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Consecutive Prime Sum

Problem

If we add the primes 11 and 23 we get 34, which is twice the prime 17.

Give that $p$ and $q$ are consecutive primes, show that the equation $p + q = 2r$, where $r$ is prime, has no solutions.

Problem ID: 332 (19 Nov 2007)     Difficulty: 2 Star

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