mersenne (C++ / GMP)

Lucas-Lehmer primality test for Mersenne numbers: M_p = 2^p - 1. CLI supports file/args input, multithreading, table or JSONL output. C++20 + GMP.

Features

• Lucas-Lehmer on mpz_class (GMP)
• Multi-threaded work queue (std::thread, atomic index)
• Inputs: positional exponents or --input file (supports commas and # comments)
• Outputs: pretty table (default) or JSON Lines (--jsonl)
• Skip composite exponents by default (--no-skip to force LL)

Dependencies

• C++20 compiler (g++, clang, MSVC)
• CMake >= 3.20
• GMP + gmpxx

Ubuntu/Debian

sudo apt-get update
sudo apt-get install -y g++ cmake make libgmp-dev libgmpxx4ldbl

macOS (Homebrew)

brew install gmp

Windows (vcpkg manifest mode)

# One-time: clone + bootstrap vcpkg
# git clone https://github.com/microsoft/vcpkg.git
# .\vcpkg\bootstrap-vcpkg.bat

# Configure + build with toolchain
cmake -S . -B build `
  -DCMAKE_TOOLCHAIN_FILE=C:/path/to/vcpkg/scripts/buildsystems/vcpkg.cmake
cmake --build build

A vcpkg.json is included; CMake + toolchain will install gmp automatically.

Build

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j

Usage

From CLI args:

./build/mersenne 31 61 89
./build/mersenne 127,521,607 --jsonl
./build/mersenne 31 61 --threads 4

From file:

./build/mersenne --input exponents.txt --threads 8

Help:

./build/mersenne --help

Input file format

• Integers separated by space/tab/comma
• # comments allowed (full line or inline)

Example exponents.txt:

# classic small ones
2 3 5 7 13
17 19 31
# bigger
61
89
127

Output

Table (default):

mersenne 0.1.0 | threads=4 | items=6 | run_id=1702755842000

p         p prime?    M_p prime?        time(s)     note
------------------------------------------------------------
2         yes         PRIME             0.0000
3         yes         PRIME             0.0000
5         yes         PRIME             0.0000
61        yes         composite         0.0001
89        yes         composite         0.0001
127       yes         PRIME             0.0001

JSON Lines (--jsonl):

{"p":2,"p_is_prime":true,"mersenne_is_prime":true,"seconds":0.000023,"note":""}
{"p":89,"p_is_prime":true,"mersenne_is_prime":false,"seconds":0.123456,"note":""}

Docker

docker build -t mersenne .
docker run --rm mersenne

Windows quick-start (PowerShell 7)

# install/update PowerShell 7 if needed: winget install Microsoft.PowerShell

# clone + bootstrap vcpkg
# git clone https://github.com/microsoft/vcpkg.git
# cd vcpkg; .\bootstrap-vcpkg.bat

# back to project
cmake -S . -B build `
  -DCMAKE_TOOLCHAIN_FILE=C:/path/to/vcpkg/scripts/buildsystems/vcpkg.cmake
cmake --build build

License

MIT (see LICENSE)