On Prime Number Systems and Core Structural Pattern Propagations

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

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Section V - The Reasons for using different modulo's for the [ Prime Number Systems ]

Summary for the Section :

• In this Section , we shall state the reasons for bringing-in the different modulo's
  • for our [ Prime Number Systems ] .

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[ Prime Number Systems ] using different modulo's :

• Let us recall that Georg Friedrich Bernhard Riemann published the paper :
  • [ On the Number of Prime Numbers less than a Given Quantity ]
    • in the year 1859 .

  This is a powerful paper and the Author do not pretend to have understood it fully .

• The Author therefore made this conjecture :
  • Suppose , for the moment , that :
    • author-and-reader-alike have fully understood the paper ;

    then :

    • we should be able to come up with techniques and procedures developed therefrom

      and

      apply these to the [ Prime Number Systems of different modulo's ]

      • to come up with the correct set of prime-numbers .

  And that-is-to-say that :

  • The purpose of the different modulo's is to test our understanding of the Riemann Paper .

• In particular , we shall be keeping track of the following items throughout our paper :
  • item 1 : the { Factorial of [ N ] } ,

  • item 2 : the L.C.M. of natural numbers up to [ N ] , and

  • item 3 : the product of prime-numbers up to [ N ] ;

    where [ N ] is the upper-limit / Given Quantity under our investigation for the time-being .

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go to the next section : Section VI - Selecting a Core Structural Pattern for our Demonstrations

go to the last section : Section IV - Other [ Prime Number Systems ] under our consideration

return to the Prime Number System and Core Pattern Propagation Homepage

Original dated 2012-10-08