Goldbach's conjecture is true for 2n where n is a multiple of 6

I meant to say equidistant from (p1+p2)/2

with n-p1 equal to a prime number then

And, of course, the most infuriating form of such a proof would be one that proved it, but neither hinted at the values of the counter- examples, not at how many there actually were.

:)

Sylvia.

At least in the first 5k evens the average number of of prime partitions of N is around .0053 of N.

Yet we have numbers like 9976 that have only 3 distinct solutions -- i.e. .00030 of N.

ers

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Can't stand Stephen Baxter. All science fiction authors (except possibly Ha l Clement) bend the laws of physics, but Stephen Baxter bends them quite a bit more than I can put up with. Getting a "that does not compute" reaction every couple of pages is excessively distracting.

If you have a provable lwb of course you have something. So I'm suspecting there isn't one and the ratio of num of distinct solutions over N can dip arbitrarily lower than .02.

So it's okay to have science fiction novels where faster-than-light travel,time travel, and alien civilizations are routine, but Stephen Baxter is just bending the laws of physics too much. Okay...

I think 6n multiples should be much more consistent!

cheers, Jamie

There isn't a proved lower bound of course. I'm talking about the lack of outliers in the computed values.

-- Richard

If you plot the number of solutions by N you get a very broad looking distribution of values with an interesting bifurfaction:

It would seems sa N->inf the lwb diverges arbitrarily from any trend line that (say) runs from the origin to (on this plot) (1e6,1300).

Upto 1e6 the "hardest" N seems to be 991316 with

I'm fairly sure looking up to 1 bn even "more unique" points will be found.

"You don't have permission to access /graphs/zzz.gif on this server."

but presumably it is Goldbach's Comet. The bands in it are easily explained:

I believe that fairly close lower bounds (to the calculated values) have been found.

-- Richard

Ooh which novels? Sounds like fun reading...

Maybe I'll search at the library.

Thanks,

Michael

Usually it's the machine in the outer layer of the onion that stops IP's in blacklists.

Usually Goldback's function upto 1000 to so is seen as such. But upto 1 mn it's more like a fuzzy triangle with a slight discoloration below the top ~1/3.

I thought you agreed that would essentially be a proof of the conjecture so was not likely to exist?

And when you say Golbach's function didn't diverge more than 10% from its "trend", were you then talking about some lower bound rather than the overall trend?

I get the same result from machines at home, at Edinburgh University, and at the W3C, so I think you have an error in your blacklist checking.

I'm not sure what you mean by that. The web page I mentioned shows it up to a million.

A proven lower bound to the number of pairs would be a proof. What people have found is various functions that are lower bounds to the so-far calculated numbers.

Yes, something like the values for 2p, p prime, which lie along the bottom.

-- Richard

I believe it's in the anthology "Vacuum Diagrams", and I think the story is in fact titled "Planck Zero."

I thought the normal heuristic is to look at the histograms, pray that the biggest peak is roughly Gaussian on the side towards 0, note that there is no obvious lower bound, and calculate the probability of an even number with g(2n)

"Your IP addr or domain name appears in a blacklist."

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