  A sieve is constructed for ordinary twin primes of the form 6m+/-1 that are
characterized by their twin rank m. It has no parity problem. Non-rank numbers
are identified and counted using odd primes p>=5. Twin- and non-ranks make up
the set of positive integers. Regularities of non-ranks allow gathering
information on them to obtain a Legendre-type formula for the number of
twin-ranks near primorial arguments.
