Re: Goldbach's Conjecture - a question about prime sums of odd numbers

[Ray Arachelian <sunder@brainlink.com>]

Jim Gillogly wrote:
> 
> Ray Arachelian wrote:
> > "Igor Chudov @ home" wrote:
> 
> > > Well, take 11, for example, it cannot be repsesented as a sum of different
> > > primes. It cannot, pure and simple.
> 
> > Bullshit: 7+5+(-1)=11.  Last I heard, negative numbers weren't excluded from
> > being primes.  7 is different from 5, -1 is different from 7 and from 5.
> 
> If this is boiling down to a definition of primes, I'll haul out my Hardy &
> Wright, page 2:
> 
>     A number p is said to be prime if (i) p > 1, (ii) p has no positive
>     divisors except 1 and p.  ...  It is important to observe that 1 is not
>     reckoned as a prime.
> 
> My number theory class at college (admittedly that was three decades ago)
> also started the prime series at 2 and went up from there.  The term
> "odd primes" always meant 3 and above, not 1 and above.

Well, I suppose negative numbers can't be included because 1 can't be included:
1*1*1*1=1 and the idea is that a prime can only have itself and 1 as factors,
where 1 can be factored by itself over and over to an infinite number of 1's,
and by that definition you can exclude -1 since -1=(-1*1*-1*1), and so if
we take -5 and factor it to -5 and 1 it's good, but it can also be factored
to -1 and 5.  IMHO 1 and -1 being shunned in this way is a bit silly, but
whatever... :^)  (Same applies to zero since 0=0*0*0*0*0, but zero has the
built in difference of that it can't be divided by itself at all.)

So I guess I have to take back 7+5+(-1) and go with Jim's 1+3+7, but fuck,
that won't work either since 1 isn't a prime...  So I guess Igor is right on
this one.  Sorry Jim... 

Any other ideas on 11?


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