More Goldbach's Conjecture
Well there are two more definitions, from the same book [1], that are not equivalent: pp. 335 For all natural numbers x, if x is even, non-zero, and not 2, then there exist prime numbers y and z such that x is the sum of y and z. pp. 673 ...every even number, n>6 (it at least takes care of my question about 4), is the sum of two odd primes. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- -------------------------------------------------------------------- [1] VNR Concise Encyclopedia of Mathematics
Jim Choate wrote:
Well there are two more definitions, from the same book [1], that are not equivalent:
pp. 335
For all natural numbers x, if x is even, non-zero, and not 2, then there exist prime numbers y and z such that x is the sum of y and z.
pp. 673
...every even number, n>6 (it at least takes care of my question about 4), is the sum of two odd primes.
[1] VNR Concise Encyclopedia of Mathematics
Evidently there is a printing error. 'n>6' should read 'n>=6'. Then they are equivalent (if one considers 4 = 2 + 2 to be known). M. K. Shen
Jim Choate wrote:
Well there are two more definitions, from the same book [1], that are not equivalent:
pp. 335
For all natural numbers x, if x is even, non-zero, and not 2, then there exist prime numbers y and z such that x is the sum of y and z.
pp. 673
...every even number, n>6 (it at least takes care of my question about 4), is the sum of two odd primes.
These conjectures are equivalent for numbers > 6. I think that the discussion of whether numbers 4 and 6 can be expressed as sum of two primes is completely uninteresting. Also, since 6 = 3+3, I question why they put strict inequality (> 6) in the definition on p 673. I think that they could say n > 4. Not that it matters in any respect. So I do not see them as "substantially" different, and the difference between these conjectures does not lead us to any profound thoughts. - Igor.
participants (3)
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ichudov＠Algebra.COM -
Jim Choate -
Mok-Kong Shen