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Let Us Open Our Minds

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  • Simon
    I want this following commentary to be given some thought, instead of scorn. Here are two conjectures: a} Every even number equal to or greater than 6 is the
    Message 1 of 2 , Aug 5, 2006
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      I want this following commentary to be given some thought, instead of scorn.

      Here are two conjectures:

      a} Every even number equal to or greater than 6 is the sum of two odd primes.

      Possibly following from (a} :

      b) Every odd number equal to or greater than 9 is the sum of three odd primes.

      Quite possibly these two conjectures attributed to Goldbach haven't yet been proven by
      the greatest mathematical minds because we are using words like " odd primes ". These
      two conjectures are obviously sitting unproven because we are dealing with the integer 2.

      The integer 2 is the spoiler!

      So why can't we explore a different definition of what we want a prime number to be.
      After all, we brought primes into existence in their present form with their present
      definitions.

      This could be the hangup.

      If instead of looking at primes being derived solely from division, ( because we seem to be
      reasonably content to say that 1 and P are the only factors of a prime P ), what if we agree
      on a new definition of a prime that safely excludes the integer 2.

      (z) A prime is always an odd integer.

      However the converse is not true. An odd integer is not always a prime.

      Therefore a prime may always have a 1,3,5,7 or 9 in the units position.

      (y) A prime number P has two factors: 1 and P.

      (x) A prime is never derived from a squaring operation, or any higher order of number.
      ( ie cubic, quartic, quintic, etc ). This follows from (y) .

      Therefore 1 is not a prime because it results from a squaring, or a greater operation.

      (w) Composites derive from not being primes. Composites are always derived
      from the addition of several summands they being 1s, or any number of P, in at least one
      addition operation.

      Now what can be built from this? What does this do to those puzzling or unsolvable
      conjectures that have existed under a previous definition of a prime?

      The Fundamental Theorem of Arithmetic is not a law, it is a theorem, and can be replaced
      by another theorem just as " fundamental ". I think that the word "fundamental" has been
      deliberately chosen to save this theorem from attack or re-examination.

      Let's not forget that Euclidean geometry was the only geometry of mathematics until
      the early 1800s, so it could have been called " fundamental " up until those new
      geometries appeared. Now several geometries exist, each valid because Euclid's 5th does
      not necessarily follow from the previous 4.

      As an aside, look at Newton's "Law of Gravity". If it is a law, then what of Einstein and the
      curvature of space. Are these not theorems, or even something less? Or is it "Einstein's
      Law of Gravity ( Curvature of Space )"?

      Okay, we may have disposed of Goldbach Conjectures or even other conjectures.
      Can Riemann be re-explored? How seriously have any existing mathematic principles
      been affected or disrupted? Can they be reconciled?

      Please do not attack my ideas from the safety of existing mathematics, and then sit back
      comfortably thinking that you have interred another " wacky " set of ideas.

      Again, thoughtfully,
      Simon

      PS I do not know what my " crackpot " score is. Maybe Dr. Cardwell, or others could help
      me here.
    • Phil Carmody
      ... Why do you discount the possibility of thought and then scorn? ... Nonsense. They are not proven yet because thus-far-performed mathematically-sound
      Message 2 of 2 , Aug 5, 2006
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        --- Simon <4_groups@...> wrote:
        > I want this following commentary to be given some thought, instead of scorn.

        Why do you discount the possibility of thought and then scorn?

        > Here are two conjectures:
        >
        > a} Every even number equal to or greater than 6 is the sum of two odd
        > primes.
        >
        > Possibly following from (a} :
        >
        > b) Every odd number equal to or greater than 9 is the sum of three odd
        > primes.
        >
        > Quite possibly these two conjectures attributed to Goldbach haven't yet been
        > proven by
        > the greatest mathematical minds because we are using words like " odd primes
        > ".

        Nonsense. They are not proven yet because thus-far-performed
        mathematically-sound manipulations of the properties of groups,
        rings, and fields have not led to the required conclusions.

        So you're doubly-wrong - scorn can follow thought, as I had predicted.

        Phil

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