libcpprime

libcpprime is an efficient C++ implementation of a primality test optimized for 64-bit integers.

Usage

cppr::IsPrime()

Header: <libcpprime/IsPrime.hpp>

namespace cppr {
    bool IsPrime(std::uint64_t n) noexcept; // C++11
    constexpr bool IsPrime(std::uint64_t n) noexcept; // C++20
}

It returns true if the input value is a prime number; otherwise, it returns false.

example

#include <libcpprime/IsPrime.hpp>
#include <cassert>
int main() {
    assert(cppr::IsPrime(998244353) == true);
    assert(cppr::IsPrime(13148563482635885461) == false);
}

cppr::IsPrimeNoTable

Header: <libcpprime/IsPrimeNoTable.hpp>

namespace cppr {
    bool IsPrimeNoTable(std::uint64_t n) noexcept; // C++11
    constexpr bool IsPrimeNoTable(std::uint64_t n) noexcept; // C++20
}

It returns true if the input value is a prime number; otherwise, it returns false. If you want to reduce the size of the executable file, use this function instead of cppr::IsPrime because cppr::IsPrime uses a 40KB table for performance optimization.

example

#include <libcpprime/IsPrimeNoTable.hpp>
#include <cassert>
int main() {
    assert(cppr::IsPrimeNoTable(998244353) == true);
    assert(cppr::IsPrimeNoTable(1314856348263588546) == false);
}

CPPR_HAS_CONSTEXPR_IS_PRIME

Header: <libcpprime/FeatureTestMacros.hpp>

#define CPPR_HAS_CONSTEXPR_IS_PRIME 1 // C++20

This is a feature test macro that determines whether cppr::IsPrime and cppr::IsPrimeNoTable are declared with constexpr.

example

#include <libcpprime/FeatureTestMacros.hpp>
#include <libcpprime/IsPrime.hpp>
#include <iostream>
int main() {
#ifdef CPPR_HAS_CONSTEXPR_IS_PRIME
    constexpr bool x = cppr::IsPrime(1000000007);
#else
    const bool x = cppr::IsPrime(1000000007);
#endif
    std::cout << x << std::endl;
}

Requirements

• C++11
• GCC, Clang, GCC (MinGW), Clang (MinGW), MSVC, clang-cl

Compilation

This library is header-only, so you only need to specify the include path.

g++ -I ./libcpprime -O3 Main.cpp

Benchmarks

Benchmarks are executed on GitHub Actions.

Workflow: bench.yml

Linux (gcc)

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Linux (clang)

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Windows (msvc)

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Windows (clang-cl)

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Releases

• 2026/02/25 ver 1.3.3
  • Update copyright year to 2026
  • Add -O3 -march=native to the compilation flags during benchmarking and testing
• 2026/01/04 ver 1.3.2
  • Improve performance
• 2025/12/24 ver 1.3.1
  • Improve performance and reduce binary size for cppr::IsPrime
• 2025/12/21 ver 1.3.0
  • Add CPPR_HAS_CONSTEXPR_IS_PRIME
  • Support clang-cl
  • Accelerating Compile-Time Computation
  • Improved compatibility
• 2025/03/10 ver 1.2.11
  • Change the name on the license
  • Change Multiprication Algorithm
  • Replace __uint128_t with unsigned __int128
• 2025/01/05 ver 1.2.10
  • Change the condition of constexpr
• 2025/01/03 ver 1.2.9
  • Fix a bug
• 2025/01/02 ver 1.2.8
  • Improve performance
  • Suppress warnings
• 2024/12/31 ver 1.2.7
  • Improve performance
• 2024/12/30 ver 1.2.6
  • Improve performance
• 2024/12/29 ver 1.2.5
  • Add copyrights notice
• 2024/12/28 ver 1.2.4
  • Improve performance
• 2024/12/26 ver 1.2.3
  • Improve performance
• 2024/12/25 ver 1.2.2
  • Improve performance
• 2024/12/23 ver 1.2.1
  • Improve performance
• 2024/12/19 ver 1.2.0
  • Split cppr::IsPrime into cppr::IsPrime and cppr::IsPrimeNoTable
• 2024/12/19 ver 1.1.2
  • Fix typo
• 2024/12/18 ver 1.1.1
  • Add include guards
• 2024/12/18 ver 1.1.0
  • Add cppr::IsPrime with a table
• 2024/12/18 ver 1.0.0
  • Add cppr::IsPrime

References

• https://miller-rabin.appspot.com/
• https://zenn.dev/mizar/articles/791698ea860581
• https://www.techneon.com/download/is.prime.32.base.data
• https://www.techneon.com/download/is.prime.64.base.data
• https://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/