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
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 |
# 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=3Usage: 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].
-n, --nth-prime Find the nth prime.
primesieve 100 -n: finds the 100th prime,
primesieve 2 100 -n: finds the 2nd prime > 100.
-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.
-S, --stress-test[=MODE] Run a stress test. The MODE can be either
CPU (default) or RAM. The default timeout is 24h.
--test Run various correctness tests (< 1 minute).
-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.
--timeout=SEC Set the stress test timeout in seconds. Supported
units of time suffixes: s, m, h, d or y.
30 minutes timeout: --timeout 30m
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 ldconfigInclude 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;
}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;
}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!