Prime Curios!: 256

256
(another Prime Pages' Curiosity)

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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.

sod(F₆) + sod(F₇) = 16² = 256, where F_n denotes the nth Fermat number. [Wesolowski]

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