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 < 264.
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.

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News

GPU version 1.12 bug
This version had a bug, so I had to cancel all work which was in progress for this version and then reissue all work units which were processed with this version only, i.e. all work units that have two results with GPU version 1.12 in "completed and validated" state. 16433 work units have been reissued, it's approximately 1 day of calculations.

The project is back to using version 1.11 for now. I'll release a proper fixed version later today.
22 Mar 2017, 10:53:19 UTC · Discuss


Update on project progress and badges
227,482 amicable pairs have been found so far, ~340,000 are yet to be found according to my estimations. Due to the way this search is organized and how amicable numbers are distributed, I expect almost all of those ~340k pairs to be found before the search reaches 50% in a couple of weeks, and only a few thousand of new pairs will be found after 50%. So if your target is to get some of the discoverer badges, now is the time to crunch with everything you've got.

Since there will be only a few new pairs after 50%, this is when I'll introduce credit badges.
17 Mar 2017, 9:44:22 UTC · Discuss


Gridcoin
The project is now included in the list of projects that give rewards on the Gridcoin Network: https://gridcoinstats.eu/projects.php

Happy crunching all Gridcoin users!
12 Mar 2017, 20:14:20 UTC · Discuss


Project status update
After the recent fix for the very short work units issue I had to regenerate remaining work units using the new code. Of course there are fewer work units left now because they are not "very short" anymore, and the server status page says that ETA for current goal is June 18th, 2017. This is correct and it means that the next goal will be to find all amicable numbers < 10^20 and it will start in the summer. 10^20 is ~5.42 times larger than 2^64 and the new application will be slower because it will have to deal with numbers that don't fit in 64 bits. So the next goal will take 8-10 times more time.
8 Mar 2017, 12:22:50 UTC · Discuss


TEAM CHALLENGE starts soon!
The first team challenge starts on March 1st, so I've temporarily increased task-in-progress limits: it's 4 tasks per CPU core + 100 tasks per GPU now. You can use the time left before the challenge to bunker more tasks.
28 Feb 2017, 7:02:40 UTC · Discuss


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