On Counting [ Candidates-for-Primes modulo 30 ] up to [ N = 1543 ]

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

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Section VIII - 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 :
  • [ 7 ] is the 4th [ prime number ] , and

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

  There are therefore 240 { prime numbers } between [ 7 ] and [ 1543 ] , both prime-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 up to [ N ]		* * *	Roving Count
  		Value of Number	Prime Factors of Number		Value of Number	Prime Factors of Number
  Category Zero	***	1	--	***	1	--	***	1
  Category I	***	7	7	***	1543	1543	***	240
  Category II	***	49	7 x 7	***	1541	23 x 67	***	157
  Category III	***	343	7 x 7 x 7	***	1519	7 x 7 x 31	***	14
  ************	***	********	**************	***	********	**************	***	************
  TOTAL								412

  Simple and straight-forward enough !

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go to the next section : Section IX - Concluding Remarks

go to the last section : Section VII - Counting [ Category III Candidates } up to [ N ]

return to the Counting via [ modulo 30 ] HomePage

Original dated 2012-10-08