PrMers: GPU-accelerated Mersenne Primality Test

PrMers is a high-performance GPU application for testing the primality of Mersenne numbers using the Lucas–Lehmer and PRP (Probable Prime) algorithms. It leverages OpenCL and Number Theoretic Transforms (NTT) for fast large-integer arithmetic, and is optimized for long-running computations.

Key features:

⚡ GPU acceleration using OpenCL (including legacy OpenCL 1.2 devices)
🔁 Automatic checkpointing with resume support
📤 Submit results directly to your mersenne.org PrimeNet account
🖥️ Runs on Linux, macOS, and Windows (build from source or use precompiled binaries)
📊 Benchmark output for performance comparison across devices

🚀 Try the PrMers Demo on Google Colab

You can test PrMers directly in your browser with GPU acceleration by opening the interactive notebook below:

📈 Sample Performance Results

🔥 Radeon VII GPU

| Exponent  | Iter/s  | ETA             |
|-----------|---------|-----------------|
| 136279841 | 290.77  | 5d 10h 10m 27s  |
| 82589933  | 544.85  | 1d 18h 5m 45s   |
| 74207281  | 544.38  | 1d 15h 46m 49s  |
| 57885161  | 552.32  | 1d 5h 6m 18s    |

🍏 MacBook Air 2022 (Apple M2)

| Exponent  | Iter/s  | ETA              |
|-----------|---------|------------------|
| 136279841 | 31.16   | 50d 14h 57m 35s  |
| 82589933  | 50.88   | 18d 18h 52m 10s  |
| 77232917  | 51.17   | 17d 11h 16m 9s   |
| 74207281  | 51.15   | 16d 18h 58m 41s  |
| 57885161  | 51.00   | 13d 3h 16m 30s   |

🧊 INTEL(R) HD Graphics Family Integrated (113 MB) (OpenCL 1.2, legacy GPU - Windows)

| Exponent  | Iter/s  | ETA              |
|-----------|---------|------------------|
| 136279841 | 2.46    | 637d 18h 5m 0s   |
| 1257787   | 245.44  | 0d 1h 24m 0s     |
| 756839    | 249.23  | 0d 0h 49m 53s    |

For a full table of benchmark results, see the section below 👇

Features

GPU-accelerated Mersenne prime testing using OpenCL
Implementation of NTT / Lucas–Lehmer algorithms / PRP / IBDWT
Automatic backup of computation state with resume support
Command-line options for performance tuning and debugging

Requirements

PrMers runs on both Linux and Windows systems with OpenCL support.

✅ Common Requirements

A GPU supporting OpenCL 1.2 or higher (OpenCL 2.0 recommended)
OpenCL-compatible drivers installed
Libcurl

🐧 On Linux

g++ with C++20 support (e.g., GNU g++ 10+)
OpenCL development libraries:
- ocl-icd-opencl-dev
- opencl-headers
Git (to clone the repository)
libcurl4-openssl-dev

Example on ubuntu : sudo apt-get install -y ocl-icd-opencl-dev opencl-headers libcurl4-openssl-dev

🪟 On Windows

A compiler supporting C++20 (e.g., MSVC or MinGW64)
OpenCL SDK (e.g., Khronos OpenCL SDK)
CMake (if building via CMake)
Git for Windows (optional, if cloning directly)
Libcurl

🍎 On macOS

Xcode (Command Line Tools)
OpenCL is preinstalled (no setup required)
g++ or clang++ with C++20 support
Compatible with macOS Big Sur or later
libcurl

✅ macOS builds are supported and automatically generated in each release.

Alternatively, precompiled binaries are available from the Releases page.

⚙️ Example Execution and Submission

Below is a typical run of PrMers.

