13 & 7
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There is only one even prime number: 2. So, representing 20 as a sum of even prime numbers would be 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2.
2 + 3 = 5
If one of the two numbers is 2, the sum of two prime numbers may sometimes be a prime number. Examples of this are 2 + 11 = 13, 2 + 521 = 523, 2 + 281 = 283. There are an infinite number of similar examples where the sum of 2 plus a prime is another prime. However if neither number is 2, then the sum of two prime numbers is always an even number greater than 2 and therefore composite.
2 and 3.
2