Assuming Dickson's conjecture, we give explicit formulas for Bhargava's factorials associated to the set P-2 of twin primes. We also characterize the polynomials of degree n which take integral values on P-2 by means of their values on {1,..., 2n+1}. Doing this, we give a negative answer to a conjecture of Mingarelli. Similar results are also obtained when replacing Z by F-q[T].