## Let Us Open Our Minds

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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
Message 1 of 2 , Aug 5 1:41 PM
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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

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.
• ... 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 1:53 PM
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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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