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Pierpont prime (another Prime Pages' Glossary entries) |
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Gauss' proved that you can subdivide a circle into n
parts using a ruler (an unmarked straightedge) and a compass
(which draws circles) if and only if n is a power of
two times a product of distinct Fermat primes. Later Pierpont
[Pierpont1895] showed that
you can divide a circle into
n parts using origami (paper folding)
if and only if n is a product of a power of two times a power
of three times a distinct product of primes of the form
2n3m+1. These primes
are now called Pierpont primes.
Simple heuristics suggest that there should be finitely many Fermat primes, but infinitely many Pierpont primes. In the following table we give a count of the numbers smaller Pierpont primes. Circles can be divided into the same numbers of parts using a straight edge, compass and an "angle trisector."
See Also: FermatNumber Related pages (outside of this work)
References:
Chris Caldwell © 1999-2009 (all rights reserved)
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