The book is now available! 65537
(another Prime Pages' Curiosity)
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+ The largest known Fermat prime (224 + 1).

+ Just a small proportion of regular polygons (n-gons) can be constructed with compass and straightedge. Gauss proved that if n is a Fermat prime, then it is possible to construct an n-gon. Wantzel later proved this condition was also necessary (for prime n-gons), so the 65537-gon is currently the largest known constructible prime n-gon. It took Hermes 10 years and a 200-page manuscript to write down a procedure for its construction. Would you like to attempt it?

+ The smallest prime that is the sum of a nonzero square and a nonzero cube in four different ways: 65537 = 1222 + 373 = 2192 + 263 = 2552 + 83 = 2562 + 13. [Post]

+ To remember the digits of 65537, recite the following mnemonic: "Fermat prime, maybe the largest." Then count the number of letters in each word. [Brent]

+ 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]

(There are 6 curios for this number that have not yet been approved by an editor.)




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