**Definition.**
Cullen Primes are prime numbers that may be expressed in the form
*C*_{n} = *n* · 2^{n} + 1, *n* ≥ 1.

The original Definition and Status page was set up in early 1998 by Ray Ballinger, as part of a more general
Proth Search Project devoted to the coordinated search for primes mainly of the forms
*k* · 2^{n} + 1 or *k* · 2^{n} − 1 by using Yves Gallot's new program
`Proth.exe`. The particular Cullen Project was later administrated by Mark Rodenkirch, who finally
organized a smooth transition to
PrimeGrid's Cullen Prime Search (CUL). As a nostalgic reminiscence we
here reproduce the original page in its frozen state at a late concluding point in 2013.

The complete results and current status of the search are summarized in the following table. As a historical curiosity it might be
mentioned that Jeff Young had completed 30000 < *n* ≤ 100000 already in November 1994, but refrained from communicating the
four new primes because he preferred to publish them in a mathematical journal. The delay implied that in May 1997 everything was
finally submitted to Chris Caldwell's Prime Pages in a quite different form.

n | Discoverer | Date |

1 | James Cullen | 1905 |

1 ≤ n ≤ 52 | 1905 | |

141 | Raphael M. Robinson | 1957 |

52 < n ≤ 1000 | 1957 | |

4713 | Wilfrid Keller | 1984 |

5795 | Wilfrid Keller | 1984 |

6611 | Wilfrid Keller | 1984 |

18496 | Wilfrid Keller | 1984 |

1000 < n ≤ 20000 | 1984 | |

20000 < n ≤ 30000 | 1987 | |

32292 | Masakatu Morii | 1997 |

32469 | Masakatu Morii | 1997 |

30000 < n ≤ 45000 | 1997 | |

59656 | Jeff Young | 1997 |

90825 | Jeff Young | 1997 |

45000 < n ≤ 100000 | 1997 | |

262419 | Darren Smith & ProthSearch | 08 Mar 1998 |

361275 | Darren Smith & ProthSearch | 31 Jul 1998 |

481899 | Masakatu Morii & ProthSearch | 30 Sep 1998 |

1354828 | Mark Rodenkirch & ProthSearch | 25 Aug 2005 |

100000 < n ≤ 1500000 | 2007 | |

6328548 | Dennis R. Gesker & PrimeGrid | 20 Apr 2009 |

6679881 | Magnus Bergman & PrimeGrid | 25 Jul 2009 |

1500000 < n ≤ 10000000 | Mar 2013 | |

10000000 < n ≤ 24377000 | Jan 2024 |