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July 30th, 2010, 07:04 AM   #1
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Goldbach's conjecture (to prove or not to prove)

Well here we have goldbach's conjecture:
Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:
Every even integer greater than 2 is a Goldbach number, a number that can be expressed as the sum of two primes. .Expressing a given even number as a sum of two primes is called a Goldbach partition of the number.
My objective:
well have started a long journey shall we say to try something bold that many have tried before, my goal is to attempt to prove Goldbach's conjecture, I already have many pages of notes including prime number theorems etc..
If you have any information that could be helpful at all, I will greatly appreciate it. And don't worry; if your info is helpful and brings me one more step closer to my goal, then you will be referenced in my thesis. Try and post ASAP
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July 30th, 2010, 07:46 AM   #2
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Re: Goldbach's conjecture (to prove or not to prove)

Have you read the basic information on the field -- say, Vinogradov's famous paper that (nearly) solves the ternary case?
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July 30th, 2010, 08:51 AM   #3
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Re: Goldbach's conjecture (to prove or not to prove)

Oh, and as a hobby I collect incorrect proofs of famous conjectures. I have ten already for GC...
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July 30th, 2010, 12:47 PM   #4
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Re: Goldbach's conjecture (to prove or not to prove)

Hi octaveous,

You should read up on Chen's theorem

http://mathworld.wolfram.com/ChensTheorem.html

Terry Tao has a great blog posting on the parity problem in sieve theory, which can be used to attack the goldbach and twin prime conjectures:

http://terrytao.wordpress.com/2007/06/0 ... ve-theory/

Good luck!

-US
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July 30th, 2010, 10:07 PM   #5
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Re: Goldbach's conjecture (to prove or not to prove)

ty for the replies, and yes I have been reading up.. at the moment, I am about 20 pages deep.. where as I included Euclid's prime number machine, but yet all it does is show not really prove along with the a couple theorems etc.. I'm hoping to try and prove it, I am just trying to figure a way on how to attack it.
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July 31st, 2010, 10:15 AM   #6
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Re: Goldbach's conjecture (to prove or not to prove)

Quote:
Originally Posted by octaveous
ty for the replies, and yes I have been reading up.. at the moment, I am about 20 pages deep.. where as I included Euclid's prime number machine, but yet all it does is show not really prove along with the a couple theorems etc.. I'm hoping to try and prove it, I am just trying to figure a way on how to attack it.
What's "Euclid's prime number machine"?
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July 31st, 2010, 04:01 PM   #7
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Re: Goldbach's conjecture (to prove or not to prove)

Quote:
Originally Posted by UnreasonableSin
What's "Euclid's prime number machine"?
The constructive form of Euclid's theorem on the infinitude of the primes?
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July 31st, 2010, 04:29 PM   #8
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Re: Goldbach's conjecture (to prove or not to prove)

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by UnreasonableSin
What's "Euclid's prime number machine"?
The constructive form of Euclid's theorem on the infinitude of the primes?
Explain?
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July 31st, 2010, 06:10 PM   #9
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Re: Goldbach's conjecture (to prove or not to prove)

Given a set S of primes, construct a number s equal to the product of the numbers of S, plus 1. This number is divisible by a prime not in S.
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July 31st, 2010, 06:31 PM   #10
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Re: Goldbach's conjecture (to prove or not to prove)

Quote:
Originally Posted by CRGreathouse
Given a set S of primes, construct a number s equal to the product of the numbers of S, plus 1. This number is divisible by a prime not in S.
Yes, but it will not yield primes directly. See http://mymathforum.com/viewtopic.php?f=40&t=15019
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