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.

• Octahedral Number
• Octahedron
• Octahedron 5-Compound
• Octahemioctacron
• Octahemioctahedron
• Octakaidecagon
• Octal
• Octant
• Octatetrahedron
• Octic Surface
• Octillion
• Octodecillion
• Octonion
• Odd Function
• Odd Number
• Odd Number Theorem
• Odd Order Theorem
• Odd Prime
• Odds
• Odd Sequence
• ODE
• Offset Rings
• Ogive
• Oldknow Points
• Omega Constant