On the Match-Up of Structural Patterns within Prime Number Systems

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

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Section XIII - Divison Lines and Power Expansions

Summary for the Section :

• In this Section , we shall take a very brief look at the Division Lines ,
  • primarily for information purposes .

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Divison Line for { Category II thru V } :

• Let us bring-in the Divison Lines for { Category II thru V } ,
  • via the following set of 4 diagrams .

  

  

  

  

• Our only comment at this point is that :
  • Divison-Lines are important ,
    • they represent the first lines-of-segregation .

  And we do take note that Riemann also used the { Power-Roots of [ N ] } ,

  • in his 1859 paper titled :
    • On the Number of Prime Numbers up to a Given Quantity ;

    when he introduced the fucntion f(x) dervied from his earlier function F(x) .

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go to the next section : Section XIV - Concluding Remarks

go to the last section : Section XII - Doing the [ Cut-Off Process } via the SWING

return to the Matching Structural Patterns HomePage

Original dated 2012-10-08