# 65537

This number is a prime.

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The smallest prime that is the sum of a nonzero square and
a nonzero cube in four different ways: 65537 = 122^{2} + 37^{3}
= 219^{2} + 26^{3} = 255^{2} + 8^{3} = 256^{2} + 1^{3}. [Post]

Largest known prime mean of a Fermat prime and a Mersenne prime 65537 = (3+131071)/2. Richard Mathar has searched through all means that can be created from the existing values of the two OEIS sequences, Mersenne primes and Fermat primes. [Post]

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