Are There Exceptions to the Goldbach Conjecture for Even Numbers of the Form 2p?

[mathman]

4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?

 

[CRGreathouse]

4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?

There is almost surely no other case, but a proof is far beyond reach.

 

[dodo]

A quick&dirty computer program shows no cases up to a hundred thousand.

 

[CRGreathouse]

I can verify that there are no further exceptions up to http://www.research.att.com/~njas/sequences/A025018 (67) = 906030579562279642 ≈ 9 × 10¹⁷.

Edit: According to Tomás Oliveira e Silva, this bound is good up to 1.609 × 10¹⁸.