An algorithmic implementation of the Pi function based on a new sieve
  In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete list of primes of absolute value greater than 3 in the interval of interest. This algorithm avoids the problem of generating large lists of numbers, and can be used to compute (even in parallel) the prime counting function $\pi(h)$. 
Damian Gulich, Gustavo Funes, Nahuel Lofeudo, Leopoldo Garavaglia and   Mario Garavaglia