On 22 juin, 14:21, mstem...@walkabout.empros.com (Michael Stemper) wrote: > In article <0556b041-cf5b-4b09-9b34-72473aebd...@n5g2000vbb.googlegroups.com>, mluttgens <lutt...@gmail.com> 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
How did you find those numbers? What do they represent? If 11028, 7526 and 5840 represent Goldbach's pairs, they are false.
> > 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. > >