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

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

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Summary and Key Findings :

• In this paper , we shall do a full count of all [ Candidates-for-Primes modulo 30 ] up to [ 1543 ] ,
  • on a category-by-category basis .

  And { Candidates-for-Primes modulo 30 } are then :

  • [ 1 / 7 / 11 / 13 / 17 / 19 / 23 / 29 modulo 30 ] ,

    ( See Section III of this paper for the full details here .)

  And the Categories here are classified as follows : ( same as before )

  • [ Category Zero ] shall contain the number [ 1 ] , this being the one-and-only element in this category ;

  • [ Category I ] shall contain all the [ prime numbers ] ;

  • [ Category II ] shall contain all [ composite numbers ] that are the product of 2 prime-numbers ;

  • [ Category III ] shall contain all [ composite numbers ] that are the product of 3 prime-numbers ;

  • And so-on-and-so-forth .

• And the Summary Table for the actual count is as follows :

  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

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Original dated 2012-10-08