{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T17:44:50Z","timestamp":1777484690272,"version":"3.51.4"},"reference-count":5,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2022,10,1]],"date-time":"2022-10-01T00:00:00Z","timestamp":1664582400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>This is Erd\u0151s\u2019s proof of the divergence of the sum of prime reciprocals, using the Mizar system [2], [3], as reported in \u201cProofs from THE BOOK\u201d [1].<\/jats:p>","DOI":"10.2478\/forma-2022-0015","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T13:08:38Z","timestamp":1672405718000},"page":"209-210","source":"Crossref","is-referenced-by-count":2,"title":["The Divergence of the Sum of Prime Reciprocals"],"prefix":"10.2478","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0470-5249","authenticated-orcid":false,"given":"Mario","family":"Carneiro","sequence":"first","affiliation":[{"name":"Carnegie Mellon University , Pittsburgh PA , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,12,30]]},"reference":[{"key":"2026042801431227435_j_forma-2022-0015_ref_001","doi-asserted-by":"crossref","unstructured":"[1] Martin Aigner and G\u00fcnter M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004.10.1007\/978-3-662-05412-3","DOI":"10.1007\/978-3-662-05412-3"},{"key":"2026042801431227435_j_forma-2022-0015_ref_002","doi-asserted-by":"crossref","unstructured":"[2] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol P\u0105k, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261\u2013279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007\/978-3-319-20615-8_17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2026042801431227435_j_forma-2022-0015_ref_003","doi-asserted-by":"crossref","unstructured":"[3] Grzegorz Bancerek, Czes\u0142aw Byli\u0144ski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, and Karol P\u0105k. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9\u201332, 2018. doi:10.1007\/s10817-017-9440-6.604425130069070","DOI":"10.1007\/s10817-017-9440-6"},{"key":"2026042801431227435_j_forma-2022-0015_ref_004","doi-asserted-by":"crossref","unstructured":"[4] Adam Grabowski. Sequences of prime reciprocals. Preliminaries. Formalized Mathematics, 26(1):69\u201379, 2018. doi:10.2478\/forma-2018-0006.","DOI":"10.2478\/forma-2018-0006"},{"key":"2026042801431227435_j_forma-2022-0015_ref_005","doi-asserted-by":"crossref","unstructured":"[5] Christoph Schwarzweller. Renamings and a condition-free formalization of Kronecker\u2019s construction. Formalized Mathematics, 28(2):129\u2013135, 2020. doi:10.2478\/forma-2020-0012.","DOI":"10.2478\/forma-2020-0012"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2022-0015","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T14:23:53Z","timestamp":1777386233000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2022-0015"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,1]]},"references-count":5,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,12,30]]},"published-print":{"date-parts":[[2022,10,1]]}},"alternative-id":["10.2478\/forma-2022-0015"],"URL":"https:\/\/doi.org\/10.2478\/forma-2022-0015","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,1]]}}}