Cullen Primes

Definition.   Cullen Primes are prime numbers that may be expressed in the form C_n = 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.