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November 22nd, 2012, 09:05 AM   #1
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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.
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November 22nd, 2012, 11:59 AM   #2
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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.
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November 23rd, 2012, 02:48 AM   #3
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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
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November 23rd, 2012, 07:24 AM   #4
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Re: Goldbach Theorem

Neither 119 nor 121 is prime; k=20.
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November 23rd, 2012, 11:14 PM   #5
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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
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November 24th, 2012, 11:10 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.
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November 24th, 2012, 03:52 PM   #7
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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.
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November 25th, 2012, 05:32 AM   #8
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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.
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November 25th, 2012, 06:49 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.
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November 26th, 2012, 03:18 AM   #10
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Re: Goldbach Theorem

Even if we donít 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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