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21122Composite number function(2)

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  • Kermit Rose
    Nov 19, 2009
    • 0 Attachment
      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.
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