there is an old problem in which one asks that the integers from 1 to N be listed so that the sum of adjacent integers are primes.  I've never seen a solution.  It is probably true that one can always do this with N at the end of the list.

if one knew that for N>9 there is always a pair of twin primes betwen N and 2N all of this would follow.  But there should be a real proof.

anyone know anything?