{"id":6136,"date":"2015-03-06T14:42:59","date_gmt":"2015-03-06T18:42:59","guid":{"rendered":"http:\/\/nycphantom.com\/journal\/?p=6136"},"modified":"2015-03-07T14:50:28","modified_gmt":"2015-03-07T18:50:28","slug":"fun-with-prime","status":"publish","type":"post","link":"http:\/\/nycphantom.com\/journal\/?p=6136","title":{"rendered":"Fun with Prime"},"content":{"rendered":"<p>It would appear that the mystery of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Prime_gap\" target=\"_blank\">prime gap<\/a> is of interest to me for the distribution of primes.<\/p>\n<p>It seems that there's a pattern of gaps building up. While there have been many conjectures out there pertaining to the gaps.<\/p>\n<p>If we start with the gaps of odd...2,2,2,2,2,...<br \/>\nFor sieving out multiples of 3, we \"squeeze\" every other 2-consequtive pairs to make it 2,4,2,4,2,4,...Sieving multiples of 5, we \"squeeze\" another specific yet consistent pattern of consecutive 2-4 to make it 6, such that 2,4,2,4,6,2,6,4,2,4,2,4,6,2,6,4,...<\/p>\n<p>I need to examine such patterns as we sieve higher multiples.<\/p>\n<p>As for the largest prime known to date: 2^57,885,161-1, which has 17,425,170 digits, the number alone requires about 7MB to store, bit-wise. Therefore, it is unlikely for me to implement a way to store all natural numbers to the largest prime, an easy way to perform the sieve. A cleverer way is required.<\/p>\n<p>I don't care much about <a href=\"https:\/\/primes.utm.edu\/mersenne\/index.html\" target=\"_blank\">Mersenne Primes<\/a>. I am more interested in having a means to find the largest prime, p, such that I should also known all primes &lt; p.<\/p>\n<p>For finding primes: Lucas-Lehmer Test is generally used.<\/p>\n<p>For proving: Perhaps <a href=\"http:\/\/en.wikipedia.org\/wiki\/AKS_primality_test\" target=\"_blank\">AKS test<\/a>?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It would appear that the mystery of prime gap is of interest to me for the distribution of primes. It seems that there's a pattern of gaps building up. While there have been many conjectures out there pertaining to the &hellip; <a href=\"http:\/\/nycphantom.com\/journal\/?p=6136\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,10],"tags":[],"class_list":["post-6136","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-projects"],"_links":{"self":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6136"}],"version-history":[{"count":6,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6136\/revisions"}],"predecessor-version":[{"id":6152,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6136\/revisions\/6152"}],"wp:attachment":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6136"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}