sebastien@cherubrock:~/prmers$ ./prmers 100003
No valid entry found in worktodo.txt
GPU Vendor: ADVANCED MICRO DEVICES, INC.
Device on-device queue preferred=262144  max=8388608
Queue size = 16384
Max CL_DEVICE_MAX_WORK_GROUP_SIZE = 256
Max CL_DEVICE_MAX_WORK_ITEM_SIZES = 1024, 1024, 1024
Max CL_DEVICE_LOCAL_MEM_SIZE = 65536 bytes
Transform Size = 4096
No valid entry found in worktodo.txt
Building OpenCL program with options:  -DWG_SIZE=16 -DLOCAL_PROPAGATION_DEPTH=8 -DCARRY_WORKER=512 -DLOCAL_PROPAGATION_DEPTH_DIV4=2 -DLOCAL_PROPAGATION_DEPTH_DIV4_MIN=1 -DLOCAL_PROPAGATION_DEPTH_DIV2=2 -DLOCAL_PROPAGATION_DEPTH_DIV2_MIN=3 -DWORKER_NTT=1024 -DWORKER_NTT_2_STEPS=256 -DMODULUS_P=100003 -DTRANSFORM_SIZE_N=4096 -DLOCAL_SIZE=256 -DLOCAL_SIZE2=256 -DLOCAL_SIZE3=256
OpenCL program built successfully from: /home/sebastien/prmers/kernels/prmers.cl
PrMers : GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas Lehmer)
Testing exponent : 100003
Device OpenCL ID : 0
Mode : PRP
Backup interval : 30 s
Save/Load path: .
Looking for loop file at "/home/sebastien/prmers/./100003prp.loop"
No valid loop file, initializing fresh state
Initial x[0] set to 3 (PRP mode)
Progress: 0.00% | Exp: 100003 | Iter: 0 | Elapsed: 0.00s | IPS: 0.00 | ETA: 0d 0h 0m 0s | RES64: 
Progress: 8.19% | Exp: 100003 | Iter: 8194 | Elapsed: 2.15s | IPS: 3812.20 | ETA: 0d 0h 0m 24s | RES64: FE049C7B28CF9800
Progress: 16.39% | Exp: 100003 | Iter: 16389 | Elapsed: 4.30s | IPS: 3812.10 | ETA: 0d 0h 0m 21s | RES64: CBE8841CD0DA8728
Progress: 24.58% | Exp: 100003 | Iter: 24584 | Elapsed: 6.44s | IPS: 3812.38 | ETA: 0d 0h 0m 19s | RES64: 6E9F608CA08C14A4
Progress: 32.78% | Exp: 100003 | Iter: 32779 | Elapsed: 8.59s | IPS: 3812.66 | ETA: 0d 0h 0m 17s | RES64: ED1AEED6832C638B
Progress: 40.97% | Exp: 100003 | Iter: 40974 | Elapsed: 10.74s | IPS: 3813.06 | ETA: 0d 0h 0m 15s | RES64: 6A03925E314AFFFF
Progress: 49.17% | Exp: 100003 | Iter: 49169 | Elapsed: 12.84s | IPS: 3814.62 | ETA: 0d 0h 0m 13s | RES64: BF436FB1EE7DA640
Progress: 57.36% | Exp: 100003 | Iter: 57364 | Elapsed: 14.99s | IPS: 3815.80 | ETA: 0d 0h 0m 11s | RES64: D72B40192A12F3D0
Progress: 65.56% | Exp: 100003 | Iter: 65559 | Elapsed: 17.13s | IPS: 3816.84 | ETA: 0d 0h 0m 9s | RES64: E04C07F04F534E24
Progress: 73.75% | Exp: 100003 | Iter: 73754 | Elapsed: 19.28s | IPS: 3817.66 | ETA: 0d 0h 0m 6s | RES64: 03AAC604F7FBB83A
Progress: 81.95% | Exp: 100003 | Iter: 81949 | Elapsed: 21.42s | IPS: 3818.39 | ETA: 0d 0h 0m 4s | RES64: 39198F5DCB0F078C
Progress: 90.14% | Exp: 100003 | Iter: 90144 | Elapsed: 23.57s | IPS: 3819.00 | ETA: 0d 0h 0m 2s | RES64: 64D9882C2A10ECB1
Progress: 98.34% | Exp: 100003 | Iter: 98339 | Elapsed: 25.72s | IPS: 3819.39 | ETA: 0d 0h 0m 0s | RES64: C2C6ED57A9EAC999
Progress: 100.00% | Exp: 100003 | Iter: 100003 | Elapsed: 26.16s | IPS: 3819.71 | ETA: 0d 0h 0m 0s | RES64: 1CF45E9503C71FD6

Warning: Cannot open file for MD5: 

M100003 PRP test: composite.

Manual submission JSON:
{"status":"C","exponent":100003,"worktype":"PRP-3","res64":"1CF45E9503C71FD6","res2048":"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","residue-type":1,"errors":{"gerbicz":0},"fft-length":4096,"shift-count":0,"program":{"name":"prmers","version":"0.1.0","port":8},"os":{"os":"Linux","architecture":"x86_64"},"user":"cherubrock","timestamp":"2025-04-27 22:01:04","checksum":{"version":1,"checksum":"445C4880"}}

Total elapsed time: 26.16 seconds.
JSON result written to: ./100003_prp_result.json
Result appended to: ./results.txt

No result is lost, and every completed test can be credited to your PrimeNet account.

