- 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. - --- 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:

Nonsense. They are not proven yet because thus-far-performed

>

> 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

> ".

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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