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Prime Circle

PrimeCircles

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime, where n is a positive integer. Rotations and reflections of an arrangement are counted as equivalent. The numbers of prime circles for n=1, 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.

2nprime circles
2{1,2}
4{1,2,3,4}
6{1,4,3,2,5,6}
8{1,2,3,8,5,6,7,4}, {1,2,5,8,3,4,7,6}

See also

Circular Permutation

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References

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."

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Prime Circle

Cite this as:

Weisstein, Eric W. "Prime Circle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrimeCircle.html

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