User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 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: 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, 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
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:
 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
Math Team

Joined: Apr 2012

Posts: 1,579
Thanks: 22

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. Tags goldbach, theorem ,

,

,

,

### prime numbers of the firm 6k

Click on a term to search for related topics.
 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mathbalarka Number Theory 3 July 2nd, 2013 09:01 AM surya Number Theory 26 January 13th, 2013 01:30 AM julian21 Number Theory 1 September 28th, 2010 11:26 PM momo Number Theory 21 February 10th, 2010 11:16 AM fucktor Number Theory 21 April 15th, 2009 09:06 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      