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.