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A prime circle of order 
 is a 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, ....
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.