Erdös has conjectured that no higher power of the first prime (i.e., 28 = 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.