On 20 juin, 17:35, Rick Decker <rdec...@hamilton.edu> wrote: > On 6/20/12 10:33 AM, mluttgens wrote: > > > > > > > On 16 juin, 19:00, Frederick Williams<freddywilli...@btinternet.com> > > wrote: > >> mluttgens wrote: > > >>> Bigger is the number, and more primes it contains. > >>> Hence, the number of possible sums of two primes corresponding to a > >>> number > >>> is proportional to the magnitude of the number. > > >> That's a big claim. Can you prove it? > > >> -- > >> The animated figures stand > >> Adorning every public street > >> And seem to breathe in stone, or > >> Move their marble feet. > > > It was easy to show that the even number 26 is the sum of two primes: > > > 26 = 3+23, 7+19, 13+13, 19+7 and 23+3. > > > Let's call those sums Goldbach's sums. > > The number 26 has thus 5 Goldbach's sums. Hence, the number 26 > > vindicates Goldbach's conjecture. > > > In order to falsify the conjecture, one should need to show that some > > even number can't be the sum of two primes. > > > Hereafter are the numbers n of Goldbach's sums for increasing even > > numbers N: > > > N n > > _ _ > > > 50 8 > > 100 12 > > 500 26 > > 1000 56 > > 5000 152 > > 10000 254 > > 50000 900 > > 100000 1628 > > > Clearly, when N increases, the number of Goldbach's sums also > > increases. > > No. All you can say with certainty is that _for the cases you have > provided_, the number of Goldbach sums increases as N increases. > You haven't provided anything of substance besides your assertion. > > > Perhaps could somebody finds a formula linking N and n. > > Now _that_ would indeed be a useful result. The problem is that > nobody has come up with such a formula.
Because that till now, no mathematician has thought of studying the relation between N and n and found that the relation between log N and log n is *linear*
Such a linear relation straightforwardly validates Goldbach's conjecture.
> > > The given example shows that n cannot decrease from some value of N > > and eventually becomes zero. > > No it doesn't. It only provides a reason why you believe that GC is > true. Being as gentle as I can here, no one is interested in your > beliefs. Lots of mathematicians believe that GC is true, but they > recognize that belief without proof isn't mathematics. > > > Thus, it vindicates Goldbach's conjecture. > > Sorry to break it to you, but it doesn't, at least for any > definition of "vindicate" that I could find. > > Regards, > > Rick > >