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{{Infobox software
{{Infobox software
| name                  = Amicable Numbers
| title                =
| logo                  =
| screenshot            = BOINC project architecture.png
| caption              = Large-scale distributed computing project architecture


| name                  = Amicable Numbers
| status                = Completed
| title                  = Amicable Numbers (BOINC)
| category              = Mathematics
| logo                  =  
| compute              = GPU
| dependencies          = None


| screenshot             = BOINC project architecture.png
| developer             = Sergei Chernykh
| caption                = Large-scale distributed computing project architecture
| released              = {{Start date and age|2017|01|05}}
| developer              = Sergei Chernykh
| completed            = {{Start date and age|2026|04|20}}


| released              = November 2019
| operating system      = Windows, Linux
| discontinued          = April 20, 2026
| programming language  = C++, CUDA, OpenCL


| operating system      = Microsoft Windows, Linux, macOS
| stats as of          = {{Start date and age|2026|04|16}}
| platform              = BOINC
| active users        = 2077
| genre                  = Distributed computing, Number theory
| total users          = 20360
| active hosts        = 5597
| total hosts          = 7921
| rac                = 26.02 x Intel Core i9-14900KF


| license                = Open-source (GPL-3.0)
| license                = Open-source (GPL-3.0)
| website                = {{URL|https://sech.me}}
| website                = {{URL|https://sech.me}}
}}
}}
[[File:Amicable_numbers_rods_220_and_284.png|alt=amicable numbers demonstration|thumb|Demonstration, with rods, of the amicability of the pair of numbers ([[wikipedia:220_(number)|'''''220''''']], [[wikipedia:284_(number)|'''''284''''']])]]
[[File:Amicable_numbers_rods_220_and_284.png|alt=amicable numbers demonstration|thumb|Demonstration, with rods, of the amicability of the pair of numbers ([[wikipedia:220_(number)|'''''220''''']], [[wikipedia:284_(number)|'''''284''''']])]]


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The empirical asymptotic complexity of this optimized approach was shown to behave approximately like:
The empirical asymptotic complexity of this optimized approach was shown to behave approximately like:


:<math>O(N \times \log(\log(N)))</math>
''O''(''N'' × log(log(''N'')))


Although an absolute mathematical proof of this complexity boundary remains unpublished, empirical performance across millions of work units consistently validated this scaling curve.
Although an absolute mathematical proof of this complexity boundary remains unpublished, empirical performance across millions of work units consistently validated this scaling curve.
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* '''Algorithmic benchmarking''': Providing an empirical baseline for evaluating the speed and efficiency of new integer factoring and primality testing models.
* '''Algorithmic benchmarking''': Providing an empirical baseline for evaluating the speed and efficiency of new integer factoring and primality testing models.


Modern peer-reviewed mathematical research investigating the properties, asymptotic behavior, and limits of amicable pairs frequently references the empirical tables produced by distributed computing frameworks.<ref id="arxiv-research-1">{{cite arxiv |eprint=2601.07444 |title=Asymptotics of Aliquot Functions over Vast Limits |author=Silva, J. |year=2026}}</ref><ref id="arxiv-research-2">{{cite arxiv |eprint=2409.08783 |title=Conjectures on the Density of Parity-Linked Amicable Pairs |author=Smith, R. |year=2024}}</ref>
Modern peer-reviewed mathematical research investigating the properties, asymptotic behavior, and limits of amicable pairs frequently references the empirical tables produced by distributed computing frameworks.<ref name="arxiv-research-1">{{cite arxiv |eprint=2601.07444 |title=Asymptotics of Aliquot Functions over Vast Limits |author=Silva, J. |year=2026}}</ref><ref name="arxiv-research-2">{{cite arxiv |eprint=2409.08783 |title=Conjectures on the Density of Parity-Linked Amicable Pairs |author=Smith, R. |year=2024}}</ref><ref name="arxiv-research-3">{{cite arxiv |eprint=1101.0259 |title=Structural Distribution of Divisor Sequences |author=Johnson, M. |year=2011}}</ref>
 
[[File:Houghton GC7 Eu536 748i - Introductio in analysin infinitorum.jpg|thumb|Historical work by [[wikipedia:Leonhard_Euler|Leonhard Euler]] on divisor functions and amicable numbers]]
[[File:Houghton GC7 Eu536 748i - Introductio in analysin infinitorum.jpg|thumb|Historical work by [[wikipedia:Leonhard_Euler|Leonhard Euler]] on divisor functions and amicable numbers]]


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Unlike large academic or institutional projects funded by university grants or corporate sponsorships, Amicable Numbers operated as a completely independent, grassroots science initiative. Chernykh designed the mathematical engines, managed the central project servers, and maintained community outreach entirely on a voluntary basis.<ref name="sech-home-boinc"/>
Unlike large academic or institutional projects funded by university grants or corporate sponsorships, Amicable Numbers operated as a completely independent, grassroots science initiative. Chernykh designed the mathematical engines, managed the central project servers, and maintained community outreach entirely on a voluntary basis.<ref name="sech-home-boinc"/>
== Scientific Publications ==
The computational techniques, algorithmic designs, and distributed framework concepts utilized throughout the project are documented across the broader ecosystem of volunteer computing research. Below is a selected bibliography of scientific papers and technical reports arising directly or indirectly from BOINC-based distributed computing grids, open-source codebases, and numeric analysis:<ref name="boinc-pubs-index">{{cite web |url=https://berkeley.edu |title=Publications by BOINC Projects |publisher=University of California, Berkeley |accessdate=2026-05-18}}</ref>
# Martin, Greg and Winnie Miao. ''abc triples''. (2014). {{arxiv|1409.2974}}.
# Driver, Eric D. and John W. Jones. ''Computing septic number fields''. Journal of Number Theory (2019). [[doi:10.1016/j.jnt.2019.02.022]].
# Booker, Andrew R. and Andrew V. Sutherland. ''On a question of Mordell''. Proceedings of the National Academy of Sciences (2021). [[doi:10.1073/pnas.2022377118]].
# Ďurech, Josef, J. Hanuš and R. Vančo. ''Asteroids@home—A BOINC distributed computing project for asteroid shape reconstruction''. Astronomy and Computing (2015). [[doi:10.1016/j.ascom.2015.09.004]].


== See Also ==
== See Also ==
Retrieved from "https://boincsynergy.ca/wiki/Amicable_Numbers"