## 19673Re: Tightened-Lightened Goldbach Conjecture

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• Nov 4, 2008
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--- In primenumbers@yahoogroups.com, Bill Krys <billkrys@...> wrote:
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> Mark,
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> I'm going to make you a gentleman's bet that I can get a prime pair
generated for each unique N and that each and every N will be used
once and only once (I think it'll ultimately depend on what ineger I
knowledge to back it up, and furthermore, I realize there are many
seductive patterns seen in numbers that just don't survive once one
gets up in numbers, and finally I've been proved wrong so many times,
I should probably know better, but a bet will add a little spice to
this tedious exercise. Will you take it on?
>
> P.S. Thanks for your past response and insight.
>
> Bill Krys

Hi Bill

A gentleman's bet, hmmm. If I bet, then that would put me in the class
called "gentleman". OK, I'm in, hehe!

N to start at. But I'll start at N = 7 (because of the obvious divine
connotations :)) and see how far I can get. So far, we're up to 30.

Mark

.

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> --- On Fri, 10/31/08, Mark Underwood <mark.underwood@...> wrote:
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> From: Mark Underwood <mark.underwood@...>
> Subject: [PrimeNumbers] Re: Tightened-Lightened Goldbach Conjecture
> Date: Friday, October 31, 2008, 6:17 PM
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> --- In primenumbers@ yahoogroups. com, "billkrys" <billkrys@ .> wrote:
> >
> > Y'all,
> >
> > given that Goldbach's Conjecture for even #s can be re-stated as
there
> > is a prime equi-distant (N = integer) on either side of all integers
> > (I), then is there a unique N for each integer such that each N is
used
> > once and only once and where all N's can be represented above some
> > minimum I?
> >
> > In other words, can a prime pair be created for each integer (above 4
> > or some other integer - and then what is it?) from each N, such
that a
> > prime pair is created as a function of N? In yet more other words,
the
> > Conjecture would be tightened by becoming a function and lightened by
> > being only concerned with 1 pair of primes for each integer.
> >
> > Is there more than 1 function depending on what I - and for that
> > matter, depending on what N - one starts with?
> >
> > I'm trying to create such a function but am doing it without a
program,
> > so it will take time - trial and error.
> >
>
> Interesting idea. I'm almost certain there would be no function of N
> which would generate a unique I. But the idea that there might be a
> unique I that can be mapped to each N over a certain range is
> intriguing.
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> For instance, for N from 7 to 30 (as far as I checked, by hand) there
> is a unique I such that N+I and N-I is prime: (N,I)
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> (7,4) (8,3) (9,2) (10,7) (11,6) (12,1) (13,10) (14,9) (15,8) (16,13)
> (17,14) (18,5) (19,12) (20,17) (21,16) (22,15) (23,18) (24,19) (25,22)
> (26,21) (27,20) (28,25) (29,24) (30,11)
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> This is just one of many possibilities. But, I strongly suppose that
> this particular one, and probably all of them, will fail at some
> higher N. But, how far can one go, that is the question....
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> Mark
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