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Amicable Numbers: Difference between revisions

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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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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"