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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