Woodall Primes

Definition.   Woodall Primes are prime numbers that may be expressed in the form Wn = 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 Wn for n ≤ 29, but could not decide about W30. Some of the primes Wn 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.

 n Discoverer Date
2     A. J. C. Cunningham & H. J. Woodall   1917  
3     A. J. C. Cunningham & H. J. Woodall   1917  
6     A. J. C. Cunningham & H. J. Woodall   1917  
    2 ≤ n ≤ 29   1917  
  30     Hans Riesel   1968  
  75     Hans Riesel   1968  
  81     Hans Riesel   1968  
    30 ≤ n ≤ 110   1968  
  115     H. C. Williams & C. R. Zarnke   1967  
  123     Wilfrid Keller   1984  
  249     Wilfrid Keller   1984  
  362     Ingemar Jönsson   1972  
  384     Hans Riesel   1968  
  462     Wilfrid Keller   1984  
  512     R. M. Robinson   30 Jan 1952  
  751     Wilfrid Keller   1984  
  822     Wilfrid Keller   1984  
  5312    Wilfrid Keller   1984  
  7755     Wilfrid Keller   1984  
  9531     Wilfrid Keller   1984  
  12379     Wilfrid Keller   1984  
    110 < n ≤ 15000   1984  
  15822    Wilfrid Keller   1987  
  18885     Wilfrid Keller   1987  
    15000 < n ≤ 20000   1987  
  22971     Jeff Young   1997  
  23005     Jeff Young   1997  
  98726     Jeff Young   1997  
    20000 < n ≤ 100000   1997  
  143018     Ray Ballinger & ProthSearch   25  Apr 1998  
  151023     Kevin O'Hare & ProthSearch   01 May 1998  
  667071     Manfred Toplic & ProthSearch   25  Sep 2000  
  1195203     Mark Rodenkirch & ProthSearch   11   Jul 2005  
  1268979     Willem Siemelink & ProthSearch   25  Jan 2007  
    100000 < n ≤ 1280000   2007  
  1467763     Willem Siemelink & PrimeGrid   07  Jun 2007  
  2013992     Lasse Mejling Andersen & PrimeGrid   09 Aug 2007  
  2367906     Stephen Kohlman & PrimeGrid   03 Sep 2007  
  3752948     Matthew J. Thompson & PrimeGrid   27 Dec 2007  
    1280000 < n ≤ 11000000   Mar 2013  
  17016602     Diego Bertolotti & PrimeGrid   21 Mar 2018  
    11000000 < n ≤ 20800000   Mar 2022