📄 worktodo.txt support

This program now supports reading assignments from a worktodo.txt file, similar to how Prime95 or other GIMPS tools operate.

✅ Supported format

Only lines beginning with the PRP= prefix are currently supported.

Each PRP= line follows this format:

PRP=assignment_id,k,b,n,c[,how_far_factored,tests_saved][,known_factors]

Where:

k × bⁿ + c defines the number to test.
For Mersenne numbers, this is typically: k=1, b=2, c=-1.
n is the exponent (this is the value your program will extract and test).
Other fields are optional and currently ignored.

📌 Example

PRP=DEADBEEFCAFEBABEDEADBEEFCAFEBABE,1,2,197493337,-1,76,0;

This line instructs the program to test the Mersenne number ( 2^{197493337} - 1 ).

🔍 Usage

You can either:

Provide the exponent manually on the command line:

./prmers 197493337

Or use a worktodo.txt file (default path: ./worktodo.txt):

./prmers -worktodo

Or specify a custom path to your worktodo file:

./prmers -worktodo /path/to/worktodo.txt

If no exponent is passed and no -worktodo is provided, the program will prompt you to enter one interactively.

Note: Only the first valid PRP= line is used for now. Multi-line batching may be added later.

🔧 Using a Configuration File (`-config`)

You can run prmers using a configuration file to avoid passing long arguments on the command line every time.

📄 Example `setting.cfg`

-d 1
-O fastmath mad
-c 16
-profile
-ll
-t 300
-f /home/user/checkpoints
-l1 256
-l2 128
-l3 64
--noask
-user myusername
-worktodo ./tasks/worktodo.txt

🚀 How to use

You can launch prmers with this configuration file using:

./prmers -config ./setting.cfg

This will load all the parameters listed in setting.cfg as if you had typed them directly on the command line.

📌 Supported use cases

✅ If an exponent is given on the command line, it takes priority:
```
./prmers 333 -config ./setting.cfg
```
✅ If no exponent is given, but -worktodo <path> is present (in config or command line), the exponent is read from the worktodo.txt file:
```
./prmers -config ./setting.cfg
# → uses the exponent found in tasks/worktodo.txt
```
✅ If no exponent and no valid worktodo.txt entry are found, the program will prompt you to enter the exponent manually.

⚠️ Notes

The config file must contain arguments exactly as they would be typed on the command line, space-separated.
You can still override values from the config file by passing extra arguments on the command line.

🔐 Submitting Results to PrimeNet

PrMers supports direct submission of results to PrimeNet using your personal account. If you don’t have an account yet, it’s free and quick to create one at:
👉 https://www.mersenne.org

After a test completes, PrMers will prompt you to submit your result to PrimeNet:

✅ JSON result written to: ./86243_prp_result.json
Do you want to send the result to PrimeNet (https://www.mersenne.org) ? (y/n): y
Enter your PrimeNet username (Don't have an account? Create one at https://www.mersenne.org)
Enter your PrimeNet username : cherubrock
Enter your PrimeNet password: 
[TRACE] Sending login with user: cherubrock
[TRACE] Login response size: 32966 bytes...
[TRACE] Server response size: 13644 bytes
✅ Server response:...

📝 Parsed PrimeNet Result Summary:
 Manually check in your results Found 1 lines to process at 2025-04-11T11:13:30 Results for M 86 243 ignored, it is a known Mersenne Prime and no further testing is required. 
Done processing: 
* Parsed 1 lines.
* Found 0 datestamps.
GHz-days Qty Work Submitted Accepted Average 
1 PRP (Probable Prime): PRIME 0.000 - 0.000 
1 - all - 0.000 
Did not understand 0 lines. 
Recognized, but ignored 0/1 of the remaining lines. 
Skipped 0 lines already in the database. 
Accepted 1 lines.

Once accepted, the result is marked as sent:

✅ Result successfully sent to PrimeNet.

If for any reason a result was not submitted (e.g. skipped, disconnected, closed), PrMers will automatically prompt you to re-submit the result later on launch.

Found unsent result: ./86243_prp_result.json
Do you want to submit it to PrimeNet now? (y/n)

This ensures you never lose credit for a completed computation.

💾 Download Precompiled Binaries (Linux, Windows & macOS)

You can download precompiled binaries for Linux, Windows, and macOS directly from the Releases page.

