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 aFermat 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 A014566in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Lemma
• Lemniscate
• Lemniscate Case
• Lemniscate Constant
• Lemniscate Function
• Lemniscate Inverse Curve
• Lemniscate (Mandelbrot Set)
• Lemniscate of Bernoulli
• Lemniscate of Gerono
• Lemoine Axis
• Lemoine Circle
• Lemoine Line
• Lemoine Point
• Lemoine's Problem
• Lemon
• Length (Curve)
• Length Distribution Function
• Length (Number)
• Length (Partial Order)
• Length (Size)
• Lengyel's Constant
• Lens
• Lens Space
• Lenstra Elliptic Curve Method
• Leonardo's Paradox