{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:40:03Z","timestamp":1750192803028,"version":"3.41.0"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2020,12,1]],"date-time":"2020-12-01T00:00:00Z","timestamp":1606780800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p>In 1879, Laisant-Beaujeux gave the following result without proof: If n is a prime, then<\/jats:p>\n          <jats:p>[EQUATION]<\/jats:p>\n          <jats:p>This paper provides proofs of the result of Laisant-Beaujeux in two cases explicitly: (1) If an integer of the form n = 4k + 1, k &gt; 0 is prime, then ([EQUATION]) and (2) If an integer of the form n = 4k + 3, k \u2265 0 is prime, then [EQUATION]. In addition, the author proposes important conjectures based on the converse of the above theorems which aim to establish primality of n. These conjectures are scrutinized by the given combinatorial primality test algorithm which can also distinguish patterns of prime n whether it is of the form 4k + 1 or 4k + 3.<\/jats:p>","DOI":"10.1145\/3465002.3465004","type":"journal-article","created":{"date-parts":[[2021,5,10]],"date-time":"2021-05-10T22:12:16Z","timestamp":1620684736000},"page":"129-133","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Combinatorial primality test"],"prefix":"10.1145","volume":"54","author":[{"given":"Maheswara Rao","family":"Valluri","sequence":"first","affiliation":[{"name":"Fiji National University, Suva, Fiji"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,5,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2004.160.781"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1910-01892-9"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9316-0"},{"volume-title":"Divisibility and primality\"","year":"1919","author":"Dickson L.E.","key":"e_1_2_1_4_1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/320211.320213"},{"key":"e_1_2_1_6_1","volume-title":"An Introduction to the Theory of Numbers","author":"Hardy G.H.","year":"1960","edition":"4"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(76)80043-8"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2312481"},{"key":"e_1_2_1_9_1","unstructured":"Online Encyclopedia Integer Sequence http:\/\/oeis.org\/  Online Encyclopedia Integer Sequence http:\/\/oeis.org\/"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(80)90084-0"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/359340.359342"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795293172"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3465002.3465004","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3465002.3465004","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:18:25Z","timestamp":1750191505000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3465002.3465004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1145\/3465002.3465004"],"URL":"https:\/\/doi.org\/10.1145\/3465002.3465004","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2020,12]]},"assertion":[{"value":"2021-05-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}