A prime circle of order
is a free circular permutation of the numbers
from 1 to
with adjacent pairs summing to a prime,
where
is a positive integer. Rotations
and reflections of an arrangement are counted as equivalent.
The numbers of prime circles for , 2, ..., are 1, 1, 1, 2, 48, 512, ... (OEIS A051252).
The prime circles for the first few even orders are given in the table below.
Filz, A. "Problem 1046." J. Recr. Math.14, 64, 1982.Filz, A. "Problem 1046." J. Recr. Math.15,
71, 1983.Guy, R. K. Unsolved
Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 105-106,
1994.Sloane, N. J. A. Sequence A051252
in "The On-Line Encyclopedia of Integer Sequences."
is a free circular permutation of the numbers
from 1 to 
with adjacent pairs summing to a prime,
where 
is a positive integer. Rotations
and reflections of an arrangement are counted as equivalent.
The numbers of prime circles for 
, 2, ..., are 1, 1, 1, 2, 48, 512, ... (OEIS A051252).
The prime circles for the first few even orders are given in the table below.
, 
