  We introduce a sieve for counting twin primes up to a given range. Our method
depends on a parameter ${\lambda}_x$ and the estimation of the number of twin
primes obtained as a result, is called a fundamental structure of the
distribution of twin primes. Combining the latter with an asymptotic bound of
${\lambda}_x$, establishes venues, conducive to a discovery of a partial result
that can be considered as a suitable variant of the prime number theorem.
Furthermore, we obtain an asymptotic bound of the number of twin primes less
than $x$.
