Further Optimization of Wilson-Type Congruences via Parameterized Factorial Decomposition

Further Optimization of Wilson-Type Congruences via Parameterized Factorial Decomposition | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 16 March 2026 V1 Latest version Share on Further Optimization of Wilson-Type Congruences via Parameterized Factorial Decomposition Authors : Chenglian Liu 0000-0002-9086-9740 [email protected] , Ruopengyu Xu , and Sonia Chien-I Chen Authors Info & Affiliations https://doi.org/10.22541/au.177369005.59912243/v1 90 views 40 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Wilson-type congruences provide classical characterizations of prime numbers but are often computationally impractical due to the rapid growth of factorial terms. A recent approach introduced a parameterized decomposition of the half-factorial, replacing part of the product with double factorials and powers of two. In this paper we extend this approach by systematically analyzing admissible parameter ranges. We establish simple divisibility conditions ensuring that the parameterized expressions are well-defined at the integer level and valid modulo an odd prime. We further derive bounds on the parameter, discuss computational implications, and present numerical evidence illustrating the trade-off between algebraic validity and computational efficiency. Supplementary Material File (optimization_wilson_type_springer.pdf) Download 171.21 KB Information & Authors Information Version history V1 Version 1 16 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keyword optimization of wilson-type Authors Affiliations Chenglian Liu 0000-0002-9086-9740 [email protected] Feng Chia university, Nanfang College Guangzhou View all articles by this author Ruopengyu Xu Feng Chia university, Nanfang College Guangzhou View all articles by this author Sonia Chien-I Chen Feng Chia university, Nanfang College Guangzhou View all articles by this author Metrics & Citations Metrics Article Usage 90 views 40 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Chenglian Liu, Ruopengyu Xu, Sonia Chien-I Chen. Further Optimization of Wilson-Type Congruences via Parameterized Factorial Decomposition. Authorea . 16 March 2026. DOI: https://doi.org/10.22541/au.177369005.59912243/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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