{"created":"2023-06-20T14:34:48.987139+00:00","id":199,"links":{},"metadata":{"_buckets":{"deposit":"786ce8f9-9807-4ff0-a4b9-5e5dbf4599ea"},"_deposit":{"created_by":15,"id":"199","owners":[15],"pid":{"revision_id":0,"type":"depid","value":"199"},"status":"published"},"_oai":{"id":"oai:kjunshin.repo.nii.ac.jp:00000199","sets":["9:41"]},"author_link":["665","666","664"],"item_1_biblio_info_14":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-03-31","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"99","bibliographicPageStart":"81","bibliographicVolumeNumber":"13","bibliographic_titles":[{"bibliographic_title":"国際人間学部紀要"},{"bibliographic_title":"International human studies","bibliographic_titleLang":"en"}]}]},"item_1_creator_6":{"attribute_name":"著者名(日)","attribute_type":"creator","attribute_value_mlt":[{"creatorAffiliations":[{"affiliationNameIdentifiers":[{"affiliationNameIdentifier":"","affiliationNameIdentifierScheme":"ISNI","affiliationNameIdentifierURI":"http://www.isni.org/isni/"}],"affiliationNames":[{"affiliationName":"","affiliationNameLang":"ja"}]}],"creatorNames":[{"creatorName":"洞田, 勝博","creatorNameLang":"ja"},{"creatorName":"ホラタ, カツヒロ","creatorNameLang":"ja-Kana"}],"familyNames":[{"familyName":"洞田","familyNameLang":"ja"},{"familyName":"ホラタ","familyNameLang":"ja-Kana"}],"givenNames":[{"givenName":"勝博","givenNameLang":"ja"},{"givenName":"カツヒロ","givenNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"664","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"9000006512671","nameIdentifierScheme":"CiNii ID","nameIdentifierURI":"http://ci.nii.ac.jp/nrid/9000006512671"}]},{"creatorNames":[{"creatorName":"篠原, 雅史"},{"creatorName":"シノハラ, マサシ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"665","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"酒井, 幸吉"},{"creatorName":"サカイ, コウキチ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{"nameIdentifier":"666","nameIdentifierScheme":"WEKO"}]}]},"item_1_description_1":{"attribute_name":"ページ属性","attribute_value_mlt":[{"subitem_description":"P(論文)","subitem_description_type":"Other"}]},"item_1_description_12":{"attribute_name":"抄録(英)","attribute_value_mlt":[{"subitem_description":"A finite ncreasing sequence {pn}, (n=1, 2, 3, ・・・, t) of prime numbers, (t〓3), is called an arithmetic progression of primes with a common differnce d, denoted by Ap(p_1) or Ap(p_1, d), if p_<k+1>-p_k=d∀k, 1〓k〓t-1 and p_t+d is a composite number. Then t is called the size of Ap(p_1). Ap(2) does not exist. For any Ap(p_1, d), prime p>2, its size is at most p, and d is an even number different from multiples of p. In this note we report various data on arithmetic progressions of primes gathered from long computation using personal computers. For example the following Ap(p, d) given the pairs (p, d) are of size 14, which are the largest size among primes p<10^7 and common differnces d<10^8. [table] We propose the following Conjecture For any prime p>2 we have 1) There exist infinitely many Ap(P). 2) There exist an Ap(P) of size p. The above 2) is true for p=3, 5, 7, 11.","subitem_description_type":"Other"}]},"item_1_source_id_13":{"attribute_name":"雑誌書誌ID","attribute_value_mlt":[{"subitem_source_identifier":"AA12012192","subitem_source_identifier_type":"NCID"}]},"item_1_text_10":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"Faculty of International Human Studies Kagoshima Immaculate Heart University"},{"subitem_text_language":"en","subitem_text_value":"Kyushu University"},{"subitem_text_language":"en","subitem_text_value":"Kagoshima University"}]},"item_1_text_2":{"attribute_name":"記事種別(日)","attribute_value_mlt":[{"subitem_text_value":"研究ノート"}]},"item_1_text_3":{"attribute_name":"記事種別(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"Research Note"}]},"item_1_text_9":{"attribute_name":"著者所属(日)","attribute_value_mlt":[{"subitem_text_value":"鹿児島純心女子大学"},{"subitem_text_value":"九州大学COE研究員"},{"subitem_text_value":"鹿児島大学"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2007-03-31"}],"displaytype":"detail","filename":"HORATA-KO13.pdf","filesize":[{"value":"818.8 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"HORATA-KO13","url":"https://kjunshin.repo.nii.ac.jp/record/199/files/HORATA-KO13.pdf"},"version_id":"efbb9300-746d-4c0a-83e6-58d17c979a37"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"等差素数列について","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"等差素数列について"},{"subitem_title":"Notes on Arithmetic Progressions of Prime Numbers","subitem_title_language":"en"}]},"item_type_id":"1","owner":"15","path":["41"],"pubdate":{"attribute_name":"公開日","attribute_value":"2007-03-31"},"publish_date":"2007-03-31","publish_status":"0","recid":"199","relation_version_is_last":true,"title":["等差素数列について"],"weko_creator_id":"15","weko_shared_id":-1},"updated":"2025-03-22T03:40:19.511917+00:00"}