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The strong Goldbach conjecture postulates that every even number can be expressed as the sum of two primes. An even number that is just twice a prime is considered a valid exemplar. For low values of n, I cannot find any example of a number that is not the sum of two distinct primes. Among the integers that have been looked at, are there any instances of an integer 2p that can only be expressed as p + p?

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    Since 1 isn't counted as a prime, 6 is such an example.2012-04-23
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    http://en.wikipedia.org/wiki/Goldbach%27s_comet2012-04-23
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    Sorry for being a bit unclear; unusual things happen with low integers, and 4 is formally another example. I was interested in larger integers, say p > 3. 2 and 3 are weird in the context of the set of all primes in that 2 is even and 3 is the only odd prime not expressible as 6k+-1.2012-04-23
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    How far did you look?2012-04-23
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    Since I'm not a computer programmer, I'm working by hand and I've looked up to several hundred. But Wikipedia says that Goldbach has been confirmed up to 10exp18, so somebody has looked by computer methods, and I wondered what they found.2012-04-23
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    What they find is that the number of representations grows, so after 6 you can always find distinct primes. Conjecturally, that is.2012-04-24
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    So, assuming Myerson's comment is valid, the slightly stronger statement of Goldbach is: Every even number greater than or equal to 8 can be represented as the sum of two distinct primes. Alternatively: Every integer greater than or equal to 4 is the average of two distinct primes.2012-04-24

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