{"id":190,"date":"2010-12-08T01:28:05","date_gmt":"2010-12-08T05:28:05","guid":{"rendered":"http:\/\/bitc.bme.emory.edu\/~lzhou\/blogs\/?p=190"},"modified":"2010-12-08T01:28:05","modified_gmt":"2010-12-08T05:28:05","slug":"new-prime-found-2740153423585863161377395295321223415217-3643121875747021497257219568-12762412273906-1","status":"publish","type":"post","link":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/?p=190","title":{"rendered":"New prime found: 2^74015*3^42*35^8*5863^16*137^73952*953^2*1223^4*15217 &#8211; ((((3643*121875747021497257)^2*19568-1)^2*7624+1)^2*273906-1)"},"content":{"rendered":"<p>Using Primo, 274^2311 &#8211; 83 is proven a prime number.<br \/>\nDefine this as p[1]=a[1]-b[1], while a[1]=274^2311 and b[1]=83.<br \/>\np[2]=16236*(a[1]^2-b[1]^2)-1<br \/>\n      =16236*274^4622 &#8211; 111849805<br \/>\nis proven prime using pfgw:<br \/>\npfgw -h&#8221;p[1]&#8221; -tp &#8220;p[2]&#8221;<\/p>\n<p>Keep going in this way, it is obtained:<br \/>\np[3]=2^9249*3^5*5*7*11^2*13^2*41^2*137^9244 &#8211; (3643*121875747021497257)<br \/>\np[4]=2^18502*3^10*5^2*7^2*11^4*13^4*41^4*137^18488*1223 &#8211; ((3643*121875747021497257)^2*19568-1)<br \/>\np[5]=2^37007*3^20*35^4*5863^8*137^36976*953*1223^2 &#8211; (((3643*121875747021497257)^2*19568-1)^2*7624+1)<br \/>\np[6]=2^74015*3^42*35^8*5863^16*137^73952*953^2*1223^4*15217 &#8211; ((((3643*121875747021497257)^2*19568-1)^2*7624+1)^2*273906-1)<\/p>\n<p>Certificate will be posted in the reply of this.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Using Primo, 274^2311 &#8211; 83 is proven a prime number. Define this as p[1]=a[1]-b[1], while a[1]=274^2311 and b[1]=83. p[2]=16236*(a[1]^2-b[1]^2)-1 =16236*274^4622 &#8211; 111849805 is proven prime using pfgw: pfgw -h&#8221;p[1]&#8221; -tp &#8220;p[2]&#8221; Keep going in this way, it is obtained: p[3]=2^9249*3^5*5*7*11^2*13^2*41^2*137^9244 &#8211; (3643*121875747021497257) p[4]=2^18502*3^10*5^2*7^2*11^4*13^4*41^4*137^18488*1223 &#8211; ((3643*121875747021497257)^2*19568-1) p[5]=2^37007*3^20*35^4*5863^8*137^36976*953*1223^2 &#8211; (((3643*121875747021497257)^2*19568-1)^2*7624+1) p[6]=2^74015*3^42*35^8*5863^16*137^73952*953^2*1223^4*15217 &#8211; ((((3643*121875747021497257)^2*19568-1)^2*7624+1)^2*273906-1) Certificate will be posted [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,6],"tags":[],"class_list":["post-190","post","type-post","status-publish","format-standard","hentry","category-to-entertain-myself","category-looking-for-a-megaprime","post-blog"],"_links":{"self":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=190"}],"version-history":[{"count":0,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/190\/revisions"}],"wp:attachment":[{"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/csic.som.emory.edu\/~lzhou\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}