the original problem was not "circular" but just a list
for example with N=12 we have:

       12, 7, 10. 9. 8. 11, 6,     5, 2, 1, 4, 3,

down thru 6 illustrates the twin prime connection (here the primes are 17 and 19)_
it also provides an inductive procedure for verifying the conjecture for N up to the linit of  tables of primes  (millions)