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

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

Top Of Page

Section IV - The Powers-of-[ 7 ] in relation to [ N ]

Summary for the Section :

• In this Section , we shall take a look at the { powers-of-[ 7 ] } in relation to [ N ] ,
  • with [ N ] being the natural number [ 1543 ] .

go to Top Of Page

Listing-out the Powers-of-[ 7 ] :

• We then have this table below for the { powers-of-[ 7 ] } :

  Powers of [ 7 ]		* * *	[ 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	7	***	220.43	***	211	47	***	223	48
  Square	49	***	31.49	***	31	12	***	37	13
  Cube	343	***	4.50	***	5	3	***	7	4
  4th-power	2401	***	0.64	***	--	--	***	--	--
  ***********	**********	***	***********	***	**********	**********	***	**********	**********

  And we simply note here that :

  • the { 4th-power-of-[ 7 ] } at [ 2401 ]
    • is the first { power-of-[ 7 ] } surpassing [ N = 1543 ] .

go to Top Of Page

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

go to the last section : Section III - The [ Candidates-for-Primes modulo 30 ] up to [ N = 1543 ]

return to the Counting via [ modulo 30 ] HomePage

Original dated 2012-10-08