Woodall Prime

Author

Eric W. Weisstein
April 10, 2018

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/WoodallPrime.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WoodallPrime.html.

©2018 Wolfram Research, Inc. except for portions noted otherwise

Code

WoodallNumber[n_]:=2^n n-1

???

Reduce[#==n 2^n-1,n,Integers]&/@{938237 2^3752950-1,1183953 2^2367907-1,251749 2^2013995-1}

Prime

http://primes.utm.edu/top20/page.php?id=7# records

A002234

Length[$WoodallPrimeIndices={2,3,6,30,75,81,115,123,249,362,384,462,512,751,822,5312,7755,9531,12379,15822,18885,22971,23005,98726,143018,151023,667071,1195203,1268979,1467763,2013992,2367906,3752948,17016602}]

TextGrid[MapIndexed[{#2[[1]],#,IntegerLength[WoodallNumber[#]]}&,$WoodallPrimeIndices],Dividers->All,Alignment->Decimal]

Select[Range[100],PrimeQ[WoodallNumber[#]]&]

WoodallNumber/@%

Check

DateString[]

$Version

$MachineName

Do[
Print[{i,n=$WoodallPrimeIndices[[i]],PrimeQ[WoodallNumber[n]]//Timing}],
{i,25}
]

Do[
Print[{i,n=$WoodallPrimeIndices[[i]],PrimeQ[WoodallNumber[n]]//Timing}],
{i,25,26}
]

Earlier version: