Ratio of Goldbach partitions

Paul Mackenzie

Hi All;

The following attachment shows a diagram of the ratio

R[2m] = g^2[2m]/g[2m-2]*g[2m+2] where g[2m] is the number of goldbach partitions for the even number 2m.

What is the reason for the "forbidden zones". I understand this is somehow to do with the factors of the even number, but why the empty zones.

Regards

Attached Files

ratio of goldbach partitions.pdf (360.9 KB, 13 views)

dodo

If you assume (out of my left sleeve) that g[2m-2],g[2m],g[2m+2] are numbers more or less close to N, whenever the corresponding 2m-2, 2m, 2m+2 are not divisible by 3 (that is, on the lower region of the 'comet'), and close to 2N otherwise (the upper region of the comet), then, as one of 2m-2, 2m, 2m+2 will be divisible by 3 and the others won't, your ratio -- assuming that you mean g^2[2m]/(g[2m-2]*g[2m+2]) -- would end up close to either (4N^2)/(N^2) = 4 or to (N^2)/(2N^2) = 0.5, which is more or less what you see.

But of course, this is just a pile of speculation and loosely founded assumptions on my part.