{"id":12736,"date":"2014-09-03T20:46:48","date_gmt":"2014-09-03T17:46:48","guid":{"rendered":"http:\/\/hgpu.org\/?p=12736"},"modified":"2014-09-03T20:46:48","modified_gmt":"2014-09-03T17:46:48","slug":"searching-for-a-counterexample-of-kurepas-conjecture","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=12736","title":{"rendered":"Searching for a counterexample of Kurepa&#8217;s Conjecture"},"content":{"rendered":"<p>Kurepa&#8217;s conjecture states that there is no odd prime p which divides !p=0!+1!+&#8230;+(p-1)!. We search for a counterexample of this conjecture for all p&lt;10^10. We introduce new optimization techniques and perform the computation using graphics processing units (GPUs). Additionally, we consider the generalized Kurepa&#8217;s left factorial given as !kn=(0!)k+(1!)k+&#8230;+((n-1)!)k and show that for all integers 1&lt;k&lt;100 there exists an odd prime p such that p|!^kp.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kurepa&#8217;s conjecture states that there is no odd prime p which divides !p=0!+1!+&#8230;+(p-1)!. We search for a counterexample of this conjecture for all p&lt;10^10. We introduce new optimization techniques and perform the computation using graphics processing units (GPUs). Additionally, we consider the generalized Kurepa&#8217;s left factorial given as !kn=(0!)k+(1!)k+&#8230;+((n-1)!)k and show that for all integers [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[157,90,3],"tags":[1639,7,1796,1162,1793],"class_list":["post-12736","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-opencl","category-paper","tag-amd-radeon-r9-280","tag-ati","tag-mathematics","tag-number-theory","tag-opencl"],"views":2630,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/12736","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12736"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/12736\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}