Woodall Primes

Definition.   Woodall Primes are prime numbers that may be expressed in the form W_n = n · 2ⁿ − 1, n ≥ 2.

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 Woodall Project was later administrated by Mark Rodenkirch, who finally organized a smooth transition to PrimeGrid's Woodall Prime Search (WOO). 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. Cunningham and Woodall had indeed factorized all numbers W_n for n ≤ 29, but could not decide about W₃₀. Some of the primes W_n had been discovered (and published) in a different context. Thus, W₃₆₂ first appeared as 181 · 2³⁶³ − 1, W₃₆₂ as 3 · 2³⁹¹ − 1, and W₅₁₂ turned out to be the 13th Mersenne prime M₅₂₁ = 2⁵²¹ − 1.