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Composite number function(2)

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  • Kermit Rose
    1a. Re: Composite integer function Posted by: Yann Guidon whygee@f-cpu.org yasep16 Date: Wed Nov 18, 2009 9:02 am ((PST)) Hello Kermit, it seems that my
    Message 1 of 2 , Nov 19, 2009
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      1a. Re: Composite integer function
      Posted by: "Yann Guidon" whygee@... yasep16
      Date: Wed Nov 18, 2009 9:02 am ((PST))

      Hello Kermit,

      it seems that my emails can't reach you
      due to some unexplainable blacklist on some router near you.
      So I answer on the list :


      can you please elaborate ?




      Hello Yann.


      ..........s=1... s=2 ... s=3 ... s=4 .. s=5 . s=6
      m=1 015 021 027 033 039 045
      m=2 035 045 055 065 075 085
      m=3 063 077 091 105 119 133
      m=4 099 117 135 153 171 189
      m=5 143 165 187 209 231 253
      m=6 195 221 247 273 299 325

      The table extends to arbitrarily large values.

      Table entry at row m and column s is (2 * m + 1) * (2 * m + 1 + 2 * s)

      For example, 153 at row 4 and column 4 is (2 * 4 + 1) * (2 * 4 + 1 + 2 *
      4) = 9 * 17

      Adjacent table entries have an additive relationship to each other.

      For example 117 in row 4, column 2,
      and 165 in row 5, column 2,
      are related as follows.

      165 = 117 + 48 = 117 + 8 * 4 + 4 * 2 + 8

      Table entry in row (m+1) and column s
      = table entry in row (m) and column s,
      plus 8 times row number m,
      plus 4 times column number s,
      plus 8.

      There is a similar addition rule to calculate entries in the next column
      over.

      The extended table lists all the non-square odd composite positive integers,
      and has both additive and multiplicative rules for determining
      table entries.


      It is not trivial to find the location of a large number in the table.

      The easiest way to find a large integer in the table is to factor the
      integer.

      However, if some other algorithm for locating a given number in the
      table is developed, that algorithm would also be a factoring algorithm.

      Kermit.
    • djbroadhurst
      ... Post hoc, ergo propter hoc? ... Your nebulous algorithm was surpassed 2200 years ago: http://www.gap-system.org/~history/Biographies/Eratosthenes.html
      Message 2 of 2 , Nov 19, 2009
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        --- In primenumbers@yahoogroups.com,
        Kermit Rose <kermit@...> wrote:

        > The easiest way to find a large integer in the table
        > is to factor the integer.

        Post hoc, ergo propter hoc?

        > However, if some other algorithm for locating a given number
        > in the table is developed, that algorithm would also be a
        > factoring algorithm.

        Your nebulous "algorithm" was surpassed 2200 years ago:
        http://www.gap-system.org/~history/Biographies/Eratosthenes.html

        David
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