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 November 22nd, 2012, 08:05 AM #1 Newbie   Joined: Nov 2012 Posts: 24 Thanks: 0 Goldbach Theorem According to euclid every prime no is of form 6k+1or 6k-1 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+6r-1 =6(p+q+r)+1 6k+3=6p+1+6q+1+6r+1 =6(p+q+r)+3 6k+5=6p-1+6q-1+6r+1 =6(p+q+r-1)+5 So every odd no. geater than 7 will be sum of three primes.
 November 22nd, 2012, 10:59 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 933 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, 01:48 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*1-1+6*1-1 and for any n either 6k+1 or 6k-1 is prime
 November 23rd, 2012, 06:24 AM #4 Newbie   Joined: Feb 2012 Posts: 5 Thanks: 0 Re: Goldbach Theorem Neither 119 nor 121 is prime; k=20.
 November 23rd, 2012, 10:14 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 6k-1 seehttp://en.wikipedia.org/wiki/Primali...#Naive_methods
November 24th, 2012, 10:10 AM   #6
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Re: Goldbach Theorem

Quote:
 Originally Posted by surya what I meant was every prime no. is of form 6k+1 or 6k-1
That's true, but doesn't give you Goldbach's theorem. All you've shown is that a number of the form 6n+-1 is the sum of three numbers of the form 6n+-1 (and given a list of which are possible), but you haven't shown that these will be (or rather, can be chosen as) primes.

 November 24th, 2012, 02:52 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 6k-1, but not every number of the forms 6k+1 or 6k-1 is prime. So your proof fails.
 November 25th, 2012, 04:32 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 6k-1 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, 05:49 AM   #9
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Re: Goldbach Theorem

Quote:
 Originally Posted by surya If we accept the proof as valid then the no. in form of 6k+1 or 6k-1 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.
The proof is not valid. Not even close.

 November 26th, 2012, 02:18 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 6k-1 which will have to be a prime .So every no. will be sum of a least 3 primes.

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