google-colab

Google Colaboratory and GIMPS

Google offers a service known as Colaboratory (Colab), which allows anyone with an internet connection free access to high-performance TPU, GPU and CPU-powered Jupyter Notebooks. This service can be used to run Distributed Computing projects such as the Great Internet Mersenne Prime Search (GIMPS) for free. GIMPS can be run on some Nvidia, AMD and Intel GPUs using the GpuOwl program or a CPU using the Prime95/MPrime program.

This repository contains two Jupyter Notebooks, a “CPU” only notebook (Colab CPU MPrime.ipynb) and a “GPU and CPU” notebook (Colab GPU GpuOwl.ipynb). The “CPU” only notebook runs MPrime, while the “GPU and CPU” notebook runs both GpuOwl and MPrime since they can run simultaneously to “crunch” more prime numbers. Previous versions of the GPU notebook ran CUDALucas. Each notebook makes use of Google Drive storage, which is provided to all Google accounts. See here for a “TPU” only notebook which runs TensorPrime.

How to Use

Please Note: you must keep each notebook OPEN in your browser to prevent it from disconnecting due to being perceived as idle. Pin the tab(s) or move them to a dedicated window for easy access to your notebook(s).

1. Choose a Persistent Storage Option Recommend Method: Copy the source of our respective “GPU and CPU” notebook and/or “CPU” notebook, pasting them into one or more new notebooks in Colab. Then, uniquely name and save the notebook(s) (Ctrl + s). Then, on the far left, click “📁”, the “Mount Drive” folder button and select “Connect to Google Drive”. Your Drive storage should automatically remount each time you run the notebook(s). You may need to repeat this last part after a while. See the official video for a walkthrough.

Alternative Method

Open “GPU and CPU” notebook: and/or the “CPU” only notebook: in Colab. Then, uniquely name and save a copy to your Drive (Ctrl + s) to avoid a warning each time you run the notebook. *WARNINGS*: This method will continually require an authorization step each time you run the notebook(s). After step 4 below, follow the link Google provides to authorize the login to your Drive and copy-and-paste the authorization string into the textbox Google provides within the notebook's output box.

2. If Running the GPU notebook, you must enable the GPU runtime. On the upper left, click “Runtime” → “Change runtime type”, under “Hardware accelerator” select one of the GPUs and then click “Save”.

3. Leave the default options to run anonymously. Alternatively, fill in your GIMPS/PrimeNet account user ID and set any other desired options. Each instance of a notebook type needs to have a unique computer_number value. Note that the PRP worktypes can use several GiB of your Drive storage. Every lower value will halve Drive storage requirements for PRP tests, but double the certification cost. Set the highest prp_proof_power value that you have available Drive storage for (see below for the space needed for several proof powers and exponents).

4. Click “▶️” to run the notebook.

5. When the Notebook Disconnects – for example due to its 12-hour usage limit, idle timeouts, Google requiring your GPU type, etc. – repeat step 4 again to continue where you left off. Use our Colab Autorun and Connect Firefox and Chrome add-on/extension to automate this step.

Google may offer you up to two GPU runtimes to disperse among your notebooks. In this case, you may create another GPU notebook by re-running the steps with a different computer_number value. For example, choose 2 if you are already running a GPU notebook with the Default (1) number.

Optional

A user may optionally perform other steps to gain more insight into GIMPS and/or this software:

1. Create a GIMPS/PrimeNet account here and join the “Portland State University” team!

2. Set the debug option to view the last 100 lines of output and the status from the respective GIMPS program. Alternatively, you may access the cpu1.out…cpuN.out, 1/gpu.out…N/gpu.out, and 1/autoprimenet.out…N/autoprimenet.out files, where N is the computer_number value, in your Google Drive under the GIMPS and mprime_gpu/mprime_cpu or gpuowl folders to see the full MPrime and/or GpuOwl output respectively.

Required Tools, Restrictions

Anyone with an internet connection and a free Google/Gmail account with just ~50 MiB of free space on Google Drive can use both our notebooks to “crunch” primes.

Drive storage (GiB) needed to store the proof interim residues file during each PRP test:

Proof Power	Exp 50M	Exp 100M	Exp 150M	Exp 200M	Exp 250M	Exp 300M	Exp 332.1M (100M digits)	Exp 1,000M (PrimeNet limit)
5	0.186	0.372	0.558	0.745	0.931	1.117	1.237	3.725
6	0.372	0.745	1.117	1.49	1.862	2.235	2.475	7.45
7	0.745	1.49	2.235	2.98	3.725	4.47	4.95	14.9
8	1.49	2.98	4.47	5.96	7.45	8.94	9.9	29.8
9	2.98†	5.96†	8.94†	11.92†	14.9†	17.88†	19.8†	59.6†
10	5.96	11.92	17.88	23.84	29.8	35.76	39.6	119.2
11	11.92	23.84	35.76	47.68	59.6	71.52	79.2	238.4
12	23.84	47.68	71.52	95.36	119.2	143	158.4	476.8

Drive storage (MiB) needed to generate proof file at the end of each PRP test:

Proof Power	Proof Power Multiplier	Certification Cost	Exp 50M	Exp 100M	Exp 150M	Exp 200M	Exp 250M	Exp 300M	Exp 332.1M	Exp 1,000M
5	1	1⁄32	35.76	71.52	107.2	143	178.8	214.5	237.6	715.2
-	2	1⁄64	71.52	143	214.5	286.1	357.6	429.1	475.2	1430
-	3	1⁄128	107.2	214.5	321.8	429.1	536.4	643.7	712.8	2145
-	4	1⁄256	143	286.1	429.1	572.2	715.2	858.3	950.4	2861
6	1	1⁄64	41.72	83.44	125.1	166.8	208.6	250.3	277.2	834.4
-	2	1⁄128	83.44	166.8	250.3	333.7	417.2	500.6	554.4	1668
-	3	1⁄256	125.1	250.3	375.5	500.6	625.8	751	831.6	2503
-	4	1⁄512	166.8	333.7	500.6	667.5	834.4	1001	1108	3337
7	1	1⁄128	47.68	95.36	143	190.7	238.4	286.1	316.8	953.6
-	2	1⁄256	95.36	190.7	286.1	381.4	476.8	572.2	633.6	1907
-	3	1⁄512	143	286.1	429.1	572.2	715.2	858.3	950.4	2861
-	4	1⁄1024	190.7	381.4	572.2	762.9	953.6	1144	1267	3814
8	1	1⁄256	53.64	107.2	160.9	214.5	268.2	321.8	356.4	1072
-	2	1⁄512	107.2	214.5	321.8	429.1	536.4	643.7	712.8	2145
-	3	1⁄1024	160.9	321.8	482.7	643.7	804.6	965.5	1069	3218
-	4	1⁄2048	214.5	429.1	643.7	858.3	1072.8	1287	1425	4291
9	1	1⁄512	59.6†	119.2†	178.8†	238.4†	298†	357.6†	396†	1192†
-	2	1⁄1024	119.2	238.4	357.6	476.8	596	715.2	792	2384
-	3	1⁄2048	178.8	357.6	536.4	715.2	894	1072	1188	3576
-	4	1⁄4096	238.4	476.8	715.2	953.6	1192	1430	1584	4768
10	1	1⁄1024	65.56	131.1	196.6	262.2	327.8	393.3	435.6	1311
-	2	1⁄2048	131.1	262.2	393.3	524.5	655.6	786.7	871.2	2622
-	3	1⁄4096	196.6	393.3	590	786.7	983.4	1180	1306	3933
11	1	1⁄2048	71.52	143	214.5	286.1	357.6	429.1	475.2	1430
-	2	1⁄4096	143	286.1	429.1	572.2	715.2	858.3	950.4	2861
12	1	1⁄4096	77.48	154.9	232.4	309.9	387.4	464.9	514.8	1549

Italic - Prime95/MPrime default proof power and multiplier, uses a maximum of 6 GiB per exponent
Bold - Optimal proof power, 9 for exponents above 26.6M, 10 above 106.5M and 11 above 414.2M
† GpuOwl default proof power, uses 8 or 9 for all exponents depending on version

Please note, though the resource limits are at times variable, generally the free version of Colab imposes a 12-hour usage limit per notebook. Additionally, a user may only assign a GPU runtime to up to two notebooks at a time whereas one may run an unknown upper-bound of notebooks with the CPU runtime enabled. (This usage limit, the GPU runtime limit, and other usage limits are increased if one purchases a Colab Pro or Colab Pro+ plan.)

GPUs Offered

Google Colab provides Nvidia GPUs where the specific model assigned to you depends on availability. The most powerful GPU currently offered is the NVIDIA A100-SXM4-40GB.

The possible GPUs that may be assigned are listed below:

GPU	Speed (MHz)	CUDA cores	GPU Memory (GiB)	Single precision/F32 (TFLOPS)	Double precision/F64 (TFLOPS)
Tesla P4	810 - 1063	2560	8	4.15 - 5.44	0.129 - 0.17
Tesla T4	585 - 1590	2560	16	8.1	0.254
Tesla K80	560 - 875	2496	12	2.8 - 4.37	0.932 - 1.46
Tesla P100-PCIE-16GB	1126 - 1303	3584	16	8.07 - 9.34	4.04 - 4.67
Tesla V100-SXM2-16GB	1455	5120	16	14.8	7.45
NVIDIA A100-SXM4-40GB	765 - 1410	6912	40	19.5	9.7

See the gpu_optimizations directory for more information about each GPU, including the ms/iter speeds for CUDALucas at different FFT lengths.

Though each GPU works well and will complete most assignments in a matter of days, one may use the following method to attain a new GPU: “Runtime” → “Factory reset runtime” → “YES”. After repeating 1-3 times, Google will usually assign a new GPU.

Acknowledgements

We acknowledge the following projects, which enabled and encouraged us to create these notebooks:

• Our Bash install scripts, which automatically download, build and setup the respective GIMPS programs on Colab.
• AutoPrimeNet, which automatically gets assignments, reports assignment results and progress for CUDALucas and GpuOwl using the PrimeNet API. Adapted from the PrimeNet Python script from Mlucas by Loïc Le Loarer and Ernst W. Mayer.
• The GPU72 notebook, whose work encouraged us to also use the form format.
• The Linux System Information script, which outputs the system information for the Colab VMs.

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