On 13/08/2013 12:56 AM, quasi wrote: > 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. > > OK. > >>> 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? > > Yes.
Then the answer is No: my proof wouldn't be sufficient for GC_4 or GC_6 (should they be true), but for a different reason compared to the weak Goldbach Conjecture.
Note that in the case of G_4, (sum of 4 primes) => (sum of 2 evens); and in the case of G_6, (sum of 6 primes) => (sum of 2 odds).
-- ----------------------------------------------------- There is no remainder in the mathematics of infinity.