Permutations: Adjacent Elements Sum to Primes

[Edwin Clark]

On Sat, 26 Mar 2005, James Buddenhagen wrote:
> 
> Yes. A051239 is your sequence, each term divided by 2, and starting at 1.
> 

This and sequence 

ID Number: A036440
URL:       http://www.research.att.com/projects/OEIS?Anum=A036440

suggests that there may be a permutation p of the natural numbers such 
that p(i) + p(i+1) is prime for all i. Is anything known about this?