  In this paper we give a new semiprimality test and we construct a new formula
for $\pi ^{(2)}(N)$, the function that counts the number of semiprimes not
exceeding a given number $N$. We also present new formulas to identify the
$n^{th}$ semiprime and the next semiprime to a given number. The new formulas
are based on the knowledge of the primes less than or equal to the cube roots
of $N : P_{1}, \; P_{2}....P_{\pi \left( \sqrt[3]{N}\right) }\leq \sqrt[3]{N}$.
