My Math Forum Goldbach's conjecture (to prove or not to prove)

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 July 30th, 2010, 08:04 AM #1 Newbie   Joined: Jul 2010 Posts: 3 Thanks: 0 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
 July 30th, 2010, 08:46 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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?
 July 30th, 2010, 09:51 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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...
 July 30th, 2010, 01:47 PM #4 Newbie   Joined: Oct 2009 Posts: 26 Thanks: 0 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
 July 30th, 2010, 11:07 PM #5 Newbie   Joined: Jul 2010 Posts: 3 Thanks: 0 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.
July 31st, 2010, 11:15 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"?

July 31st, 2010, 05:01 PM   #7
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Re: Goldbach's conjecture (to prove or not to prove)

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 Originally Posted by UnreasonableSin What's "Euclid's prime number machine"?
The constructive form of Euclid's theorem on the infinitude of the primes?

July 31st, 2010, 05:29 PM   #8
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Re: Goldbach's conjecture (to prove or not to prove)

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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?

 July 31st, 2010, 07:10 PM #9 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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.
July 31st, 2010, 07:31 PM   #10
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Re: Goldbach's conjecture (to prove or not to prove)

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 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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