{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:08Z","timestamp":1776728288826,"version":"3.51.2"},"reference-count":5,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,3,30]],"date-time":"2002-03-30T00:00:00Z","timestamp":1017446400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The Repunit R\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"49081 equals left-parenthesis 10 Superscript 49081 Baseline minus 1 right-parenthesis slash 9\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>49081<\/mml:mn>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>49081<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>9<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">49081=(10^{49081}-1)\/9<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is a probable prime. In order to prove primality R49080 must be approximately 33.3% factored. The status of this factorization is included.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01319-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"833-835","source":"Crossref","is-referenced-by-count":3,"title":["Repunit R49081 is a probable prime"],"prefix":"10.1090","volume":"71","author":[{"given":"Harvey","family":"Dubner","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,3,30]]},"reference":[{"key":"1","first-page":"3","article-title":"Sur un th\u00e9or\u00e8m de M. Fej\u00e9r","volume":"2","author":"Zygmund, Antoni","year":"1939","journal-title":"Bull. S\\'{e}m. Math. Univ. Wilno"},{"key":"2","series-title":"Contemporary Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/022","volume-title":"Factorizations of $b^n \\pm1$","volume":"22","author":"Brillhart, John","year":"1988","ISBN":"https:\/\/id.crossref.org\/isbn\/0821850784","edition":"2"},{"issue":"204","key":"3","doi-asserted-by":"publisher","first-page":"927","DOI":"10.2307\/2153263","article-title":"Generalized repunit primes","volume":"61","author":"Dubner, Harvey","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"176","key":"4","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2307\/2008184","article-title":"The primality of \ud835\udc451031","volume":"47","author":"Williams, H. C.","year":"1986","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"148","key":"5","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.2307\/2006470","article-title":"Some primes of the form (\ud835\udc4e\u207f-1)\/(\ud835\udc4e-1)","volume":"33","author":"Williams, H. C.","year":"1979","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01319-9\/S0025-5718-01-01319-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01319-9\/S0025-5718-01-01319-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:56:54Z","timestamp":1776725814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01319-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3,30]]},"references-count":5,"journal-issue":{"issue":"238","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0025-5718-01-01319-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01319-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2001,3,30]]}}}