November 22nd, 2012, 09:05 AM  #1 
Newbie Joined: Nov 2012 Posts: 24 Thanks: 0  Goldbach Theorem
According to euclid every prime no is of form 6k+1or 6k1 and every odd no of form 6k+1,6k+3or6k+5 let three distinct integers p,q,r for 6k+1= 6p+1+6q+1+6r1 =6(p+q+r)+1 6k+3=6p+1+6q+1+6r+1 =6(p+q+r)+3 6k+5=6p1+6q1+6r+1 =6(p+q+r1)+5 So every odd no. geater than 7 will be sum of three primes. 
November 22nd, 2012, 11:59 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 Theorem
You have proven that every number coprime to 6 is the sum of three integers coprime to 6. You haven't proven that the three will be prime.

November 23rd, 2012, 02:48 AM  #3 
Newbie Joined: Nov 2012 Posts: 24 Thanks: 0  Re: Goldbach Theorem
it is not that for ex 17=6*2+5 =6*1+1+6*11+6*11 and for any n either 6k+1 or 6k1 is prime 
November 23rd, 2012, 07:24 AM  #4 
Newbie Joined: Feb 2012 Posts: 5 Thanks: 0  Re: Goldbach Theorem
Neither 119 nor 121 is prime; k=20.

November 23rd, 2012, 11:14 PM  #5 
Newbie Joined: Nov 2012 Posts: 24 Thanks: 0  Re: Goldbach Theorem
what I meant was every prime no. is of form 6k+1 or 6k1 seehttp://en.wikipedia.org/wiki/Primali...#Naive_methods 
November 24th, 2012, 11:10 AM  #6  
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 Theorem Quote:
 
November 24th, 2012, 03:52 PM  #7 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Goldbach Theorem
Every prime greater than 3 is of the form 6k+1 or 6k1, but not every number of the forms 6k+1 or 6k1 is prime. So your proof fails.

November 25th, 2012, 05:32 AM  #8 
Newbie Joined: Nov 2012 Posts: 24 Thanks: 0  Re: Goldbach Theorem
If we accept the proof as valid then the no. in form of 6k+1 or 6k1 can be rewritten as sum of some no. which at a stage will become prime . So every no. is sum of at least 3 primes.

November 25th, 2012, 06:49 AM  #9  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Goldbach Theorem Quote:
 
November 26th, 2012, 03:18 AM  #10 
Newbie Joined: Nov 2012 Posts: 24 Thanks: 0  Re: Goldbach Theorem
Even if we don’t accept the proof as valid every no. of the form 6k+1 will be sum of 2 no. of the form 6k+1 and 6k1 which will have to be a prime .So every no. will be sum of a least 3 primes.


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