Prime Circle
المؤلف:
Guy, R. K.
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
3-9-2020
1080
Prime Circle
A prime circle of order 
is a free circular permutation of the numbers from 1 to 
with adjacent pairs summing to a prime. The number 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.
 |
prime circles |
| 2 |
![<span style=]() {1,2}" src="https://mathworld.wolfram.com/images/equations/PrimeCircle/Inline5.gif" style="height:15px; width:32px" /> |
| 4 |
![<span style=]() {1,2,3,4}" src="https://mathworld.wolfram.com/images/equations/PrimeCircle/Inline6.gif" style="height:15px; width:62px" /> |
| 6 |
![<span style=]() {1,4,3,2,5,6}" src="https://mathworld.wolfram.com/images/equations/PrimeCircle/Inline7.gif" style="height:15px; width:92px" /> |
| 8 |
![<span style=]() {1,2,3,8,5,6,7,4}" src="https://mathworld.wolfram.com/images/equations/PrimeCircle/Inline8.gif" style="height:15px; width:122px" />, ![<span style=]() {1,2,5,8,3,4,7,6}" src="https://mathworld.wolfram.com/images/equations/PrimeCircle/Inline9.gif" style="height:15px; width:122px" /> |
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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