Prime Curios!: 65537

65537
(another Prime Pages' Curiosity)

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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?

Submitted: 1999-09-02 18:40:00; Last Modified: 2009-08-15 07:10:10.