On Counting Natural Numbers up to [ N = 1543 ]

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

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Section XV - Counting Summary for all Categories

Summary for the Section :

• In this Section , we shall present the Counting Summary for all Categories .

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The Counting Summary for all Categories :

• Let us recall that :
  • [ 2 ] is the 1st-and-smallest [ prime number ] , and

  • [ 1543 ] is the 243th [ prime number ] .

  There are therefore 243 { prime numbers } between [ 2 ] and [ 1543 ] , both numbers inclusive .

• We then present this table below for the full count of all categories :

  Category of Number	* * *	Smallest Number in Category		* * *	Largest Number in Category		* * *	Roving Count
  		Value of Number	Prime Factors of Number		Value of Number	Prime Factors of Number
  Category Zero	***	1	--	***	1	--	***	1
  Category I	***	2	2	***	1543	1543	***	243
  Category II	***	4	2 x 2	***	1541	23 x 67	***	450
  Category III	***	8	2 x 2 x 2	***	1542	2 x 3 x 257	***	387
  Category IV	***	16	2 x 2 x 2 x 2	***	1528	2 x 2 x 2 x 191	***	236
  Category V	***	32	2 x 2 x 2 x 2 x 2	***	1539	3 x 3 x 3 x 3 x 19	***	123
  Category VI	***	64	2 x 2 x 2 x 2 x 2 x 2	***	1504	2 x 2 x 2 x 2 x 2 x 47	***	61
  Category VII	***	128	2 x 2 x 2 x 2 x 2 x 2 x 2	***	1512	2 x 2 x 2 x 3 x 3 x 3 x 7	***	25
  Category VIII	***	256	2 x 2 x 2 x 2 x 2 x 2 x 2 x 2	***	1408	2 x 2 x 2 x 2 x 2 x 2 x 2 x 11	***	11
  Category IX	***	512	2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2	***	1280	2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5	***	4
  Category X	***	1024	2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2	***	1536	2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3	***	2
  **********	***	********	***************************	***	********	***************************	***	**********
  TOTAL								1543

  • Isn't that wonderful !

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go to the next section : Section XVI - Concluding Remarks

go to the last section : Section XIV - Counting { Category X Numbers } up to [ N ]

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Original dated 2012-10-08