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.

• Fibonacci n-Step Number
• Fibonacci Number
• Fibonacci Polynomial
• Fibonacci Pseudoprime
• Fibonacci Q-Matrix
• Fibonacci Sequence
• Fibration
• Field
• Field Axioms
• Field Extension
• Fields Medal
• Fifteen Theorem
• Figurate Number
• Figurate Number Triangle
• Figure Eight Knot
• Figure Eight Surface
• Figure-of-Eight Knot
• Figures
• Filon's Integration Formula
• Filter
• Fine's Equation
• Finite
• Finite Difference
• Finite Field
• Finite Game