prime Number
  	( X )	*	( Z )	*	( P-j )	( j )	*	( P-k )	( k )
  SELF	2	***	771.50	***	769	136	***	773	137
  Square	4	***	385.75	***	383	76	***	389	77
  Cube	8	***	192.88	***	191	43	***	193	44
  4th-power	16	***	96.44	***	89	24	***	97	25
  5th-power	32	***	48.22	***	47	15	***	53	16
  6th-power	64	***	24.11	***	23	9	***	29	10
  7th-power	128	***	12.05	***	11	5	***	13	6
  8th-power	256	***	6.03	***	5	3	***	7	4
  9th-power	512	***	3.01	***	3	2	***	5	3
  10th-power	1024	***	1.51	***	--	--	***	2	1
  11th-power	2048	***	0.75	***	--	--	***	--	--
  ***********	**********	***	***********	***	**********	**********	***	**********	**********

  And we simply note here that :

  • the { 11th-power-of-[ 2 ] } at [ 2048 ]
    • is the first { power-of-[ 2 ] } surpassing [ N = 1543 ] .

  As such , it is unlikely that :

  • our count here will involve a [ Category XI Number ] or higher-category-numbers .

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go to the next section : Section V - The Power-Roots of [ N ]

go to the last section : Section III - Explaining the Choice of [ N = 1543 ]

return to the Counting Natural Numbers HomePage

Original dated 2012 10-08