Each release contains:

A compiled executable: prmers (Linux/macOS) or prmers.exe (Windows)
Required OpenCL kernel files inside a kernels/ folder
A SHA256 checksum file to verify integrity

All releases are built automatically using GitHub Actions, a continuous integration system provided by GitHub. This ensures that the binaries are consistently built from the source code in the repository.

You can view the exact build process and logs by visiting: 👉 GitHub Actions for PrMers

This setup guarantees that even users without development tools can safely download and verify that the binaries match the public source code.

🍏 macOS: Allow Execution of the Binary

On macOS, running unsigned executables downloaded from the internet will trigger Gatekeeper, blocking the file by default.

If you see this error:

“prmers” cannot be opened because the developer cannot be verified.

Follow these steps to allow it:

Attempt to run prmers once (via Terminal or double-click).
Open System Preferences → Security & Privacy → General.
At the bottom, you will see a message:

“prmers” was blocked from use because it is not from an identified developer.
Click "Allow Anyway".
Run the file again from Terminal:
```
./prmers
```
A dialog will appear asking for confirmation. Click "Open".

✅ The binary will now execute normally in the future.

(Optional) Local code signing

If you're a developer or wish to suppress some security warnings (e.g., killed: 9), you can locally self-sign the binary:

codesign -s - --deep --force --timestamp --options runtime ./prmers

Note: This is not a notarized signature, but it may prevent runtime security blocks.

To distribute a notarized macOS app without this issue, an Apple Developer Account is required.

Installation from sources

Clone the repository:

git clone https://github.com/cherubrock-seb/PrMers.git
cd PrMers

Compile the software:
```
make
```
Install the executable and kernel file: The following command installs the executable to /usr/local/bin and the OpenCL kernel file to /usr/local/share/prmers.

 sudo make install

The Makefile compiles the executable with a compile-time macro (KERNEL_PATH) so that, after installation, PrMers automatically finds its kernel file.

Compilation

Once installed, you can run PrMers directly from the command line. The basic syntax is:

prmers <p> [options]

for example

prmers 127 -O fastmath mad -c 16 -profile -ll -t 120 -f /your/backup/path

🛠️ Building PrMers on Windows (Manual Instructions)

This guide explains how to build PrMers manually on Windows, with different options.

⚙️ Option 1: CMake + vcpkg + Visual Studio (RECOMMENDED)

1. Install prerequisites:

CMake
Visual Studio (with C++ Desktop Development and OpenCL support)
vcpkg

2. Clone the repository:

git clone https://github.com/cherubrock-seb/PrMers.git
cd PrMers

3. Install libcurl via vcpkg:

git clone https://github.com/microsoft/vcpkg.git
cd vcpkg
.\bootstrap-vcpkg.bat
.\vcpkg install curl:x64-windows
cd ..

4. Configure CMake:

cmake -S . -B build -DCMAKE_TOOLCHAIN_FILE=./vcpkg/scripts/buildsystems/vcpkg.cmake -DCMAKE_BUILD_TYPE=Release

5. Build the project:

cmake --build build --config Release

6. Fix missing DLLs:

Copy the DLLs from vcpkg\installed\x64-windows\bin\ into the folder with prmers.exe
- OR add this path to your system PATH environment variable.

Typical required DLLs:

libcurl-4.dll
libssh2-1.dll
libnghttp2-14.dll
libbrotlicommon.dll
libwinpthread-1.dll
libstdc++-6.dll
libgcc_s_seh-1.dll
libidn2-0.dll

⚙️ Option 2: MinGW / MSYS2 + Makefile

1. Install MSYS2: https://www.msys2.org/

2. Update MSYS2:

pacman -Syu

3. Install required packages:

pacman -S mingw-w64-x86_64-gcc mingw-w64-x86_64-opencl-icd-loader mingw-w64-x86_64-curl

4. Build using Makefile:

make

5. Run from the MSYS2 shell (it uses the proper environment for DLLs).

⚙️ Option 3: Visual Studio IDE (CMake Project)

Open Visual Studio.
Create a new CMake Project.
Point it to the PrMers directory.
In CMakeSettings.json, add:

{
  "variables": [
    {
      "name": "CMAKE_TOOLCHAIN_FILE",
      "value": "C:/path/to/vcpkg/scripts/buildsystems/vcpkg.cmake"
    }
  ]
}

Install libcurl with vcpkg.
Build directly from Visual Studio.

📝 Notes:

If you get libcurl-4.dll not found, make sure the DLLs from vcpkg are accessible.
You can add the path to DLLs to PATH or copy them next to prmers.exe.

