Woodall Prime
A Woodall prime is a Woodall number
| W_n=2^nn-1 |
that is prime. The first few Woodall primes are 7, 23, 383, 32212254719, 2833419889721787128217599, ... (OEIS A050918), corresponding to n=2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, ... (OEIS A002234).
The following table summarizes large known Woodall primes. As of Mar. 2018, all n<16838832 have been checked (PrimeGrid).
n decimal digits date
1467763 441847 Jun. 2007
2013992 606279 Aug. 2007
2367906 712818 Aug. 2007
3752948 1129757 Dec. 2007
17016602 5122515 Mar. 2018
See also
Integer Sequence Primes, Mersenne Prime, Woodall NumberExplore with Wolfram|Alpha
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References
Caldwell, C. K. "The Top Twenty: Woodall Primes." https://t5k.org/top20/page.php?id=7#records.Keller, W. "New Cullen Primes." Math. Comput. 64, 1733-1741, 1995.Leyland, P. http://research.microsoft.com/~pleyland/factorization/cullen_woodall/2-.txt.PrimeGrid. "Subprojects: Woodall Prime Search." https://www.primegrid.com/server_status_subprojects.php.PrimeGrid. "PrimeGrid Primes: Subproject: (WOO) Woodall Prime Search." https://www.primegrid.com/primes/primes.php?project=WOO.Rodenkirch, M. and Ballinger, R. "Woodall Primes: Definition and Status." http://www.prothsearch.com/wPrimes.html.Sloane, N. J. A. Sequences A002234/M0820 and A050918 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Woodall PrimeCite this as:
Weisstein, Eric W. "Woodall Prime." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WoodallPrime.html