{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T09:53:15Z","timestamp":1776765195349,"version":"3.51.2"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"213","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    If\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P\">\n                        <mml:semantics>\n                          <mml:mi>P<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">P<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is a prime and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2 upper P plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mi>P<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">2P+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is also prime, then\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P\">\n                        <mml:semantics>\n                          <mml:mi>P<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">P<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is a Sophie Germain prime. In this article several new Sophie Germain primes are reported, which are the largest known at this time. The search method and the expected search times are discussed.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00670-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"393-396","source":"Crossref","is-referenced-by-count":11,"title":["Large Sophie Germain primes"],"prefix":"10.1090","volume":"65","author":[{"given":"Harvey","family":"Dubner","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"620","DOI":"10.2307\/2005583","article-title":"New primality criteria and factorizations of 2^{\ud835\udc5a}\u00b11","volume":"29","author":"Brillhart, John","year":"1975","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","unstructured":"[2] C. Caldwell, Review of the Cruncher PC plug-in board, J. Recreational Math. 25 (1993), 56\u201357."},{"key":"3","unstructured":"[3] \\bysame, The largest known primes, updated regularly and is available on request. Tel. (901) 587\u20137360, E-mail: caldwell@UTmartn.bitnet"},{"key":"4","isbn-type":"print","volume-title":"An introduction to the theory of numbers","author":"Hardy, G. H.","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0198531702","edition":"5"},{"key":"5","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0507-1","volume-title":"The book of prime number records","author":"Ribenboim, Paulo","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0387970428","edition":"2"},{"key":"6","unstructured":"[6] H. Riesel, Prime numbers and computer methods for factorization, Birkh\u00e4user, Boston, 1958."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00670-9\/S0025-5718-96-00670-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00670-9\/S0025-5718-96-00670-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:02:41Z","timestamp":1776718961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00670-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":6,"journal-issue":{"issue":"213","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["S0025-5718-96-00670-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00670-9","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":[[1996]]}}}