🔧 Optional: Provide this batch file to automate:

Create build_windows.bat:

@echo off
echo Setting up vcpkg and building prmers...

if not exist "vcpkg" (
    git clone https://github.com/microsoft/vcpkg.git
    cd vcpkg
    call bootstrap-vcpkg.bat
    cd ..
)

.\vcpkg\vcpkg install curl:x64-windows

cmake -S . -B build -DCMAKE_TOOLCHAIN_FILE=./vcpkg/scripts/buildsystems/vcpkg.cmake -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release

echo Build complete! Check the build\Release folder.
pause

🎉 DONE!

You should now have prmers.exe ready to run!

Command-Line Options

<p>: Minimum exponent to test (required)
-d <device_id>: Specify the OpenCL device ID (default: 0)
-O <options>: Enable OpenCL optimization flags (e.g., fastmath, mad, unsafe, nans, optdisable)
-c <localCarryPropagationDepth>: Set the local carry propagation depth (default: 8)
-profile: Enable kernel execution profiling
-prp: Run in PRP mode (default), with an initial value of 3 and no execution of kernel_sub2 (final result must equal 9)
-ll: Run in Lucas–Lehmer mode, with an initial value of 4 and p-2 iterations of kernel_sub2
-t <backup_interval>: Specify the backup interval in seconds (default: 60)
-f <path>: Specify the directory path for saving/loading backup files (default: current directory)
-enqueue_max <value>: Manually set the maximum number of enqueued kernels before clFinish is called (default: autodetect)
--noask: Automatically submit results to PrimeNet without prompting
-user <username>: PrimeNet account username to use for automatic result submission
-computer <computername>: computer name to use for PrimeNet result submission
password <password> : PrimeNet account password (used only when -no-ask is set, used to automatically put the result in primenet without prompt).
-worktodo [path]: Use a worktodo.txt file to load an exponent automatically.
- If no path is given, the default ./worktodo.txt is used.
- Only the first valid PRP= line is processed.
-config <path>: Load configuration from a specified .cfg file instead of passing options manually

📌 Typical Usage Scenarios

This program is designed for flexible, automated testing of Mersenne numbers using OpenCL. The most common use case involves running multiple tests in sequence using a worktodo.txt file, with automatic result submission enabled:

You can specify a list of exponents in worktodo.txt and run the program with --noask, -user <username>, and -password <password> to automatically submit results to PrimeNet without interaction.
For advanced control, backup files can be stored at a custom path using -f, and fine-grained OpenCL settings like local sizes or profiling can be adjusted with -l1, -l2, -l3, or -profile.
Command-line overrides (-O, -c, etc.) allow tailoring the run for performance tuning or testing alternative kernel behaviors.
You may also run single tests manually by specifying the exponent as a positional argument.

This enables full automation on servers or multi-GPU rigs with minimal supervision.

Uninstallation

To uninstall PrMers, run:

sudo make uninstall

Cleaning Up

To remove compiled files from the build directory, run:

make clean

Ubuntu Setup for OpenCL Development

Below is an example of the commands you need to install the necessary components to compile C++ code with OpenCL support and to run PrMers on Ubuntu. This includes installing the OpenCL headers and ICD loader, as well as the GPU drivers for NVIDIA, AMD, and Intel.

Update package lists

sudo apt-get update

Install OpenCL development packages and tools

sudo apt-get install ocl-icd-opencl-dev opencl-headers clinfo

For NVIDIA GPUs Install the proprietary NVIDIA driver (adjust version as needed) along with its OpenCL ICD.

sudo apt-get install nvidia-driver-525 nvidia-opencl-icd-525

For AMD GPUs Download the AMDGPU-PRO driver package from AMD's website. Then install it with OpenCL support using the following command (run in the extracted directory):

./amdgpu-pro-install -y --opencl=pal,legacy

For Intel GPUs

sudo apt-get install intel-opencl-icd

Verify your OpenCL installation by running: clinfo

Another option for manual compilation

To compile:

g++ -std=c++20 -I. -o prmers prmers.cpp proof/common.cpp proof/proof.cpp proof/md5.cpp proof/sha3.cpp -lOpenCL -O3 -Wall

Usage

Example of execution:

prmers 9279 -d 1
PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
Testing exponent: 9279
Using OpenCL device ID: 1

Launching OpenCL kernel (p = 9279); computation may take a while depending on the exponent.
Max global workers possible: 256
Final workers count: 256
Progress: 100.00% | Elapsed: 11.09s | Iterations/sec: 836.78 | ETA: 0.00s       
M9279 is composite.
Kernel execution time: 11.09 seconds
Iterations per second: 836.77 (9277 iterations in total)

Or without specifying a device:

prmers 216091
PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
Testing exponent: 216091
Using OpenCL device ID: 0

Launching OpenCL kernel (p = 216091); computation may take a while depending on the exponent.
Max global workers possible: 256
Final workers count: 256
Progress: 0.11% | Elapsed: 4.05s | Iterations/sec: 57.50 | ETA: 3754.28s

Output Example

PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
Testing exponent: 13
Using OpenCL device ID: 1

Launching OpenCL kernel (p_min_i = 13) without progress display; computation may take a while depending on the exponent.

