# primesieve
[](https://ci.appveyor.com/project/kimwalisch/primesieve)
[](https://github.com/kimwalisch/primesieve/releases)
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](https://en.wikipedia.org/wiki/Prime_k-tuple)
up to 2<sup>64</sup>.
primesieve generates primes using the segmented
[sieve of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) with
[wheel factorization](https://en.wikipedia.org/wiki/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](http://sweet.ua.pt/tos/software/prime_sieve.html)
algorithm which improves the cache efficiency when generating primes > 2<sup>32</sup>.
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](doc/ALGORITHMS.md)
## 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```.
<table>
<tr>
<td><b>Windows:</b></td>
<td><code>winget install primesieve</code></td>
</tr>
<tr>
<td><b>macOS:</b></td>
<td><code>brew install primesieve</code></td>
</tr>
<tr>
<td><b>Arch Linux:</b></td>
<td><code>sudo pacman -S primesieve</code></td>
</tr>
<tr>
<td><b>Chocolatey:</b></td>
<td><code>choco install primesieve</code></td>
</tr>
<tr>
<td><b>Debian/Ubuntu:</b></td>
<td><code>sudo apt install primesieve</code></td>
</tr>
<tr>
<td><b>Fedora:</b></td>
<td><code>sudo dnf install primesieve</code></td>
</tr>
<tr>
<td><b>FreeBSD:</b></td>
<td><code>pkg install primesieve</code></td>
</tr>
<tr>
<td><b>openSUSE:</b></td>
<td><code>sudo zypper install primesieve</code></td>
</tr>
</table>
## Usage examples
```sh
# 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.
```sh
cmake .
make -j
sudo make install
sudo ldconfig
```
* [Detailed build instructions](doc/BUILD.md)
## C++ API
Include the ```<primesieve.hpp>``` header to use libprimesieve's C++ API.
```C++
#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](doc/CPP_API.md)
## C API
Include the ```<primesieve.h>``` header to use libprimesieve's C API.
```C
#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](doc/C_API.md)
## Bindings for other languages
primesieve natively supports C and C++ and has bindings available for:
<table>
<tr>
<td><b>Common Lisp:</b></td>
<td><a href="https://github.com/AaronChen0/cl-primesieve">cl-primesieve</a></td>
</tr>
<tr>
<td><b>Janet:</b></td>
<td><a href="https://github.com/bunder/janet-primesieve">janet-primesieve</a></td>
</tr>
<tr>
<td><b>Julia:</b></td>
<td><a href="https://github.com/jlapeyre/PrimeSieve.jl">PrimeSieve.jl</a></td>
</tr>
<tr>
<td><b>Nim:</b></td>
<td><a href="https://github.com/nandub/primesievec-nim">primesievec-nim</a></td>
</tr>
<tr>
<td><b>Haskell:</b></td>
<td><a href="https://hackage.haskell.org/package/primesieve">primesieve-haskell</a></td>
</tr>
<tr>
<td><b>Pascal:</b></td>
<td><a href="https://github.com/JulStrat/primesieve-pas">primesieve-pas</a></td>
</tr>
<tr>
<td><b>Perl:</b></td>
<td><a href="https://gitlab.com/oesiman/primesieve">Primesieve</a></td>
</tr>
<tr>
<td><b>Python:</b></td>
<td><a href="https://github.com/kimwalisch/primesieve-python">primesieve-python</a></td>
</tr>
<tr>
<td><b>Raku:</b></td>
<td><a href="https://github.com/CurtTilmes/raku-primesieve">raku-primesieve</a></td>
</tr>
<tr>
<td><b>Ruby:</b></td>
<td><a href="https://github.com/robertjlooby/primesieve-ruby">primesieve-ruby</a></td>
</tr>
<tr>
<td><b>Rust:</b></td>
<td><a href="https://github.com/pthariensflame/primesieve.rs">primesieve.rs</a></td>
</tr>
</table>
Many thanks to the developers of these bindings!
Generated by dwww version 1.15 on Sun Jun 16 09:16:37 CEST 2024.