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June 15th, 2014, 02:13 AM   #1
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Goldbach's conjecture - proof ???

Hi everyone,

If you follow the link at the bottom of this post, you'll find yet another (proposed) proof of Goldbach's conjecture. The proof's been written by my uncle and I just translated it into English since his English is basic at best. Not being a mathematician myself, the translated text probably contains some terminology that is slightly off but hopefully the content will make up for that. The formatting of the manuscript leaves a lot to be desired too but I hope that it won't matter much.

One final thing, since the author doesn't speak English, he will not answer your questions regularly but you might expect to hear from him from time to time (provided, of course, that the text sparks your interest).

http://www.ibhr.info/downloads/Goldbach_conjecture.pdf
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June 16th, 2014, 07:29 PM   #2
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What language is the original paper in, and may I see it?
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June 16th, 2014, 09:48 PM   #3
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Is this a mathematical breakthrough?
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June 17th, 2014, 10:53 AM   #4
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It's in Croatian, and yes, you can see the original text if you wish.
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June 17th, 2014, 10:59 AM   #5
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Quote:
Originally Posted by CRGreathouse View Post
Well, the paper claims to solve the Goldbach conjecture. But it's certainly not compliant with what is written in that link.
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June 17th, 2014, 11:34 AM   #6
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Quote:
Originally Posted by notIntoMath View Post
Well, the paper claims to solve the Goldbach conjecture. But it's certainly not compliant with what is written in that link.
Do you have an example so I can expand on it?
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June 17th, 2014, 12:11 PM   #7
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Since it's not the original paper, #1 and #5 don't seem to apply.
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June 17th, 2014, 02:01 PM   #8
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The paper does list some examples relating to natural number decompositions. These examples alone can't prove Goldbach's conjecture but the equations derived from them were used in the proof.

While the proof uses very simple math, it can be heavy going at times (and the translation doesn't help either) so I'll try to outline its main points in a day or two, when I find the time.
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June 18th, 2014, 06:21 AM   #9
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It's worrying that the terms are ill-defined early on:

S is defined as
a) number of pairs of odd composites within 2K
b) number of different odd composites which form pairs within 2K

Which is two different numbers. Not sure if this affects the maths but it makes it hard to read as you can't be sure which definition applies.
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June 18th, 2014, 06:40 AM   #10
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Also, while some of the argument is a bit confused, I think there is a more serious problem here: Q is defined as a number that you can multiply PP by to reach S

S = Q x PP

If PP = 0 then there is no solution for Q (or Q is infinite). This means that the equation manipulations that follow are flawed when PP = 0. In particular this step (I've added the missing brackets) is illegitimate:

5) (NP x Q) – (NP x Q) = NP – PR
Which is cancelled down to
NP - PR = 0

This seems to lead on to the rather odd theory that a counterexample to Goldbach must have a symmetrical array where each prime is symmetrically matched against a composite which is of course impossible. I think it is the illegitimate bit above that leads to this flawed approach.

Last edited by Hedge; June 18th, 2014 at 06:46 AM.
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