What is Amicable Numbers?

Amicable Numbers is an independent research project that uses Internet-connected computers to find new amicable pairs. You can contribute to our research by running a free program on your computer.

Current goal of the project is to find all amicable pairs with smallest member < 1020.
All new findings are published regularly on the Amicable pairs list page.

What is the end goal of Amicable Numbers?
Why participate in it?

Though mathematics is not an experimental science, mathematicians often look for examples to test conjectures (which they then hope to prove). As the number of examples increases, so does (in a sense) their understanding of the distribution.

The goal is to collect all amicable numbers up to a very large limit. This data will facilitate theoretical research in the field: 1, 2, 3 to name a few examples. It will also help to improve understanding of the properties of Divisor function.

Join Amicable Numbers

User of the Day

User profile Profile Joern Gerken   
If you pay peanuts, you get monkeys. Lee Kuan Yew


The search up to 10^21
The search up to 1021 has started! Over 50,000 new amicable pairs have been found in the first few days.

Due to the huge size of search space, first stage of the search will only look for all amicable pairs where smaller number is of the form 3N*...*p where N > 0 and p < 1011. I expect that this will find 2-3 million new amicable pairs in a year or so.

Note that system memory requirements are higher now because all prime numbers < 1011 need to be stored in memory for the search.
25 Oct 2019, 13:11:37 UTC · Discuss

GPU version bugfix release
GPU versions for all platforms were updated to fix "Error -58" computation error when resuming stopped task.
8 Apr 2019, 11:00:47 UTC · Discuss

Power outage
The server was down today between 11:04 and 14:20 (CEST) because of a major power outage in Hetzner datacenter. Everything should be up and running again now.
24 May 2018, 12:41:34 UTC · Discuss

GPU version fix
There was a serious bug in GPU version: https://github.com/SChernykh/Amicable/commit/3470ed855d244100f37b0b7ab4c912d2b9365a93
Unfortunately, it skipped some numbers in an unpredictable way for "large primes" work units for the last 20 days 9 days. I'll have to reissue all such work units to cover everything missed. The GPU versions for all platforms are already updated.

Sorry for the mess, but it's good that the bug is fixed relatively early, because it was hard to notice.
27 Mar 2018, 17:45:25 UTC · Discuss

MacOS GPU version released
GPU requirements are the same as for Windows and Linux versions: AMD (HD 5xxx or newer) or NVIDIA (GTX 4xx or newer) GPU with OpenCL support and at least 2 GB of video memory.

The MacOS GPU version has been confirmed to work on OS X El Capitan and MacOS Sierra. Older MacOS versions have poor OpenCL support and may fail to run the GPU version.
16 Sep 2017, 8:24:36 UTC · Discuss

The search up to 2^64 is complete!
Congratulations to everyone who took part in this search!

- There are 2,390,655 amicable pairs with smaller member below 2^64 in total
- BOINC volunteers found 552,874 new amicable pairs below 2^64

A more detailed analysis of amicable pairs distribution will follow later this month. And don't forget to edit your preferences and check that you're all set up to run the current search up to 10^20.
16 Aug 2017, 7:26:12 UTC · Discuss

Credits for the old application (search up to 2^64) doubled
It's sad to see everyone leave the old (and unfinished) application "Amicable Numbers up to 2^64" so I decided to double credit points for it.

Everyone can switch their CPUs back to gain some more credits.

Note that you can run "Amicable Numbers up to 2^64" on CPU and "Amicable Numbers up to 10^20" on GPU on the same PC at the same time!

Here's what you need to set in project preferences:
Run application 2^64 = yes
Run application 10^20 = no
Accept work from other applications = yes

With these settings your CPU will get tasks (and more credits in general) from "2^64" only, and your GPU will get tasks from "10^20" thanks to "Accept work from other applications = yes" selected.
3 Jul 2017, 16:09:14 UTC · Discuss

The search up to 10^20
It will be started tomorrow (July 1st)!

I've decided to speed up the launch of the next search due to performance issues with GPU version that everyone experiences now.

What will happen on July 1st:

1) "Amicable Numbers up to 10^20" application will start receiving tasks.
2) All GPU versions for the old application "Amicable Numbers up to 2^64" will be deprecated.
3) Credit points for both applications will be re-balanced to make sure that RAC doesn't change.

So all GPUs should automatically switch to the new application, and the old application will remain as CPU-only until it finishes.
30 Jun 2017, 16:11:33 UTC · Discuss

New application for double checking current search
I've launched a new application called Amicable Numbers up to 2^64 (double check). It will re-run some of past work units.

If you don't want to run WUs which were already done before, you can deselect this application on the preferences page: https://sech.me/boinc/Amicable/prefs.php?subset=project

NOTE: If you are unable to achieve 100% GPU load (to maximize RAC) with work units from the main application, I recommend to switch to this new application: it will have GPU-friendly work units.
16 Jun 2017, 14:27:55 UTC · Discuss

Finish line of the current search and next steps
Hello all crunchers!

The search for amicable numbers up to 2^64 is almost done: all previously known numbers are already covered by the search, zero numbers were missed which is very good and gives me confidence. It's extremely unlikely to find anything in the remaining WUs, but they need to be processed to complete the search.

The next steps will be:

1) Double check a small portion of the search space to increase confidence that nothing is missed. It will be a separate application so everyone will have choice whether to move to the next search range or help verify the current range.
2) Start the search for amicable numbers up to 10^20. It will be a separate application as well and it will become the default application as soon as the current search runs out of WUs. CPU version is ready, GPU version is work in progress and hopefully will be finished before the start of the search.
8 Jun 2017, 10:19:57 UTC · Discuss

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