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Erdös has conjectured that no higher power of the first prime (i.e., 2^{8} = 256) is a sum of distinct powers of 3. 256 = (21701  19937)  (23209  21701). Note the use of three consecutive Mersenne prime exponents! [Noll] 256 = (2^2^2)^2 is the smallest prime power of a prime power of a prime power of a prime.
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