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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 0.45 seconds on an Intel Core i7-6700 CPU (4 x 3.4 GHz). primesieve can generate primes and prime k-tuplets up to 2^64.

primesieve windows screenshot

Algorithm complexity

primesieve generates primes using the segmented sieve of Eratosthenes with wheel factorization. This algorithm has a run time complexity of operations and uses memory. Furthermore primesieve uses the bucket sieve algorithm for large sieving primes which reduces the memory usage to bytes per thread.


The primesieve console application can be installed using your operating system's package manager. The primesieve GUI application can be downloaded from https://primesieve.org/downloads.

# Debian/Ubuntu
sudo apt install primesieve

# macOS
brew install primesieve

# Windows using Chocolatey package manager
choco install primesieve

Usage examples

The primesieve console application can generate primes and prime k-tuplets.

# Count the primes below 1e10 using all CPU cores
primesieve 1e10

# Print the primes below 1000000
primesieve 1000000 --print

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

# Print an option summary
primesieve --help

Build instructions

Building primesieve requires a compiler which supports C++11 (or later) and CMake β‰₯ 3.4. If your compiler does not yet support C++11 you can fall back to primesieve-5.7.3 which is written in C++98.

cmake .
make -j
sudo make install

Build C/C++ examples

make -j

Run the tests

make -j
make test


Below is an example with the most common libprimesieve use cases.

#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 it;
  uint64_t prime = it.next_prime();

  // iterate over the primes below 10^6
  for (; prime < 1000000; prime = it.next_prime())
    std::cout << prime << std::endl;

  return 0;


primesieve's functions are exposed as C API via the primesieve.h header.

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

int main()
  primesieve_iterator it;
  uint64_t prime;

  /* iterate over the primes below 10^6 */
  while ((prime = primesieve_next_prime(&it)) < 1000000)
    printf("%llu\n", prime);

  return 0;

Linking against libprimesieve

Unix-like OSes

c++ -O2 primes.cpp -lprimesieve
cc  -O2 primes.c   -lprimesieve

If you have built primesieve yourself then the default installation path is /usr/local/lib which is not part of LD_LIBRARY_PATH on many OSes. Hence you need to export some environment variables:

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:$CPLUS_INCLUDE_PATH
export C_INCLUDE_PATH=/usr/local/include:$C_INCLUDE_PATH

Microsoft Visual C++

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

CMake support

Since primesieve-6.4 you can easily link against libprimesieve in your CMakeLists.txt:

find_package(primesieve REQUIRED)
target_link_libraries(your_target primesieve::primesieve)

To link against the static libprimesieve use:

find_package(primesieve REQUIRED static)
target_link_libraries(your_target primesieve::primesieve)

Bindings for other languages

primesieve natively supports C and C++ and has bindings available for:

Python: primesieve-python
Perl: perl6-primesieve
Ruby: primesieve-ruby
Rust: primesieve.rs
Haskell: primesieve-haskell

Many thanks to the developers of these bindings!