Lucas-Lehmer test results:
Mp with p = 13 is a Mersenne prime.
Kernel execution time: 0.00150793 seconds
Iterations per second: 7294.76 (11 iterations in total)

New Features

Modes:
- -prp: Run in PRP mode (default).
  Sets the initial value to 3 and performs p iterations without executing kernel_sub2.
  The final result must equal 9.
- -ll: Run in Lucas-Lehmer mode.
  Sets the initial value to 4 and performs p-2 iterations, including the execution of kernel_sub2.
Backup / Save and Resume:
- The program periodically saves its state (the contents of buf_x) and the current loop iteration into files.
- Use -t <backup_interval> to specify the backup interval in seconds (default: 60 seconds).
- Use -f <path> to specify the directory for saving and loading files (default: current directory).
- If backup files (for example, "127prp.mers" and "127prp.loop") exist in the specified path, the program will resume computation from the saved iteration.
- During computation, when a backup occurs (either because the backup interval has elapsed or the user presses Ctrl-C), a status line is displayed with the same progress information as the normal progress display but in a distinct color (MAGENTA) and prefixed by "[Backup]".

Proof Generation (Experimental)

This project includes an experimental implementation of proof generation for verifying Mersenne prime tests.
The proof system is heavily based on the one used in GpuOwl, with substantial code reuse.

The proof process generates a .proof file, which contains:

The final residue after all PRP iterations.
A sequence of intermediate residues at exponentially spaced iteration points.
A verification mechanism that ensures B == A^(2^span) (mod 2^E - 1).

Currently, verification is not fully stable and needs further debugging.
Performance is also significantly slower than GpuOwl, as optimizations are still in progress.

📊 Full Performance Table on Radeon VII

| Exponent  | Iter/s  | ETA             |
|-----------|---------|-----------------|
| 136279841 | 275.75  | 5d 17h 15m 57s  |
| 82589933  | 473.57  | 2d 0h 25m 47s   |
| 77232917  | 474.60  | 1d 21h 11m 22s  |
| 74207281  | 473.48  | 1d 19h 31m 18s  |
| 57885161  | 473.77  | 1d 9h 55m 28s   |
| 43112609  | 469.56  | 1d 1h 29m 25s   |
| 42643801  | 471.80  | 1d 1h 5m 35s    |
| 37156667  | 849.48  | 0d 12h 8m 10s   |
| 32582657  | 889.28  | 0d 10h 9m 49s   |
| 30402457  | 888.15  | 0d 9h 29m 41s   |
| 25964951  | 895.79  | 0d 8h 2m 15s    |
| 24036583  | 886.68  | 0d 7h 30m 58s   |
| 20996011  | 1117.04 | 0d 5h 12m 26s   |
| 13466917  | 1150.65 | 0d 3h 14m 13s   |
| 6972593   | 1783.91 | 0d 1h 4m 18s    |
| 3021377   | 1833.43 | 0d 0h 26m 37s   |
| 2976221   | 1837.81 | 0d 0h 26m 9s    |
| 1398269   | 2226.52 | 0d 0h 9m 38s    |
| 1257787   | 2292.34 | 0d 0h 8m 18s    |
| 859433    | 2257.62 | 0d 0h 5m 30s    |
| 756839    | 2238.93 | 0d 0h 4m 48s    |
| 216091    | 2540.35 | 0d 0h 0m 35s    |
| 132049    | 3299.74 | 0d 0h 0m 0s     |
| 110503    | 2872.99 | 0d 0h 0m 0s     |
| 86243     | 3732.72 | 0d 0h 0m 0s     |
| 44497     | 4223.44 | 0d 0h 0m 0s     |

Example Executions

Using backup option with a 10-second interval:

Command:

 prmers 216091 -t 10

Output:

 PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
 Testing exponent: 216091
 Using OpenCL device ID: 0
 Mode selected: PRP
 Backup interval: 10 seconds
 Save/Load path: .
 Max CL_DEVICE_MAX_WORK_GROUP_SIZE = 256
 Max CL_DEVICE_MAX_WORK_ITEM_SIZES = 1024

 Launching OpenCL kernel (p = 216091); computation may take a while.
 Transform size: 16384
 Final workers count: 16384
 Work-groups count: 256
 Work-groups size: 64
 Workers for carry propagation count: 2048
 Local carry propagation depht: 8
 Local size carry: 256
 Building OpenCL program with options:  -DWG_SIZE=64 -DLOCAL_PROPAGATION_DEPTH=8 -DCARRY_WORKER=2048
 Resuming from iteration 27938 based on existing file ./216091prp.loop
 Loaded state from ./216091prp.mers
 Progress: 15.56% | Elapsed: 5.00s | Iterations/sec: 6724.69 | ETA: 27.13s       
 State saved to ./216091prp.mers
 Loop iteration saved to ./216091prp.loop
 [Backup] Progress: 18.16% | Elapsed: 10.00s | Iterations/sec: 3923.30 | ETA: 45.09s       
 Progress: 20.76% | Elapsed: 15.00s | Iterations/sec: 2989.41 | ETA: 57.28s       
 State saved to ./216091prp.mers
 Loop iteration saved to ./216091prp.loop
 [Backup] Progress: 23.37% | Elapsed: 20.00s | Iterations/sec: 2524.39 | ETA: 65.60s       
 Progress: 26.00% | Elapsed: 25.00s | Iterations/sec: 2246.94 | ETA: 71.17s       
 [Backup] Progress: 28.61% | Elapsed: 30.00s | Iterations/sec: 2060.63 | ETA: 74.86s       
 Progress: 31.25% | Elapsed: 35.01s | Iterations/sec: 1928.95 | ETA: 77.02s       
 [Backup] Progress: 33.91% | Elapsed: 40.00s | Iterations/sec: 1831.86 | ETA: 77.96s       
 Progress: 36.57% | Elapsed: 45.01s | Iterations/sec: 1756.06 | ETA: 78.05s       
 [Backup] Progress: 39.23% | Elapsed: 50.00s | Iterations/sec: 1695.30 | ETA: 77.46s       
 Progress: 41.83% | Elapsed: 55.01s | Iterations/sec: 1643.42 | ETA: 76.48s       
 [Backup] Progress: 44.44% | Elapsed: 60.00s | Iterations/sec: 1600.28 | ETA: 75.03s       
 Progress: 47.10% | Elapsed: 65.01s | Iterations/sec: 1565.57 | ETA: 73.02s       
 ^C
 State saved to ./216091prp.mers
 Loop iteration saved to ./216091prp.loop
 [Backup] Progress: 49.62% | Elapsed: 69.87s | Iterations/sec: 1534.73 | ETA: 70.93s       
 Exiting early due to interrupt.

PRP mode with default backup interval:

Command:

 prmers 127 -prp

Output:

 PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
 Testing exponent: 127
 Using OpenCL device ID: 0
 Mode selected: PRP
 Backup interval: 60 seconds
 Save/Load path: .
 Max CL_DEVICE_MAX_WORK_GROUP_SIZE = 256
 Max CL_DEVICE_MAX_WORK_ITEM_SIZES = 1024

 Launching OpenCL kernel (p = 127); computation may take a while.
 Transform size: 16
 Final workers count: 16
 Work-groups count: 4
 Work-groups size: 4
 Workers for carry propagation count: 2
 Local carry propagation depht: 8
 Local size carry: 2
 Building OpenCL program with options:  -DWG_SIZE=4 -DLOCAL_PROPAGATION_DEPTH=8 -DCARRY_WORKER=2
 Progress: 100.00% | Elapsed: 0.03s | Iterations/sec: 4102.95 | ETA: 0.00s       
 M127 PRP test succeeded (result is 9).
 Kernel execution time: 0.03 seconds
 Iterations per second: 4098.09 (127 iterations in total)

PRP mode with a larger exponent:

Command:

 prmers 756839 -prp

Output:

 PrMers: GPU-accelerated Mersenne primality test (OpenCL, NTT, Lucas-Lehmer)
 Testing exponent: 756839
 Using OpenCL device ID: 0
 Mode selected: PRP
 Backup interval: 60 seconds
 Save/Load path: .
 Max CL_DEVICE_MAX_WORK_GROUP_SIZE = 256
 Max CL_DEVICE_MAX_WORK_ITEM_SIZES = 1024

