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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).

ndecimal digitsdate
1467763441847Jun. 2007
2013992606279Aug. 2007
2367906712818Aug. 2007
37529481129757Dec. 2007
170166025122515Mar. 2018

See also

Integer Sequence Primes, Mersenne Prime, Woodall Number

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References

Caldwell, C. K. "The Top Twenty: Woodall Primes." http://primes.utm.edu/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." http://www.primegrid.com/server_status_subprojects.php.PrimeGrid. "PrimeGrid Primes: Subproject: (WOO) Woodall Prime Search." http://www.primegrid.com/primes/primes.php?project=WOO.Rodenkirch, M. and Ballinger, R. "Woodall Primes: Definition and Status." http://www.prothsearch.net/woodall.html.Sloane, N. J. A. Sequences A002234/M0820 and A050918 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Woodall Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WoodallPrime.html

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