- Nov 4, 2008--- In primenumbers@yahoogroups.com, Bill Krys <billkrys@...> wrote:
>

generated for each unique N and that each and every N will be used

> Mark,

>

> I'm going to make you a gentleman's bet that I can get a prime pair

once and only once (I think it'll ultimately depend on what ineger I

start with). I'm speculating and you know I have little formal

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?>

Hi Bill

> P.S. Thanks for your past response and insight.

>

> Bill Krys

A gentleman's bet, hmmm. If I bet, then that would put me in the class

called "gentleman". OK, I'm in, hehe!

The thing I don't like about this is the seeming arbitrariness of what

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

.

>

there

> --- On Fri, 10/31/08, Mark Underwood <mark.underwood@...> wrote:

>

> From: Mark Underwood <mark.underwood@...>

> Subject: [PrimeNumbers] Re: Tightened-Lightened Goldbach Conjecture

> To: primenumbers@yahoogroups.com

> 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

> > is a prime equi-distant (N = integer) on either side of all integers

used

> > (I), then is there a unique N for each integer such that each N is

> > once and only once and where all N's can be represented above some

that a

> > 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

> > 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

program,

> > 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

> > 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.

>

> 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)

>

> (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)

>

> 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....

>

> Mark

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