Prove that the Goldbach conjecture that every even integer greater than 2 is the sum of two primes is equivalent to the statement that every integer greater than 5 is the sum of three primes.
[Hint: If 2n − 2 = p1 + p2, then 2n−p1 + p2 + 2 and 2n + 1 = p1 + p2 + 3.]
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