{"id":19669,"date":"2013-05-09T21:23:01","date_gmt":"2013-05-09T21:23:01","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=19669"},"modified":"2013-05-09T21:23:01","modified_gmt":"2013-05-09T21:23:01","slug":"day-129-all-about-129","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/05\/09\/day-129-all-about-129\/","title":{"rendered":"Day 129: All About 129"},"content":{"rendered":"<p>129 is a fabulous number. It is one of my favourites.<\/p>\n<p>For a start, it is the sum of the first ten <a class=\"zem_slink\" title=\"Prime number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Prime_number\" target=\"_blank\" rel=\"wikipedia\">prime numbers<\/a>:\u00a02, 3, 5, 7, 11, 13, 17, 19, 23, 29. I know this because the sum of the first nine is 100 &#8211; a fact that not many people know I would imagine.<\/p>\n<p>1, \u00a0by the way, is not a prime number. In fact, most early <a class=\"zem_slink\" title=\"Greeks\" href=\"http:\/\/en.wikipedia.org\/wiki\/Greeks\" target=\"_blank\" rel=\"wikipedia\">Greeks<\/a> did not even consider 1 to be a number,\u00a0and so they certainly did not consider it a prime. Times moved on, of course, and in the 19th century, many mathematicians did consider the number 1 a prime.\u00a0For example, the number 15 can be factored as 3 x 5 or\u00a01 x 3 x 5. If 1 were prime, these would be considered different factorizations of 15 into prime numbers.<\/p>\n<p>Anyway, that&#8217;s the first reason. The second is that it is\u00a0the <a class=\"zem_slink\" title=\"Infinitesimal\" href=\"http:\/\/en.wikipedia.org\/wiki\/Infinitesimal\" target=\"_blank\" rel=\"wikipedia\">smallest number<\/a> that can be expressed as a sum of three squares in four different ways:<\/p>\n<ul>\n<li>11\u00b2 + 2\u00b2 + 2\u00b2<\/li>\n<li>10\u00b2 + 5\u00b2 + 2\u00b2<\/li>\n<li>8\u00b2 + 8\u00b2 + 1\u00b2<\/li>\n<li>8\u00b2 + 7\u00b2 + 4\u00b2<\/li>\n<\/ul>\n<p>Thirdly, 129 is a <a class=\"zem_slink\" title=\"Happy number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Happy_number\" target=\"_blank\" rel=\"wikipedia\">happy number<\/a>, so how can it not be liked?!\u00a0A happy number begins with any positive integer (a whole number), which is then replaced by the sum of the squares of its digits, which gets repeated until the number equals 1. If this process creates an <a class=\"zem_slink\" title=\"Infinite loop\" href=\"http:\/\/en.wikipedia.org\/wiki\/Infinite_loop\" target=\"_blank\" rel=\"wikipedia\">endless loop<\/a> which never reaches 1 &#8211; such a number is unhappy.<\/p>\n<p>For 129, this is the process:<\/p>\n<ul>\n<li>129 &#8211;&gt; 1\u00b2 + 2\u00b2 + 9\u00b2 = 86<\/li>\n<li>86 &#8211;&gt; 8\u00b2 + 6\u00b2 = 100<\/li>\n<li>100 &#8211;&gt; 1\u00b2 + 0\u00b2 + 0\u00b2 = 1<\/li>\n<\/ul>\n<p>There you go. Tells you nothing about my day. But I&#8217;ve done nothing as exciting as the number 129 today.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"zemanta-pixie\" style=\"margin-top: 10px; height: 15px;\"><a class=\"zemanta-pixie-a\" title=\"Enhanced by Zemanta\" href=\"http:\/\/www.zemanta.com\/?px\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"zemanta-pixie-img\" style=\"border: none; float: right;\" alt=\"Enhanced by Zemanta\" src=\"https:\/\/i0.wp.com\/img.zemanta.com\/zemified_e.png?w=1165\" \/><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>129 is a fabulous number. It is one of my favourites. For a start, it is the sum of the first ten prime numbers:\u00a02, 3, 5, 7, 11, 13, 17, 19, 23, 29. I know this because the sum of the first nine is 100 &#8211; a fact that not many people know I would [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_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":[2,18],"tags":[666,947,1341,1442,1909,2199,2440,3200],"class_list":["post-19669","post","type-post","status-publish","format-standard","hentry","category-2","category-maths","tag-china","tag-districts-of-mongolia","tag-greeks","tag-home-shopping-network","tag-math","tag-number-theory","tag-prime-number","tag-walmart","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-57f","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/19669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=19669"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/19669\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=19669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=19669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=19669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}