TimeStamp: 07/09/97 at 00:25:46
Date: Wed, 9 Jul 1997 04:25:08 +0000
From: LMARTIN-NORTHFIELD@worldnet.att.net (LAWRENCE MARTIN)
To: "Dr. Math" <dr.math@mathforum.org>
Subject: Re: Goldbach's Conjecture
Date of most recent message in thread: 07/09/97 at 00:25:46

At 06:05 AM 7/8/97 +0000, you wrote:

>As to your main question:  I'm not aware of any "proof" of Goldbach's 
>Conjecture existing yet.  (Maybe you'll be the one to find it someday.
:) ) 
> But that doesn't mean it should be abandoned or ignored.  One thing I
often 
>ask my students to do is to find all possible prime number pairs whose
sum 
>is a particular even number, say 100.  For example, 3 & 97 make a
sum of 
>100, but so do 11 & 89.  My question then becomes: how many more
pairs can 
>be found?  It usually gets my students to thinking a lot, plus they
learn 
>more about the primes less than 100.

I read about that in the book GREAT MATHEMATICAL MYSTERIES.  It seems that
the higher the even number, the more ways there are of representing it as
the sum of two primes. This makes a counterexample extremely unlikely, but,
as mathematicians know, that is no proof!

>Perhaps you are not aware of another lesser known extension to the main, 
>popular Conjecture, the 3 prime case.  It says: All odd integers greater 
>than 5 can be expressed as the sum of THREE primes.  For example, 

        I have heard of this. It is called Goldbach's Ternary Conjecture,
while the better known part is Goldbach's Binary Conjecture.  This was also
in the book I referred to above.  It said that the Ternary Conjecture has
been proven for every "sufficiently large" number.  Although the book didn't
say this, I figured out that if Goldbach's Binary Conjecture is true,
Goldbach's Ternary conjecture would have to be true.  However, if the
Ternary Conjecture is proven true for sure, that would not automatically
mean that the Binary Conjecture is true.
        
        Thanks for answering my letter!  Could you tell me if you know of
any other good books besides the one I spoke of above, GREAT MATHMATICAL
MYSTERIES, that contain good discussions of Goldbach's conjecture?

                        Sincerely,
                        Daniel

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