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)