On 22 juin, 03:19, Gus Gassmann <horand.gassm...@googlemail.com> wrote: > On Jun 21, 7:29 pm, mluttgens <lutt...@gmail.com> wrote: > > > For N = 1000000, one gets 10804 Goldbach's pairs. > > The relation between log N and log n is log n = 0.727*log N -0.436 > > Note that this is not an equation, as it is not satisfied for N = 4.
The linear relation has been calculated from N = 50 to N = 1000000. Using it, one gets n = 8433 when N = 1000000, which is less than the exact value 10804. With the help of a graph, one could infer that another relationship, probably exponential, would be more appropriate. This would of course still clearer vindicate Goldbach's conjecture.
> It is at best an estimate, and there is error. This error may very > well turn out to be bounded in such a way that n can never be zero, > but you have not shown this. I will be generous and assume that to you > "vindication" means something different than "proof". Note, however, > that there are quite a few partial results already, based on a > probabilistic analysis, see, e.g., the wikipedia article (http:// > en.wikipedia.org/wiki/Goldbach%27s_conjecture), along with some very > nice pictures. None of this constitutes mathematical proof, however. > > > > > For N = 60,119,912, log n = 5.219 and the number of pairs is 165577