# Pierpont prime

A Pierpont prime^{} is a prime number^{} of the form $p=1+{2}^{x}{3}^{y}$ with $$. If $x>0$ and $y=0$ then the resulting prime is a Fermat prime^{}. In the Erdős-Selfridge classification of primes (http://planetmath.org/ErdHosSelfridgeClassificationOfPrimes), the Pierpont primes are class 1-. The first few Pierpont primes are 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, etc., listed in A005109 of Sloane’s OEIS.

In 1988, Gleason showed that an $n$-sided regular polygon^{} can be constructed with ruler and compass if $n$ is the product of two Pierpont primes.

Title | Pierpont prime |
---|---|

Canonical name | PierpontPrime |

Date of creation | 2013-03-22 16:52:39 |

Last modified on | 2013-03-22 16:52:39 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A41 |