Definition. Cullen Primes are prime numbers that may be expressed in the form Cn = n · 2n + 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 · 2n + 1 or k · 2n − 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.
|1 ≤ n ≤ 52||1905|
|141||Raphael M. Robinson||1957|
|52 < n ≤ 1000||1957|
|1000 < n ≤ 20000||1984|
|20000 < n ≤ 30000||1987|
|30000 < n ≤ 45000||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 ≤ 21400000||Mar 2022|