A Different Way to View Goldbach's Conjecture

You probably have heard of Goldbach's Conjecture, that any even integer can be expressed as the sum of two primes. In this video, I make a restatement of this conjecture in terms of the sequences made by composite integers backwards from some number.

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Science & Technology

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• goldbach
• number
• theory
• conjecture
• open
• proof
• interesting
• student
• understanding

[PeeteyP]

Thanks. I think this is a very revealing way of thinking about the Goldbach conjecture. It seems to me that Chebychev's proof that there's always a prime between N and 2N (or N/2 and N) is important in studying this conjecture.

[idontcaresocry]

"I make a restatement of this conjecture in terms of the sequences made by composite integers backwards from some number."

You just mention a trivial fact. But this doesnt help in any way...

[Tural192]

I think that for prime numbers formulas for one way to prove make graphics or something like picture like circle or something that dont pass you page....goldbachs conjecture or others conjectures which lnked with prime numbers we can prove with graphic or picrure..

make symmetric cases... and on this basis ı am trying, working on these problems..

[Calculusman08]

@messakg123 Well message me this conjecture and I"ll be happy to work on it with you. We can see if there is any truth or falsity to this together.

[messakg123]

@Calculusman08 Thats a shame..

My conjecture is that you'd need "n" variables, to the power of "n", to sum together in order ti produce a number raised to the power of "n"

i.e. a(1)^(n-1)+a(2)^(n-1)+...+a(n-­1)^(n-1)=/=a(n)^n

The proof of fermat's is implicit in that (where there are only two additive numbers but we're trying to produce a power greater than 2)..

I wonder if there may be a grain of truth in that?

I can't think of a counterexample..

[Calculusman08]

The reason why I direct you to the modularity theorem is because Taniyama told Andrew Wiles that if he could prove this, then the Fermat's last theorem would follow. He was right.

[Calculusman08]

@messakg123 Well unfortunately, layman's knowledge doesn't exist for the proof of Fermat's last theorem. You're looking for the Taniyama-Shimura Conjecture or Modularity Theorem. It involves some extremely complicated mathematics, and the proof is some 100+pages in length. I study math for about 4 hours a day, and have for many years. This proof is still far beyond me. If you want some more understanding. Try and read up on the Modularity Th. maybe that will help you some :)

[messakg123]

@Calculusman08 I'd just like to have some layman's knowledge of how the proof works. I know it involves elliptic curves.. but.. like.. not much else.. Also, I have a "conjecture" of my own that sort of relates to it.. i have no idea whether its true or not though..

[Calculusman08]

@messakg123 What would you like to know about it? I'd happily make a video explaining it for you.

[Calculusman08]

Not to be picky, but as a mathematician, Goldbach's Conjeture actually states: Every even integer greater than 2 can be expressed as a sum of 2 primes. But! This is a very interesting way to view it. Thank you. If you want to discuss this in theory, please message me :)