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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.
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[1] VNR Concise Encyclopedia of Mathematics