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Re: Multiplying Primes and Numbers in General

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  • mikeoakes2
    ... It s not complicated at all, Geoff, it s just high-school algebra. Let the 2 numbers be x=6*a+a1 and y=6*b+b1, where a1 and b1 are each either +1 or -1.
    Message 1 of 7 , Jun 4 11:27 PM
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      --- In primenumbers@yahoogroups.com, "G Fischer" <golfbum71@...> wrote:
      >
      > Hit send again and realized I misspoke below for the 6N+1 multiplied by 6N-1
      > numbers...
      > c = 6ab + a - b
      > This formula will show differently since a and b can be different... when
      > the numbers are interchanged.
      >
      > As an example: 59*67 = 3953
      > The formula for c in this case is: c = 6ab + a - b
      > a = 10
      > b = 11
      > c = 659
      > c = 6*10*11 - 10 + 11
      > c = 660 + 1
      > c = 661
      >
      > and flopped:
      > a = 11, b = 10, c = 659
      > c = 6*10*11 - 11 + 10
      > c = 660 - 1
      > c = 659
      >
      > Perhaps a rule for whichever number is 6N-1 is added and 6N+1 is subtracted?

      It's not complicated at all, Geoff, it's just high-school algebra.

      Let the 2 numbers be x=6*a+a1 and y=6*b+b1, where a1 and b1 are each either +1 or -1.
      Then x*y = (6*a+a1)*(6*b+b1) = 6*c+c1,
      where c = 6*a*b+a1+b1,
      and c1 = a1*b1 (= +1 or -1).

      Mike
    • djbroadhurst
      ... Not at my high school, where c = 6*a*b + a*b1 + b*a1 David
      Message 2 of 7 , Jun 5 2:41 AM
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        --- In primenumbers@yahoogroups.com,
        "mikeoakes2" <mikeoakes2@...> wrote:

        > (6*a+a1)*(6*b+b1) = 6*c+c1,
        > where c = 6*a*b+a1+b1,
        > and c1 = a1*b1

        Not at my high school, where
        c = 6*a*b + a*b1 + b*a1

        David
      • Kermit Rose
        Yes. I understand your concept. I have worked with those equations also. (6 a -1)(6b - 1) = (36 a b - 6 a - 6 b + 1) = 6 ( 6 ab - a - b) + 1 (6 a - 1) (6 b +
        Message 3 of 7 , Jun 19 8:30 PM
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          Yes.

          I understand your concept.

          I have worked with those equations also.

          (6 a -1)(6b - 1) = (36 a b - 6 a - 6 b + 1) = 6 ( 6 ab - a - b) + 1

          (6 a - 1) (6 b + 1) = 36 a b + 6 a - 6 b - 1 = 6 ( 6 a b + a - b) - 1

          (6 a + 1) (6 b - 1) = 36 a b - 6 a + 6 b - 1 = 6 ( 6 a b - a + b) - 1

          (6 a + 1) (6 b + 1) = 36 a b + 6 a + 6 b + 1 = 6 ( 6 a b + a + b) + 1


          Kermit
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