## Sierpinski Number of the First Kind

Numbers of the form . The first few are 2, 5, 28, 257, 3126, 46657, 823544, 16777217, ... (Sloane's A014566). Sierpinski proved that if is Prime with , then , where is a Fermat Number with . The first few such numbers are , , , , , and . Of these, 5 and 257 are Prime, and the first unknown case is .

References

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, p. 155, 1979.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 74, 1989.

Sloane, N. J. A. Sequence A014566 in The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.