Goldbach's conjecture is that every even integer greater or equal to four can be written as the sum of two prime numbers. (Try it: $4 = 2 + 2$, $6 = 3 + 3$, $8 = 3 + 5$, $10 = 3 + 7$, $12 = 5 + 7$...) It occurred to me that if this conjecture were true, it could be used as a way to encode even integers greater than four, and that this encoding would need to be no more efficient than the most efficient encoding, which simply enumerates the even integers $n \ge 4$. If it were more efficient, this would constitute a counterproof of the conjecture, which is widely believed to be true.
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