Woodall Number

Numbers of the form

$$W_n=2^n n-1.$$

The first few are 1, 7, 23, 63, 159, 383, ... (Sloane's A003261). The only Woodall numbers $W_n$ for $n<100,000$ which are Prime are for $n=5312$, 7755, 9531, 12379, 15822, 18885, 22971, 23005, 98726, ... (Sloane's A014617; Ballinger).

See also Cullen Number, Cunningham Number, Fermat Number, Mersenne Number, Sierpinski Number of the First Kind

References

Ballinger, R. ``Cullen Primes: Definition and Status.'' http://vamri.xray.ufl.edu/proths/cullen.html.

Guy, R. K. ``Cullen Numbers.'' §B20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 77, 1994.

Leyland, P. ftp://sable.ox.ac.uk/pub/math/factors/woodall.

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 360-361, 1996.

Sloane, N. J. A. Sequences A014617 and A003261/M4379 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.