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.
> 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.