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Topic: A finite set of all naturals
Replies: 32   Last Post: Aug 15, 2013 4:07 PM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: A finite set of all naturals
Posted: Aug 13, 2013 1:15 AM

Nam Nguyen wrote:
>
>More than once, I was asked what the difference between the
>Goldbach Conjecture and its weaker form that an odd number
>greater than 7 is the sum of three odd primes.
>
>The point is though the essences of the 2 conjectures are
>drastically different: _an odd number can not be defined
>without addition_ while an even number can (as per Def-03b
>above).

Consider the following statements:

GC_2: All sufficiently large even numbers can be expressed as
the sum of 2 primes.

GC_4: All sufficiently large even numbers can be expressed as
the sum of 4 primes.

GC_6: All sufficiently large even numbers can be expressed as
the sum of 6 primes.

etc ...

It seems you claim to have proved:

"It impossible to know whether or not GC_2 is true."

Would your proof method also suffice to prove the same for
GC_4? For GC_6? etc?

quasi

Date Subject Author
8/12/13 Ben Bacarisse
8/12/13 Peter Percival
8/12/13 fom
8/12/13 Ben Bacarisse
8/12/13 namducnguyen
8/12/13 namducnguyen
8/12/13 antani
8/12/13 namducnguyen
8/13/13 Marshall
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/13/13 namducnguyen
8/13/13 quasi
8/13/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/14/13 quasi
8/14/13 namducnguyen
8/15/13 namducnguyen
8/15/13 Virgil
8/15/13 namducnguyen
8/15/13 antani
8/13/13 antani
8/13/13 Peter Percival
8/13/13 Ben Bacarisse
8/13/13 namducnguyen
8/14/13 Peter Percival
8/14/13 Shmuel (Seymour J.) Metz