{"id":142,"date":"2006-10-09T18:45:00","date_gmt":"2006-10-09T18:45:00","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=142"},"modified":"2006-10-09T18:45:00","modified_gmt":"2006-10-09T18:45:00","slug":"why-complexity-is-better-than-cannabis","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=142","title":{"rendered":"Why complexity is better than cannabis"},"content":{"rendered":"<p>Whether there exist subexponential-size locally decodable codes, and sub-n<sup>\u03b5<\/sup>-communication private information retrieval (PIR) protocols, have been major open problems for a decade.  A <a href=\"http:\/\/eccc.hpi-web.de\/eccc-reports\/2006\/TR06-127\/index.html\">new preprint<\/a> by Sergey Yekhanin reveals that both of these questions hinge on &#8212; wait for this &#8212; whether or not there are infinitely many <a href=\"http:\/\/en.wikipedia.org\/wiki\/Mersenne_prime\">Mersenne primes<\/a>.  By using the fact (<a href=\"http:\/\/www.mersenne.org\/\">discovered<\/a> a month ago) that 2<sup>32,582,657<\/sup>-1 is prime, Yekhanin can already give a 3-server PIR protocol with communication complexity O(n<sup>1\/32,582,658<\/sup>), improving the previous bound of O(n<sup>1\/5.25<\/sup>).   Duuuuuude.  If you&#8217;ve ever wondered what it is that motivates complexity theorists, roll this one up and smoke it.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Whether there exist subexponential-size locally decodable codes, and sub-n\u03b5-communication private information retrieval (PIR) protocols, have been major open problems for a decade. A new preprint by Sergey Yekhanin reveals that both of these questions hinge on &#8212; wait for this &#8212; whether or not there are infinitely many Mersenne primes. By using the fact (discovered [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[5],"tags":[],"class_list":["post-142","post","type-post","status-publish","format-standard","hentry","category-complexity"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/142","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=142"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/142\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}