{"id":503,"date":"2012-08-29T03:25:33","date_gmt":"2012-08-29T03:25:33","guid":{"rendered":"http:\/\/www.rationalargumentator.com\/index\/?p=503"},"modified":"2012-08-29T03:25:33","modified_gmt":"2012-08-29T03:25:33","slug":"2-factors-for-ecm","status":"publish","type":"post","link":"https:\/\/www.rationalargumentator.com\/index\/blog\/2012\/08\/2-factors-for-ecm\/","title":{"rendered":"Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project"},"content":{"rendered":"
\n
\"The<\/div>\n<\/div>\n
G. Stolyarov II<\/big><\/big><\/strong><\/span><\/div>\n
August 28, 2012<\/big><\/strong><\/span><\/div>\n
Recommend this page<\/a>.<\/strong><\/div>\n
******************************<\/div>\n
\n

Since the discovery<\/a> in April 2012 of a factor for (118^67 + 67^118), I have continued to donate extensive computing resources to the ECM distributed computing project<\/a> (organized via Yoyo@home<\/a>). Today I am pleased to announce that two more large factors of even larger numbers have been discovered as a result of this endeavor. I am credited with the discoveries here<\/a>. The following is now known:<\/p>\n

\u25cf The number (141^141 + 142^142) (see long form here<\/a>) has a 33-digit factor: 168,853,190,844,095,597,109,245,277,698,729.<\/p>\n

\u25cf The number (148^148 + 149^149) (see long form here<\/a>) has a 28-digit factor: 9,055,497,748,306,357,299,810,062,467.<\/p>\n

To date, my computer has examined 2729 project workunits (each involving an attempt to factor a large number). I have thus far accumulated 528,533.42 BOINC credits<\/a> for the ECM project.<\/p>\n

The magnitudes involved are astounding, considering that the factors discovered are several hundred orders of magnitude less <\/em>than the original numbers. As an example, (148^148 + 149^149) is equal to approximately 6.39 * 10^323. And yet our advancing technology is enabling us already to explore these immense quantities and derive meaningful conclusions regarding them.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

G. Stolyarov II August 28, 2012 Recommend this page. ****************************** Since the discovery in April 2012 of a factor for (118^67 + 67^118), I have continued to donate extensive computing resources to the ECM distributed computing project (organized via Yoyo@home). Today I am pleased to announce that two more large factors of even larger numbers have been discovered as a result of this endeavor. I am credited with the discoveries here. The following is now known: \u25cf The number (141^141…<\/p>\n

Read More Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[292],"tags":[303,304,300,293,296,299,164,40,297,295,294,298,302,261,305,301],"class_list":["post-503","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-boinc","tag-discovery","tag-distributed-computing","tag-ecm","tag-elliptic-curve-factorization","tag-factors","tag-free","tag-g-stolyarov-ii","tag-large-number","tag-math","tag-mathematics-2","tag-numbers","tag-project","tag-science","tag-truth","tag-yoyohome"],"_links":{"self":[{"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/posts\/503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/comments?post=503"}],"version-history":[{"count":2,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/posts\/503\/revisions"}],"predecessor-version":[{"id":505,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/posts\/503\/revisions\/505"}],"wp:attachment":[{"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/media?parent=503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/categories?post=503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rationalargumentator.com\/index\/wp-json\/wp\/v2\/tags?post=503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}