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We show calculations, together with a heuristic argument, to suggest that these sequences contain only finitely many primes.<\/jats:p>","DOI":"10.1112\/s1461157000000772","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T07:42:44Z","timestamp":1375774964000},"page":"1-13","source":"Crossref","is-referenced-by-count":20,"title":["Primes in Elliptic Divisibility Sequences"],"prefix":"10.1112","volume":"4","author":[{"given":"Manfred","family":"Einsiedler","sequence":"first","affiliation":[]},{"given":"Graham","family":"Everest","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Ward","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000000772_ref004","first-page":"1","article-title":"\u2018Computer assisted number theory with applications\u2019","author":"Chudnovsky","year":"1984","journal-title":"Number theory"},{"key":"S1461157000000772_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2374733"},{"key":"S1461157000000772_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(86)90023-0"},{"key":"S1461157000000772_ref007","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.2001.2682"},{"key":"S1461157000000772_ref006","article-title":"\u2018Morphic heights and periodic points\u2019","author":"Einsiedler","year":"2001","journal-title":"New York Number Th. 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Conference A: Mathematics and Theoretical Physics"},{"key":"S1461157000000772_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"S1461157000000772_ref018","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1983-0679454-X"},{"key":"S1461157000000772_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-00981-3"},{"key":"S1461157000000772_ref019","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-48-01582-8"},{"key":"S1461157000000772_ref015","unstructured":"15. Shipsey R. 'Elliptic divisibility sequences', PhD Thesis, Goldsmith's College (University of London), 2000."},{"key":"S1461157000000772_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/2007169"},{"key":"S1461157000000772_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0439-3"},{"key":"S1461157000000772_ref017","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0851-8"},{"key":"S1461157000000772_ref009","article-title":"\u2018The canonical height of an algebraic point on an elliptic curve\u2019","volume":"6","author":"Everest","year":"2000","journal-title":"New York J. Math."}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157000000772","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T14:29:11Z","timestamp":1559831351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157000000772\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"references-count":20,"alternative-id":["S1461157000000772"],"URL":"https:\/\/doi.org\/10.1112\/s1461157000000772","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001]]}}}