Primecount is a command-line program and C++ library that counts the primes below an integer x<=10**31 using highly optimized implementations of the combinatorial prime counting algorithms. Primecount includes implementations of all important combinatorial prime counting algorithms known up to this date all of which have been parallelized using OpenMP. Primecount contains the first ever open source implementations of the Deleglise-Rivat algorithm and Xavier Gourdon's algorithm (that works). Primecount also features a novel load balancer that is shared amongst all implementations and that scales up to hundreds of CPU cores. Primecount has already been used to compute several world records e.g. pi(10**27) (www.mersenneforum.org/showthread.php?t=20473) and nth_prime(10**24) (oeis.org/A006988).