6-line proof of the binary Goldbach conjecture for even integers congruent to 2 mod 4.

Tatenda · 2022-10-16, 13:35

There is a somehow forgotten but elegant identify of Buchstab on the number of Goldbach partitions. By exploiting that identity, we demonstrate within 6 lines that every even integer congruent to 2 mod 4 can be expressed as a sum of two odd primes.

This proves the binary Goldbach conjecture for the specified integers. Kindly see:

https://figshare.com/articles/prepri...cture/21342042

Presumably, the reason why the identity has been forgotten, is that it's quite difficult to treat analytically, hence numbee theorists shifted focus to other approaches, most notably the circle method. Your constructive comments are most welcome.

Regards,

Tatenda.

R. Gerbicz · 2022-10-16, 15:03

Have you lost your arxiv account ? And I would strongly suggest to return to the Millenium prize problems (https://en.wikipedia.org/wiki/Millennium_Prize_Problems), and leave the easy problems for us.

Tatenda · 2022-10-16, 21:12

I will indeed post on arXiv. Only that Figshare is much quicker.

2022-10-16, 13:35	#1
Tatenda Oct 2022 13 Posts	6-line proof of the binary Goldbach conjecture for even integers congruent to 2 mod 4. There is a somehow forgotten but elegant identify of Buchstab on the number of Goldbach partitions. By exploiting that identity, we demonstrate within 6 lines that every even integer congruent to 2 mod 4 can be expressed as a sum of two odd primes. This proves the binary Goldbach conjecture for the specified integers. Kindly see: https://figshare.com/articles/prepri...cture/21342042 Presumably, the reason why the identity has been forgotten, is that it's quite difficult to treat analytically, hence numbee theorists shifted focus to other approaches, most notably the circle method. Your constructive comments are most welcome. Regards, Tatenda. Last fiddled with by masser on 2022-10-16 at 14:32 Reason: Moved Post to Math forum, where it seems more appropriate.

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2022-10-16, 15:03	#2
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 64B₁₆ Posts	Have you lost your arxiv account ? And I would strongly suggest to return to the Millenium prize problems (https://en.wikipedia.org/wiki/Millennium_Prize_Problems), and leave the easy problems for us.

2022-10-16, 21:12	#3
Tatenda Oct 2022 13 Posts	I will indeed post on arXiv. Only that Figshare is much quicker.