# Cullen number

A Cullen number^{} ${C}_{m}$ is a number of the form ${2}^{m}m+1$, where $m$ is an integer. Almost all Cullen numbers are composite, and they have $2m-1$ as a factor if that number is a prime of the form $8k-3$ (with $k$ a positive integer). The first few Cullen numbers are 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609 (listed in A002064 of Sloane’s OEIS). With the exception of 3, no Proth number is also a Cullen number.

Title | Cullen number |
---|---|

Canonical name | CullenNumber |

Date of creation | 2013-03-22 17:21:34 |

Last modified on | 2013-03-22 17:21:34 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A51 |

Related topic | WoodallNumber |