title: Feasible implementation of a prime-counting function
body: <p>What would be a computationally feasible pseudocode of any <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html" rel="nofollow noreferrer">prime-counting function</a> implementation?</p>
  <p>I initially attempted coding the <a href="http://mathworld.wolfram.com/images/equations/PrimeCountingFunction/NumberedEquation7.gif" rel="nofollow noreferrer">Hardy-Wright algorithm</a>, but its factorials began generating miserable overflows, and many others appear bound to yield similar problems. I've scoured Google for practical solutions, but, at best, have found very esoteric mathematics which I haven't ever seen implemented in conventional programs.</p>