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G. W. H. Beeger</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Dutch mathematician</div> <p><b>Nicolaas George Wijnand Henri Beeger</b> (1884, in <a href="/wiki/Utrecht_(city)" class="mw-redirect" title="Utrecht (city)">Utrecht</a> – 1965, in <a href="/wiki/Amsterdam" title="Amsterdam">Amsterdam</a>) was a Dutch <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>. His 1916 <a href="/wiki/Doctorate" title="Doctorate">doctorate</a> was on <a href="/wiki/Dirichlet_series" title="Dirichlet series">Dirichlet series</a>. He worked for most of his life as a teacher, working on mathematics papers in his spare evenings. After his retirement as a teacher at 65, he began corresponding with many contemporary mathematicians and dedicated himself to his work. </p><p>He is known for having proved that 3511 is a <a href="/wiki/Wieferich_prime" title="Wieferich prime">Wieferich prime</a> in 1922 <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and for introducing the term <a href="/wiki/Carmichael_number" title="Carmichael number">Carmichael number</a> in 1950. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Beeger_Lecture">Beeger Lecture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=N._G._W._H._Beeger&action=edit&section=1" title="Edit section: Beeger Lecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1989 the board of trustees of the Mathematical Centre in Amsterdam established the <b>Beeger lectures</b>, in honor of N.G.W.H. Begger, to be held biannually at the congress of the <a href="/wiki/Royal_Dutch_Mathematical_Society" title="Royal Dutch Mathematical Society">Royal Dutch Mathematical Society</a>. Their purpose is to promote research and exchange of ideas in the field of algorithmic and computational number theory. The first Beeger Lecture was delivered in 1992. </p> <ul><li><b>2024</b> <a href="/wiki/Andrew_Sutherland_(mathematician)" title="Andrew Sutherland (mathematician)">Andrew Sutherland</a></li> <li><b>2022</b> <a href="/wiki/Shafi_Goldwasser" title="Shafi Goldwasser">Shafi Goldwasser</a></li> <li><b>2021</b> <a href="/w/index.php?title=David_Harvey_(mathematician)&action=edit&redlink=1" class="new" title="David Harvey (mathematician) (page does not exist)">David Harvey</a></li> <li><b>2018</b> <a href="/w/index.php?title=Fernando_Rodriguez_Villegas&action=edit&redlink=1" class="new" title="Fernando Rodriguez Villegas (page does not exist)">Fernando Rodriguez Villegas</a></li> <li><b>2016</b> <a href="/wiki/James_Maynard_(mathematician)" class="mw-redirect" title="James Maynard (mathematician)">James Maynard</a></li> <li><b>2014</b> <a href="/w/index.php?title=Daniele_Micciancio&action=edit&redlink=1" class="new" title="Daniele Micciancio (page does not exist)">Daniele Micciancio</a></li> <li><b>2012</b> <a href="/w/index.php?title=Yuri_Bilu&action=edit&redlink=1" class="new" title="Yuri Bilu (page does not exist)">Yuri Bilu</a></li> <li><b>2010</b> <a href="/wiki/Florian_Luca" title="Florian Luca">Florian Luca</a></li> <li><b>2008</b> <a href="/wiki/Daniel_J._Bernstein" title="Daniel J. Bernstein">Daniel Bernstein</a></li> <li><b>2006</b> <a href="/wiki/Manindra_Agrawal" title="Manindra Agrawal">Manindra Agrawal</a></li> <li><b>2004</b> <a href="/wiki/Manjul_Bhargava" title="Manjul Bhargava">Manjul Bhargava</a></li> <li><b>2002</b> <a href="/wiki/Bjorn_Poonen" title="Bjorn Poonen">Bjorn Poonen</a></li> <li><b>2000</b> <a href="/wiki/Peter_Borwein" title="Peter Borwein">Peter Borwein</a></li> <li><b>1998</b> <a href="/wiki/Hendrik_Lenstra" title="Hendrik Lenstra">Hendrik Lenstra</a></li> <li><b>1996</b> <a href="/wiki/John_Conway" class="mw-redirect" title="John Conway">John Conway</a></li> <li><b>1994</b> <a href="/wiki/Hugh_C._Williams" title="Hugh C. Williams">Hugh Williams</a></li> <li><b>1992</b> <a href="/wiki/Carl_Pomerance" title="Carl Pomerance">Carl Pomerance</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=N._G._W._H._Beeger&action=edit&section=2" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="languageicon">(in French)</span> (N. G. W. H. Beeger ed.), <a href="/wiki/Yakov_Kulik" class="mw-redirect" title="Yakov Kulik">Jakob Philipp Kulik</a>, <a href="/wiki/Luigi_Poletti_(mathematician)" title="Luigi Poletti (mathematician)">Luigi Poletti</a>, R. J. Porter, <i>Liste des nombres premiers du onzième million: (plus précisément de 10.006.741 à 10.999.997)</i>, <a href="/w/index.php?title=Association_fran%C3%A7aise_pour_l%27avancement_des_sciences&action=edit&redlink=1" class="new" title="Association française pour l'avancement des sciences (page does not exist)">Association française pour l'avancement des sciences</a>, Ed. "Werto", 1951</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=N._G._W._H._Beeger&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBeeger1922" class="citation cs2"><a class="mw-selflink selflink">Beeger, N. G. W. H.</a> (1922), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121111110125/http://www.archive.org/stream/messengerofmathe5051cambuoft#page/148/mode/2up">"On a new case of the congruence 2<sup><i>p</i> − 1</sup> ≡ 1 (<i>p</i><sup>2</sup>)"</a>, <i><a href="/wiki/Messenger_of_Mathematics" title="Messenger of Mathematics">Messenger of Mathematics</a></i>, <b>51</b>: 149–150, archived from <a rel="nofollow" class="external text" href="https://archive.org/stream/messengerofmathe5051cambuoft">the original</a> on November 11, 2012</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Messenger+of+Mathematics&rft.atitle=On+a+new+case+of+the+congruence+2%3Csup%3Ep+%E2%88%92+1%3C%2Fsup%3E+%E2%89%A1+1+%28p%3Csup%3E2%3C%2Fsup%3E%29&rft.volume=51&rft.pages=149-150&rft.date=1922&rft.aulast=Beeger&rft.aufirst=N.+G.+W.+H.&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Fmessengerofmathe5051cambuoft&rfr_id=info%3Asid%2Fen.wikipedia.org%3AN.+G.+W.+H.+Beeger" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=N._G._W._H._Beeger&action=edit&section=4" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=51391">N. G. W. H. Beeger</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://www.math.rug.nl/~top/pi-dag/beeger.html">Tilburg University information</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul 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