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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.

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Q: Does the sum of two prime numbers equal a prime number?
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