Why Do 'Forbidden Zones' Exist in 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

 

[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.