On the Unique-Factorization Equation within Prime Number Systems

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

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Section X - Short-Cut #1 - [ 49 = 7 x 7 ]

Summary for the Section :

• In this Section , we shall look at the [ 1st ] of 3 short-cuts to arrive at a solution to the equation .

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The basis for the Short Cut :

• Since [ 7 ] is the smallest prime-number under our consideration in the [ Modulo 30 Prime Number System ] ,
  • the smallest [ composite number ] that can formulated under the system is therefore :
    • [ 49 ] = 7 x 7

  As such , { candidates-for-primes } less than [ 49 ] can never be knocked-off as [ non-prime numbers ] ,

  • and these { candidates-for-primes } can now be marked-off as prime-numbers .

  That is :

  • [ 11 / 13 / 17 / 19 / 23 / 31 / 37 / 41 / 43 / 47 ] are prime-numbers .

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The Revised [ Start-Off Position ] :

• Based on the above , we can now use this as our revised [ Start-Off Position ] :

  

• Rather simple and straight forward indeed .

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go to the next section : Section XI - Sbort-Cut #2 - [ 1543 over 7 ]

go to the last section : Section IX - Setting up the Equation

return to the Unique-Factorization Equation Homepage

Original dated 2012-10-08