## Re: RE To summarize the question

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• Hi Jose 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
Message 1 of 2 , Apr 23, 2005
Hi Jose

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"):
>
> 1) We select a prime p. We list in rows all the odd primes from 3
to p.
>
> 2) We select two random mods for every prime and we put a 1 on
their columns. For example,
> if we take p = 5 and we "block off" 1,2 (mod 3) and 0,2 (mod 5)
then we get:
>
> 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).
>
> Q2: Why two mods? Why random?
>
> 3) We search the columns where there are only zeros and we call
them numbers n+1. So the
> numbers n are those columns minus one.
>
> 4) We define R<p^2 to be a number with GCD(R,p#) = 1. We want to
confirm that R exists so
> that the integer part of a multiple of p# / R is in the set of
numbers n.
>
> Q3: Do we really need one R or every R to fulfill this condition?
(I think we need one).
>
> --------------------------------------------------------------------
-----
>
> Is that it? I don't want to waste time in a wrong question (time is
gold for me!). If we
> 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) ).
>
> Jose Brox
>
> ----- Original Message -----
> From: "Mark Underwood" <mark.underwood@s...>
> 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
each
> of them to get what Chris called our "n" numbers.
>
> 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
of
> 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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>
>