{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:37:20Z","timestamp":1776724640008,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"222","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Vinogradov\u2019s theorem states that any sufficiently large odd integer is the sum of three prime numbers. This theorem allows us to suppose the conjecture that this is true for all odd integers. In this paper, we describe the implementation of an algorithm which allowed us to check this conjecture up to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"10 Superscript 20\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mn>10<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>20<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">10^{20}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00928-4","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"863-866","source":"Crossref","is-referenced-by-count":16,"title":["Checking the odd Goldbach conjecture up to 10\u00b2\u2070"],"prefix":"10.1090","volume":"67","author":[{"given":"Yannick","family":"Saouter","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"203","key":"1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.2307\/2152935","article-title":"Elliptic curves and primality proving","volume":"61","author":"Atkin, A. O. L.","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","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":"3","unstructured":"J.R. Chen, On the representation of a large even integer as the sum of a prime and the product of at most two primes, Kexue Tongbao (1966), no. 17, 385\u2013386."},{"key":"4","doi-asserted-by":"crossref","unstructured":"J.M. Deshouillers, G.Effinger, H. te Riele, and D.Zinoviev, A complete Vinogradov 3-primes theorem under the Riemann Hypothesis, Preprint, 1997.","DOI":"10.1090\/S1079-6762-97-00031-0"},{"key":"5","unstructured":"T. Grandlung, The GNU multiple precision arithmetic library, Technical documentation, 1993."},{"key":"6","doi-asserted-by":"crossref","unstructured":"L. Schnirelmann, \u00dcber additive Eigenschaften von Zahlen, Math. Ann. (1933), no. 107, 649\u2013660.","DOI":"10.1007\/BF01448914"},{"issue":"204","key":"7","doi-asserted-by":"publisher","first-page":"931","DOI":"10.2307\/2153264","article-title":"Checking the Goldbach conjecture up to 4\u22c510\u00b9\u00b9","volume":"61","author":"Sinisalo, Matti K.","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","unstructured":"I.M. Vinogradov, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR (1937), no. 15, 169\u2013172."},{"issue":"6","key":"9","first-page":"682","article-title":"On odd Goldbach problem under general Riemann hypothesis","volume":"36","author":"Wang, Tian Ze","year":"1993","journal-title":"Sci. China Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/1001-6511","issn-type":"print"},{"key":"10","doi-asserted-by":"crossref","unstructured":"D.Zinoviev, On Vinogradov\u2019s constant in Goldbach\u2019s ternary problem, J. Number Theory 65 (1997), 334\u2013358.","DOI":"10.1006\/jnth.1997.2141"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00928-4\/S0025-5718-98-00928-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00928-4\/S0025-5718-98-00928-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:45:28Z","timestamp":1776721528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-222\/S0025-5718-98-00928-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":10,"journal-issue":{"issue":"222","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["S0025-5718-98-00928-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-00928-4","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":[[1998]]}}}