A051252

[Gordon Royle]

Sequence A051252 is the number of ways of arranging the integers 1..2n on a
circle so that the sum of any two adjacent numbers is prime.

The numbers get large very quickly.

But is there any proof that this can always be done?  ie that each entry is
strictly positive?

(This question arises from a question on another mailing list by Santo
Spadaro seeking a hamilton cycle in the graph on vertex set {1..2n} with
adjacency being given by vertex labels summing to a prime; obviously such a
ham cycle is precisely a "prime circle").

Cheers

gordon