
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 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 2^{n}3^{m}+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)
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Chris K. Caldwell © 19992019 (all rights reserved)
