{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,30]],"date-time":"2026-10-30T08:45:44Z","timestamp":1793349944202,"version":"4.5.0"},"reference-count":40,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2021,1,22]],"date-time":"2021-01-22T00:00:00Z","timestamp":1611273600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/K034383\/1"],"award-info":[{"award-number":["EP\/K034383\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Bulletin of London Math Soc"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1112\/blms.12460","type":"journal-article","created":{"date-parts":[[2021,1,23]],"date-time":"2021-01-23T01:20:51Z","timestamp":1611364851000},"page":"792-797","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":70,"title":["The Riemann hypothesis is true up to 3\u00b71012"],"prefix":"10.1112","volume":"53","author":[{"given":"Dave","family":"Platt","sequence":"first","affiliation":[{"name":"School of Mathematics University of Bristol University Walk Bristol BS8 1TW United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tim","family":"Trudgian","sequence":"additional","affiliation":[{"name":"School of Science The University of New South Wales Canberra at ADFA Building 26 Canberra ACT 2610 Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,1,22]]},"reference":[{"key":"e_1_2_6_2_1","unstructured":"ACRC. \u2018BlueCrystal User Guide\u2019 2015 https:\/\/www.acrc.bris.ac.uk\/pdf\/bc\u2010user\u2010guide.pdf."},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1552442669"},{"key":"e_1_2_6_4_1","unstructured":"S.Broadbent H.Kadiri A.Lumley N.NgandK.Wilk \u2018Sharper bounds for the Chebyshev function\u03b8(x)\u2019 Preprint 2020 arXiv:2002.11068v1."},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3060"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3264"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2015-02930-5"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11139-016-9839-4"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3340"},{"key":"e_1_2_6_10_1","first-page":"25","volume-title":"Number Theory for the Millennium II","author":"Ford K.","year":"2002"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3038"},{"key":"e_1_2_6_12_1","unstructured":"X.Gourdon \u2018Computation of zeros of the Zeta function\u2019 http:\/\/numbers.computation.free.fr\/Constants\/Miscellaneous\/zetazeroscompute.html#Gourdon2004."},{"key":"e_1_2_6_13_1","unstructured":"M. J.Griffin K.Ono K.Rolen J.Thorner Z.TrippandI.Wagner \u2018Jensen polynomials for the Riemann xi function\u2019 Preprint 2019 arXiv:1910.01227v2."},{"key":"e_1_2_6_14_1","article-title":"The ternary Goldbach problem","author":"Helfgott H. A.","journal-title":"Ann. of Math. Stud."},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2017.2690633"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.4064\/aa160-2-6"},{"key":"e_1_2_6_17_1","first-page":"#A61","article-title":"Short effective intervals containing primes","volume":"14","author":"Kadiri H.","year":"2014","journal-title":"Integers"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2018.04.071"},{"key":"e_1_2_6_19_1","first-page":"1869","article-title":"Sur la distribution des nombres premiers","volume":"158","author":"Littlewood J. E.","year":"1914","journal-title":"Comptes Rendus"},{"key":"e_1_2_6_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2015.05.010"},{"key":"e_1_2_6_21_1","unstructured":"NCI.\u2018NCI HPC Systems\u2019 2020 https:\/\/nci.org.au\/our\u2010systems\/hpc\u2010systems."},{"key":"e_1_2_6_22_1","unstructured":"D. J.Platt \u2018Computing degree 1L\u2010functions rigorously\u2019 PhD Thesis University of Bristol Bristol 2011."},{"key":"e_1_2_6_23_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3198"},{"key":"e_1_2_6_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2014.08.019"},{"key":"e_1_2_6_25_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3021"},{"key":"e_1_2_6_26_1","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3583"},{"key":"e_1_2_6_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40687-019-0193-1"},{"key":"e_1_2_6_28_1","doi-asserted-by":"publisher","DOI":"10.4064\/aa159-2-2"},{"key":"e_1_2_6_29_1","unstructured":"N.RevolandF.Rouillier \u2018A library for arbitrary precision interval arithmetic\u2019 10th GAMM\u2010IMACS International Symposium on Scientific Computing Computer Arithmetic and Validated Numerics(2002)."},{"key":"e_1_2_6_30_1","doi-asserted-by":"publisher","DOI":"10.1017\/fmp.2020.6"},{"key":"e_1_2_6_31_1","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1255631807"},{"key":"e_1_2_6_32_1","first-page":"337","article-title":"Sharper bounds for the Chebyshev functions \u03b8(x) and \u03c8(x), II","volume":"30","author":"Schoenfeld L.","year":"1976","journal-title":"Math. Comp."},{"key":"e_1_2_6_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2020.124303"},{"key":"e_1_2_6_34_1","unstructured":"C. R.Smith \u2018The hunt for Skewes\u2019 number\u2019 MSc Thesis University of York York 2016."},{"key":"e_1_2_6_35_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2013-02733-0"},{"key":"e_1_2_6_36_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2011-02470-1"},{"key":"e_1_2_6_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2013.07.017"},{"key":"e_1_2_6_38_1","doi-asserted-by":"publisher","DOI":"10.7169\/facm\/2015.52.2.5"},{"key":"e_1_2_6_39_1","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2016-46-1-325"},{"key":"e_1_2_6_40_1","unstructured":"S.Wedeniwski \u2018ZetaGrid \u2014 Computational verification of the Riemann hypothesis\u2019 Conference in number theory in honour of Professor H. C. Williams Banff Alberta Canada 2003."},{"key":"e_1_2_6_41_1","unstructured":"Wikipedia.\u2018The Riemann hypothesis\u2019 https:\/\/en.wikipedia.org\/wiki\/Riemann_hypothesis(accessed April 2020)."}],"container-title":["Bulletin of the London Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1112\/blms.12460","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1112\/blms.12460","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1112\/blms.12460","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T02:20:43Z","timestamp":1651630843000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1112\/blms.12460"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,22]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1112\/blms.12460"],"URL":"https:\/\/doi.org\/10.1112\/blms.12460","archive":["Portico"],"relation":{},"ISSN":["0024-6093","1469-2120"],"issn-type":[{"value":"0024-6093","type":"print"},{"value":"1469-2120","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,22]]},"assertion":[{"value":"2020-04-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}