{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T18:39:19Z","timestamp":1771007959313,"version":"3.50.1"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2020R1I1A1A01065877"],"award-info":[{"award-number":["2020R1I1A1A01065877"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2019R1A6A1A11051177"],"award-info":[{"award-number":["2019R1A6A1A11051177"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p> Goldbach\u2019s conjecture is one of the oldest and famous unproved problems in number theory. Using a deep learning model, we obtain an approximation of the Goldbach partition function, which counts the number of ways of representing an even number greater than 4 as a sum of two primes. We use residues of number modulo first 25 primes as features and archive a more accurate approximation, which reduces error rate from [Formula: see text] to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830921501524","type":"journal-article","created":{"date-parts":[[2021,7,11]],"date-time":"2021-07-11T12:50:58Z","timestamp":1626007858000},"source":"Crossref","is-referenced-by-count":1,"title":["Deep learning-based approximation of Goldbach partition function"],"prefix":"10.1142","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-0190","authenticated-orcid":false,"given":"Eunmi","family":"Kim","sequence":"first","affiliation":[{"name":"Institute of Mathematical Sciences, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Republic of Korea"}]}],"member":"219","published-online":{"date-parts":[[2021,7,10]]},"reference":[{"key":"S1793830921501524BIB001","first-page":"544","volume":"168","author":"Brun V.","year":"1919","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S1793830921501524BIB002","first-page":"157","volume":"16","author":"Chen J. R.","year":"1973","journal-title":"Sci. Sinica"},{"key":"S1793830921501524BIB003","first-page":"421","volume":"21","author":"Chen J. R.","year":"1978","journal-title":"Sci. Sinica"},{"key":"S1793830921501524BIB004","first-page":"209","volume":"61","author":"Deshouillers J.-M.","year":"1993","journal-title":"Math. Comp."},{"issue":"1","key":"S1793830921501524BIB005","first-page":"1","volume":"21","author":"Fliegel H. F.","year":"1989","journal-title":"J. Recreat. Math."},{"key":"S1793830921501524BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02403921"},{"key":"S1793830921501524BIB007","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-22.1.46"},{"key":"S1793830921501524BIB012","doi-asserted-by":"publisher","DOI":"10.4064\/aa-27-1-353-370"},{"key":"S1793830921501524BIB013","first-page":"717","volume":"14","author":"Shanker O.","year":"2012","journal-title":"Adv. Model. Optim."},{"key":"S1793830921501524BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2013-02787-1"},{"key":"S1793830921501524BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/WI.2018.00-46"},{"issue":"1","key":"S1793830921501524BIB016","first-page":"4","volume":"4","author":"Sylvester J. J.","year":"1871","journal-title":"Proc. London Math. Soc."},{"key":"S1793830921501524BIB017","first-page":"179","volume":"16","author":"Vinogradov I. M.","year":"1937","journal-title":"Dokl. Akad. Nauk SSSR"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921501524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T04:51:21Z","timestamp":1659415881000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830921501524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,10]]},"references-count":13,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["10.1142\/S1793830921501524"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921501524","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,10]]},"article-number":"2150152"}}