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]
To link to this page use http://primes.utm.edu/curios/page.php?number_id=89
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