primesieve

primesieve is a command-line program and C/C++ library for quickly generating prime numbers. It is very cache efficient, it detects your CPU's L1 & L2 cache sizes and allocates its main data structures accordingly. It is also multi-threaded by default, it uses all available CPU cores whenever possible i.e. if sequential ordering is not required. primesieve can generate primes and prime k-tuplets up to 2⁶⁴.

primesieve generates primes using the segmented sieve of Eratosthenes with wheel factorization. This algorithm has a run time complexity of $O(n\log{\log{n}})$ operations and uses $O(\sqrt{n})$ memory. Furthermore primesieve uses the bucket sieve algorithm which improves the cache efficiency when generating primes > 2³². primesieve uses 8 bytes per sieving prime, in practice its memory usage is about $\pi(\sqrt{n})\times 8$ bytes per thread.

• More algorithm details

Installation

The primesieve command-line program can be installed using your operating system's package manager. For doing development with libprimesieve you may need to install libprimesieve-dev or libprimesieve-devel.

Windows:	winget install primesieve
macOS:	brew install primesieve
Arch Linux:	sudo pacman -S primesieve
Debian/Ubuntu:	sudo apt install primesieve
Fedora:	sudo dnf install primesieve
FreeBSD:	pkg install primesieve
openSUSE:	sudo zypper install primesieve

Usage examples

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

# Print the primes ≤ 1000000
primesieve 1000000 --print

# Store the primes ≤ 1000000 in a text file
primesieve 1000000 --print > primes.txt

# Print the twin primes ≤ 1000000
primesieve 1000000 --print=2

# Count the prime triplets inside [1e10, 1e10+2^32]
primesieve 1e10 --dist=2^32 --count=3

Command-line options

Usage: primesieve [START] STOP [OPTION]...
Generate the primes and/or prime k-tuplets inside [START, STOP]
(< 2^64) using the segmented sieve of Eratosthenes.

Options:
  -c, --count[=NUM+]  Count primes and/or prime k-tuplets, NUM <= 6.
                      Count primes: -c or --count (default option),
                      count twin primes: -c2 or --count=2,
                      count prime triplets: -c3 or --count=3, ...
      --cpu-info      Print CPU information (cache sizes).
  -d, --dist=DIST     Sieve the interval [START, START + DIST].
  -h, --help          Print this help menu.
  -n, --nth-prime     Find the nth prime.
                      primesieve 100 -n: finds the 100th prime,
                      primesieve 2 100 -n: finds the 2nd prime > 100.
      --no-status     Turn off the progressing status.
  -p, --print[=NUM]   Print primes or prime k-tuplets, NUM <= 6.
                      Print primes: -p or --print,
                      print twin primes: -p2 or --print=2,
                      print prime triplets: -p3 or --print=3, ...
  -q, --quiet         Quiet mode, prints less output.
  -s, --size=SIZE     Set the sieve size in KiB, SIZE <= 8192.
                      By default primesieve uses a sieve size that
                      matches your CPU's L1 cache size (per core) or is
                      slightly smaller than your CPU's L2 cache size.
      --test          Run various sieving tests.
  -t, --threads=NUM   Set the number of threads, NUM <= CPU cores.
                      Default setting: use all available CPU cores.
      --time          Print the time elapsed in seconds.
  -v, --version       Print version and license information.

Build instructions

You need to have installed a C++ compiler which supports C++11 (or later) and CMake ≥ 3.4.

cmake .
cmake --build . --parallel
sudo cmake --install .
sudo ldconfig

• Detailed build instructions

C++ API

Include the <primesieve.hpp> header to use libprimesieve's C++ API.

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

int main()
{
  primesieve::iterator it;
  uint64_t prime = it.next_prime();

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

  return 0;
}

• C++ API documentation

C API

Include the <primesieve.h> header to use libprimesieve's C API.

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

int main()
{
  primesieve_iterator it;
  primesieve_init(&it);
  uint64_t prime;

  /* Iterate over the primes < 10^6 */
  while ((prime = primesieve_next_prime(&it)) < 1000000)
    printf("%" PRIu64 "\n", prime);

  primesieve_free_iterator(&it);
  return 0;
}

• C API documentation

Bindings for other languages

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

Common Lisp:	cl-primesieve
Janet:	janet-primesieve
Julia:	PrimeSieve.jl
Nim:	primesievec-nim
Haskell:	primesieve-haskell
Pascal:	primesieve-pas
Perl:	Primesieve
Python:	primesieve-python
Raku:	raku-primesieve
Ruby:	primesieve-ruby
Rust:	primesieve.rs

Many thanks to the developers of these bindings!