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• ## Re: [PrimeNumbers] Fwd: The solution of Goldbach's conjecture-first doc

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• In a message dated 12/16/04 10:09:08 AM Eastern Standard Time, ... How can gap numbers as opposed to gap sizes lie in the middle? I understood that gap
Message 1 of 11 , Dec 20 1:14 PM
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In a message dated 12/16/04 10:09:08 AM Eastern Standard Time,
zaljohar@... writes:
> O + O and O+ O1 are both binary summation of odds(b .s .o)
> b. s. o= 2O U 2 E = 2 ( O U E) = 2 N =E.
> The question is solved!
> The reason for slide summation effect is because every gap number lies in
> the middle of at least one pair of members , so for series O, it is obvious
> that ( O, ni )+ 1= O,(gap number)i = (E, ni)

How can gap numbers as opposed to gap sizes "lie in the middle?"
I understood that gap numbers are sequential integers
So O_(gap number)i represents an O_ni increased by 1?
But gaps between members of E and gaps between members of O are a only 2.
I'm lost again.

> Now O, ni + O, ni + 2 =2(O, ni ) +2 = 2[( O, ni ) + 1] = 2[O, (gap
> number)i] =2(E ,ni).

You want add 2 to an even, then fine.
You get a single member of the set E.
Lets see how you get 2E as in:
2[O, (gap number)i] =2(E ,ni).
Perhaps you mean something like
Eg. 5 + 5 + 2 = 2(3 + 3)?

>
> A series X is called slidable for its members if all its members(except the
> first) have equidistant member pairs from them.

Hold on. You just ruled out all of the series where members do NOT have
equidistant member pairs.
That's a bit like saying Goldbach is true when it works but we don't care to
look at all possible pairs.
How come you focus on slideables and ignore the rest which may also confirm
Goldbach?

> A series X is called slidable for its gap numbers if all its gap numbers
> have equidistant member pairs from them.

Again you focus on gaps that must be equidistant which breaks the gap
sequence into bits and pieces.
Why do you feel its OK to discard so many gaps that fail your criteria?
Perhaps its best to await clarification on the above.

Finally, I agree that ONLY one reply as opposed to seven should be
sufficient.

Greg

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