{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1878"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1878","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"On Prime Generation Through Primitive Divisors Of Recurrence Sequences","abstract":"We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. 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We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.","abstract_has_math":false,"creators":["Russell, Richard"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Mohapatra, Ram N."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-01-01T08:00:00Z","date_published":"2006-01-01T08:00:00Z","updated_at":"2026-07-24T05:09:25Z","subjects":["prime divisor","primitive divisor","recurrence sequence","marsenne prime","polynomial sequence","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0001013"],"render_values":[{"text":"CFE0001013","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/879","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mohapatra, Ram N."]},{"key":"dc:creator","label":"Author","values":["Russell, Richard"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Masters Thesis (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["prime divisor","primitive divisor","recurrence sequence","marsenne prime","polynomial sequence","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0001013"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/879"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On Prime Generation Through Primitive Divisors Of Recurrence Sequences"]}]}],"canonical_facts":{"dc:contributor":["Mohapatra, Ram N."],"dc:creator":["Russell, Richard"],"dc:description":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Master of Science (M.S.)","College of Arts and Sciences","Mathematics"],"dc:description.abstract":["We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. 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