In article <email@example.com>, mluttgens <firstname.lastname@example.org> writes: >On 17 juin, 20:17, quasi <qu...@null.set> wrote:
>> To prove Goldbach's Conjecture, you have to show, for the >> general even n > 4, not a just a particular case, that a pair >> of odd primes exists whose sum is n. That you haven't done.
>It was easy to show that the even number 26 is the sum of two primes: > >26 =3D 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.
Except when it doesn't:
450000 11028 455000 7526 460000 5840
which, by your reasoning, would show that Goldbach's conjecture is false.
>Perhaps could somebody finds a formula linking N and n. >The given example shows that n cannot decrease from some value of N >and eventually becomes zero. >Thus, it vindicates Goldbach's conjecture.
The point isn't to show a general trend, but to show that it's *always* the case. The general trend is what led Goldbach to make this conjecture, and the reason that most mathematicians think that the conjecture is probably true.
"Probably true" is easy; "proved" is hard.
-- Michael F. Stemper #include <Standard_Disclaimer> Life's too important to take seriously.