primesieve is a program and C/C++ library that generates primes using a highly optimized sieve of Eratosthenes implementation. It counts the primes below 10^10 in just 0.57 seconds on an Intel Core i7‑4770 CPU (4 x 3.4GHz). primesieve can generate primes and prime k-tuplets up to 2^64.

• Homepage: http://primesieve.org
• Binaries: http://primesieve.org/downloads
• API: http://primesieve.org/api

The screenshot shows the primesieve GUI application running on Windows. There is also a primesieve console application available. Binaries for Windows, Mac OS X and Linux can be downloaded from http://primesieve.org/downloads.

primesieve generates primes using the segmented sieve of Eratosthenes with wheel factorization, this algorithm has a complexity of operations and uses space, more precisely primesieve's memory usage per thread is about bytes.

primesieve is written in C++03 and includes C bindings for all its functions. primesieve compiles with every C++ compiler and runs on both little and big endian CPUs. The parallelization is implemented using OpenMP. The primesieve GUI application (not built by default) uses the Qt framework.

Download the latest release tarball from http://primesieve.org/downloads, extract it and cd into the newly created directory. Then build and install primesieve using:

$ ./configure
$ make
$ sudo make install

If you have cloned primesieve or downloaded a zip archive from GitHub then the GNU Build System (a.k.a. Autotools) must be installed and autogen.sh must be executed once. To install the GNU Build System install GNU Autoconf, GNU Automake and GNU Libtool using your package manager.

$ ./autogen.sh
$ ./configure
$ make
$ sudo make install

To enable building the example programs use:

$ ./configure --enable-examples

Open a Visual Studio Command Prompt, cd into the primesieve directory and build primesieve using:

> nmake -f Makefile.msvc

In order to get the best performance you can indicate your CPU's L1 data cache size in kilobytes per core (default 32), e.g. for a CPU with 64 kilobytes L1 data cache use:

> nmake -f Makefile.msvc L1_DCACHE_SIZE=64

To build the example programs use:

> nmake -f Makefile.msvc
> nmake -f Makefile.msvc examples

The primesieve console application can print and count primes and prime k-tuplets and find the nth prime. Below are a few usage examples:

# Print the primes below 1000000 to the standard output
$ ./primesieve 1000000 --print

# Print the twin primes below 1000000 to the standard output
$ ./primesieve 1000000 --print=2

# Count the primes below 1e10 using all CPU cores
$ ./primesieve 1e10 --count

# Count the primes within [1e10, 2e10] using 4 threads
$ ./primesieve 1e10 2e10 --count --threads=4

# Print an option summary
$ ./primesieve --help

After having built and installed primesieve you can easily use it in your C++ program, below is an example. primesieve's API is documented online at http://primesieve.org/api.

#include <primesieve.hpp>
#include <iostream>
#include <vector>

int main()
{
  // store the primes below 1000
  std::vector<int> primes;
  primesieve::generate_primes(1000, &primes);

  primesieve::iterator pi;
  uint64_t prime;

  // iterate over the primes below 10^9
  while ((prime = pi.next_prime()) < 1000000000)
    std::cout << prime << std::endl;

  return 0;
}

On Unix-like operating systems compile using:

# Only needed if your operating system misses the ldconfig program
$ export LIBRARY_PATH=/usr/local/lib:$LIBRARY_PATH
$ export LD_LIBRARY_PATH=/usr/local/lib:$LD_LIBRARY_PATH
$ export CPLUS_INCLUDE_PATH=/usr/local/include:$CPLUS_INCLUDE_PATH

$ c++ -O2 primes.cpp -lprimesieve

On Windows (MSVC) compile using:

> cl /O2 /EHsc primes.cpp /I primesieve\include /link primesieve\primesieve.lib

All of primesieve's functions are exposed as C API (C99 or later) via the primesieve.h header. You can browse primesieve's C API online at http://primesieve.org/api.

#include <primesieve.h>
#include <stdint.h>
#include <stdio.h>

int main()
{
  uint64_t start = 0;
  uint64_t stop = 10000;
  size_t i;
  size_t size;

  /* get an array with primes below 10000 */
  int* primes = (int*) primesieve_generate_primes(start, stop, &size, INT_PRIMES);

  for (i = 0; i < size; i++)
    printf("%i\n", primes[i]);

  /* deallocate primes array generated using primesieve */
  primesieve_free(primes);
  return 0;
}

On Unix-like operating systems compile using:

# Only needed if your operating system misses the ldconfig program
$ export LIBRARY_PATH=/usr/local/lib:$LIBRARY_PATH
$ export LD_LIBRARY_PATH=/usr/local/lib:$LD_LIBRARY_PATH
$ export C_INCLUDE_PATH=/usr/local/include:$C_INCLUDE_PATH

$ cc -O2 primes.c -lprimesieve