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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.
Retrieved from "https://boincsynergy.ca/wiki/Amicable_Numbers"