 Launching OpenCL kernel (p = 756839); computation may take a while.
 Transform size: 65536
 Final workers count: 65536
 Work-groups count: 256
 Work-groups size: 256
 Workers for carry propagation count: 8192
 Local carry propagation depht: 8
 Local size carry: 256
 Building OpenCL program with options:  -DWG_SIZE=256 -DLOCAL_PROPAGATION_DEPTH=8 -DCARRY_WORKER=8192
 Progress: 6.21% | Elapsed: 55.01s | Iterations/sec: 854.12 | ETA: 831.10s       
 State saved to ./756839prp.mers
 Loop iteration saved to ./756839prp.loop
 [Backup] Progress: 6.79% | Elapsed: 60.00s | Iterations/sec: 856.94 | ETA: 823.10s       
 Progress: 7.30% | Elapsed: 65.01s | Iterations/sec: 850.30 | ETA: 825.08s

Notes

The code uses OpenCL for GPU acceleration.
It implements both PRP and Lucas-Lehmer (LL) tests.
State saving is performed periodically based on the backup interval.
When interrupted (Ctrl-C), the program saves its state before exiting, allowing you to resume later.
The project implements an integer-based NTT and IBDWT using modular arithmetic modulo 2^64 - 2^32 + 1.
The chosen modulus enables fast modular reduction using only bit shifts and additions.
For more details on the underlying techniques, refer to Nick Craig-Wood's ARM Prime Math: https://www.craig-wood.com/nick/armprime/math/

Resources & Community

GIMPS (Great Internet Mersenne Prime Search): https://www.mersenne.org
Mersenne Forum: https://www.mersenneforum.org

Inspiration

Nick Craig-Wood's IOCCC2012 entry: https://github.com/ncw/ioccc2012
Armprime project: https://github.com/ncw/
Genefer by Yves Gallot: https://github.com/galloty/genefer22
GPUOwl: https://github.com/preda/gpuowl

Author: Cherubrock

Name		Name	Last commit message	Last commit date
Latest commit History 462 Commits
.github/workflows		.github/workflows
include		include
kernels		kernels
old		old
src		src
.gitignore		.gitignore
CMakeList.txt		CMakeList.txt
Makefile		Makefile
README.md		README.md
prmers.ipynb		prmers.ipynb
unit_tests.sh		unit_tests.sh

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PrMers: GPU-accelerated Mersenne Primality Test

🚀 Try the PrMers Demo on Google Colab

📈 Sample Performance Results

🔥 Radeon VII GPU

🍏 MacBook Air 2022 (Apple M2)

🧊 INTEL(R) HD Graphics Family Integrated (113 MB) (OpenCL 1.2, legacy GPU - Windows)

Features

Requirements

✅ Common Requirements

🐧 On Linux

🪟 On Windows

🍎 On macOS

⚙️ Example Execution and Submission

📄 worktodo.txt support

✅ Supported format

📌 Example

🔍 Usage

🔧 Using a Configuration File (-config)

📄 Example setting.cfg

🚀 How to use

📌 Supported use cases

⚠️ Notes

🔐 Submitting Results to PrimeNet

💾 Download Precompiled Binaries (Linux, Windows & macOS)

🍏 macOS: Allow Execution of the Binary

(Optional) Local code signing

Installation from sources

Compilation

🛠️ Building PrMers on Windows (Manual Instructions)

⚙️ Option 1: CMake + vcpkg + Visual Studio (RECOMMENDED)

1. Install prerequisites:

2. Clone the repository:

3. Install libcurl via vcpkg:

4. Configure CMake:

5. Build the project:

6. Fix missing DLLs:

⚙️ Option 2: MinGW / MSYS2 + Makefile

1. Install MSYS2: https://www.msys2.org/

2. Update MSYS2:

3. Install required packages:

4. Build using Makefile:

5. Run from the MSYS2 shell (it uses the proper environment for DLLs).

⚙️ Option 3: Visual Studio IDE (CMake Project)

📝 Notes:

🔧 Optional: Provide this batch file to automate:

🎉 DONE!

Command-Line Options

Uninstallation

Cleaning Up

Ubuntu Setup for OpenCL Development

Update package lists

Install OpenCL development packages and tools

Another option for manual compilation

Usage

Output Example

New Features

Proof Generation (Experimental)

📊 Full Performance Table on Radeon VII

Example Executions

Notes

Resources & Community

Inspiration

About

Resources

Stars

Watchers

Forks

Releases

Packages

Contributors

Languages

🔧 Using a Configuration File (`-config`)

📄 Example `setting.cfg`