To clarify and answer your questions, yes we do need a solution for

every possible mod configuration and set of "n" values. (as you

suspect).

Why do two mods have to be blocked off for every prime? Actually it

is a maximum of two mods blocked off. I don't know how this plays a

part in the larger GB proof.

So we are looking for a proof that there is always one R (gcd(p#,R)=1

and R<p^2 ) and a k such that the integer portion of k*p#/R produces

at least one "n" value from any one given set of n's.

Mark

--- In primenumbers@yahoogroups.com, Jose RamÃ³n Brox <ambroxius@t...>

wrote:> Let's see If I have understood the definition (I have some problems

with "Chris chains"):

>

to p.

> 1) We select a prime p. We list in rows all the odd primes from 3

>

their columns. For example,

> 2) We select two random mods for every prime and we put a 1 on

> if we take p = 5 and we "block off" 1,2 (mod 3) and 0,2 (mod 5)

then we get:

>

affirmative answer for

> 3 011011011011

> 5 101001010010

>

> Q1: If this is correct, then I have one question: do we need an

> Chris question for EVERY random selection of two mods, or it is

enough to find ANY random

> selection that satisfies his question? (I think we need it for

everyone).

>

them numbers n+1. So the

> Q2: Why two mods? Why random?

>

> 3) We search the columns where there are only zeros and we call

> numbers n are those columns minus one.

confirm that R exists so

>

> 4) We define R<p^2 to be a number with GCD(R,p#) = 1. We want to

> that the integer part of a multiple of p# / R is in the set of

numbers n.

>

(I think we need one).

> Q3: Do we really need one R or every R to fulfill this condition?

>

-----

> --------------------------------------------------------------------

>

gold for me!). If we

> Is that it? I don't want to waste time in a wrong question (time is

> could use any random selection of the patterns, we could find one

that fits some useful

> conditions and answer in the affirmative (for example, take always

0,1 (mod p_i) ).

>

each

> Jose Brox

>

> ----- Original Message -----

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

> To: <primenumbers@yahoogroups.com>

> Sent: Saturday, April 23, 2005 2:28 PM

> Subject: [PrimeNumbers] To summarize the question

>

>

>

>

>

> Let's focus on the mathematical aspects of this problem.

>

> Let p# = 2*3*5*7*...*p

>

> We know that if we block off any two mods for each of the odd primes

> there will be exactly (3-2)*(5-2)*(7-2)*(11-2)*...*(p-2) values

> within

> the p# length cycle which do not coincide with any blocks. These are

> Chris' "zero columns". We take those values and subtract 1 from

> of them to get what Chris called our "n" numbers.

of

>

> Here's the question: Can we select a number t which is relatively

> prime

> to p# and less than p^2, such that the integer (truncated) portion

> the series of numbers

>

> k*p#/t for k=1,2,3....

>

> is coincident at least once with at least one of the "n" numbers?

>

> I'm sure the answer is in the affirmative but I'm still struggling

> for a proof. (He's been patiently waiting on me to provide one in

> private correspondence but I haven't produced!) If any one can prove

> this, or if a respected theorist can say that the validity of this

> proposition can be assumed, Chris has promised the list he will post

> his attempted Goldbach proof.

>

> Any takers?

>

>

>

>

>

>

>

>

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