Nam Nguyen wrote: >quasi wrote: >> 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." > >That's not what I claimed ... > >... my much more restricted claim to prove (as opposed to my >own about cGC) would be: > >(*) If the Goldbach conjecture is true in the natural numbers, > then it's impossible to structure theoretically prove, verify > it so.
>> Would your proof method also suffice to prove the same for >> GC_4? For GC_6? etc? > >Before this, do you agree there has been a misunderstanding >on what I had said to Virgil I could prove here, in relation >to GC_2?
Sure, no problem -- agreed.
>If you do agree, would your questions about GC_4 and GC_6 >_still_ stand?