TimeStamp: 07/08/97 at 02:05:34
From: Doctor Terrel
To: LMARTIN-NORTHFIELD@worldnet.att.net (LAWRENCE MARTIN)
Subject: Re: Goldbach's Conjecture
Approved-by: sydney
Date of most recent message in thread: 07/09/97 at 00:25:46

As LAWRENCE MARTIN wrote to Dr. Math
On 07/06/97 at 22:28:47 (Eastern Time),
>Dear Dr. Math,
>
> Hello!  I recently completed eighth grade.  My name is Daniel 
Martin, but I'm using 
>my dad's address, because I don't have my own.   I became interested in 
number theory after doing 
>a math project on it in seventh grade.  I have discovered some things
about 
primes tby myself that 
>I later found in books, such as the method of determining if a number is 
prime by taking its 
>square root and dividing it by all integers below or equal to it.  I
also 
figured out  by myself 
>from that the method of generating the list of primes.  Anyway, one
thing 
I am fascinated with 
>and have investigated somewhat is Goldbach's conjecture.  Can you tell
me 
if that has been solved 
>or may have been solved?  Thanks.
>
> 
>                                  Daniel
>
>
Hi Daniel,

I'm glad you hear that you really like number theory so much.  And that you 
are quite interested in primes specifically.  You will find out as you 
continue to study math that this information will help you a lot.  
Congratulations!

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.

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, 

15 = 5+5+5  =  3+5+7

Again the "how many ways possible" question naturally arises here as well.  
Why don't you investigate this?  It's fun, too.

By the way, I'd like to add a comment about your prime testing procedure.   
It's sufficient, after finding the square root, to divide only by the PRIMES 
less than the square root value.  It takes less time than dividing by  all 
the integers, as you said. Okay?

Well, good luck, and happy prime hunting!!!

-Doctor Terrel,  The Math Forum
 Check out our web site!  </dr.math/>

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