Re: RE To summarize the question
- 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
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.
--- In email@example.com, Jose Ramón Brox <ambroxius@t...>
> Let's see If I have understood the definition (I have some problemswith "Chris chains"):
> 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 isenough to find ANY random
> selection that satisfies his question? (I think we need it foreveryone).
>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 ofnumbers 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 onethat fits some useful
> conditions and answer in the affirmative (for example, take always0,1 (mod p_i) ).
> Jose Brox
> ----- Original Message -----
> From: "Mark Underwood" <mark.underwood@s...>
> To: <firstname.lastname@example.org>
> 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
> 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
> 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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