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=3primesieve includes support for stress testing both the CPU and memory. This feature is useful for checking system stability under maximum load and verifying whether your cooling solution (fans, heatsinks, thermal paste, etc.) is adequate. primesieve's stress test supports two modes: CPU (highest CPU load, uses little memory) and RAM (high memory usage, uses about 1.2 GiB per thread).
$ primesieve --stress-test --timeout 5m
Started CPU stress testing using 14 threads.
The expected memory usage is: 14 threads * 2.85 MiB = 39.90 MiB.
The stress test keeps on running until either a miscalculation occurs
(due to a hardware issue) or the timeout of 5m expires.
You may cancel the stress test at any time using Ctrl+C.
[Apr 12 19:09] Thread 14, 25.19 secs, PrimePi(1e13+98e11, 1e13+99e11) = 3265923128 OK
[Apr 12 19:09] Thread 9, 32.48 secs, PrimePi(1e13+63e11, 1e13+64e11) = 3286757785 OK
[Apr 12 19:09] Thread 14, 22.32 secs, PrimePi(1e13+ 0e11, 1e13+ 1e11) = 3340141707 OK
[Apr 12 19:10] Thread 2, 17.10 secs, PrimePi(1e13+16e11, 1e13+17e11) = 3323791292 OK
[Apr 12 19:10] Thread 14, 18.45 secs, PrimePi(1e13+ 3e11, 1e13+ 4e11) = 3336895789 OK
[Apr 12 19:11] Thread 13, 16.96 secs, PrimePi(1e13+96e11, 1e13+97e11) = 3267004191 OK
[Apr 12 19:11] Thread 2, 31.79 secs, PrimePi(1e13+20e11, 1e13+21e11) = 3320071119 OK
[Apr 12 19:12] Thread 11, 29.96 secs, PrimePi(1e13+84e11, 1e13+85e11) = 3273743021 OK
[Apr 12 19:13] Thread 4, 32.45 secs, PrimePi(1e13+37e11, 1e13+38e11) = 3305523133 OK
All tests passed successfully!
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].
-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.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;
}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;
}primesieve natively supports C and C++ and has bindings available for:
| Common Lisp: | cl-primesieve |
| Java: | primesieve-java |
| Janet: | janet-primesieve |
| Julia: | PrimeSieve.jl |
| Lua: | lua-primesieve |
| 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!
Thanks to all current and past sponsors of primesieve! Your donations help me purchase (or rent) the latest CPUs and ensure primesieve runs at maximum performance on them. Your donations also motivate me to continue maintaining primesieve.
