Has it been proven that all positive even numbers > 2 are either the sum of two primes or the difference between two primes?

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If a Maillet number is a positive even integer that can be expressed as the difference between two primes and a Goldbach number is a positive even integer that can be expressed as the sum of two primes, the conjecture (theorem?) is that every positive even integer is either a Goldbach number or a Maillet number. Does anyone know if this has been proven, or if one implies the other?