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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: 937 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: 937 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 ... vetheory/ 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  
Newbie Joined: Oct 2009 Posts: 26 Thanks: 0  Re: Goldbach's conjecture (to prove or not to prove) Quote:
 
July 31st, 2010, 05:01 PM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Goldbach's conjecture (to prove or not to prove) Quote:
 
July 31st, 2010, 05:29 PM  #8  
Senior Member Joined: Apr 2010 Posts: 215 Thanks: 0  Re: Goldbach's conjecture (to prove or not to prove) Quote:
 
July 31st, 2010, 07:10 PM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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  
Senior Member Joined: Apr 2010 Posts: 215 Thanks: 0  Re: Goldbach's conjecture (to prove or not to prove) Quote:
 

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