{"id":606,"date":"2016-01-30T15:57:42","date_gmt":"2016-01-30T15:57:42","guid":{"rendered":"https:\/\/mathematics.mousoulides.com\/?p=606"},"modified":"2016-11-05T12:09:50","modified_gmt":"2016-11-05T12:09:50","slug":"o-%ce%bc%ce%b5%ce%b3%ce%b1%ce%bb%cf%8d%cf%84%ce%b5%cf%81%ce%bf%cf%82-%cf%80%cf%81%cf%89%cf%84%ce%bf%cf%83-%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%cf%8c%cf%82","status":"publish","type":"post","link":"https:\/\/mathematics.mousoulides.com\/?p=606","title":{"rendered":"O \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03a0\u03a1\u03a9\u03a4\u039f\u03a3 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2"},"content":{"rendered":"<div id=\"header-about\">\n<h1>\u2026. \u03ad\u03c7\u03b5\u03b9 22 338 618 \u03c8\u03b7\u03c6\u03af\u03b1<\/h1>\n<\/div>\n<div class=\"entry\">\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-36484\" src=\"https:\/\/physicsgg.files.wordpress.com\/2016\/01\/prime.png?w=594\" alt=\"prime\" \/>\u03a0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03af \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03b9 \u03c4\u03bf\u03c5 1) \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03b9\u03c1\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03bc\u03cc\u03bd\u03bf \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b5\u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1, \u03cc\u03c0\u03c9\u03c2 \u03bf\u03b9 2, 3, 5, 7, 11, 13, \u03ba.\u03bf.\u03ba.<\/p>\n<p>\u039f\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c0\u03bf\u03c5 \u03b3\u03c1\u03ac\u03c6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03bc\u03bf\u03c1\u03c6\u03ae 2<sup>\u03bd<\/sup>-1, \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03c4\u03bf\u03c5 Mersenne, \u03b1\u03c0\u03cc \u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03b1 \u03c4\u03bf\u03c5 \u0393\u03ac\u03bb\u03bb\u03bf\u03c5 \u03bc\u03bf\u03bd\u03b1\u03c7\u03bf\u03cd <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mersenne_prime\" target=\"_blank\">Marin Mersenne<\/a>, \u03c4\u03bf\u03bd\u00a0\u03c0\u03c1\u03ce\u03c4\u03bf \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b5\u03c1\u03b5\u03cd\u03bd\u03b7\u03c3\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2 \u03c4\u03ad\u03c4\u03bf\u03b9\u03b5\u03c2\u00a0\u03bc\u03bf\u03c1\u03c6\u03ae\u03c2.<\/p>\n<p>\u03a4\u03bf \u03bd\u03ad\u03bf \u03c1\u03b5\u03ba\u03cc\u03c1 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c5 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd \u03b5\u03c0\u03b9\u03c4\u03b5\u03cd\u03c7\u03b8\u03b7\u03ba\u03b5 \u03c0\u03ac\u03bb\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c0\u03c1\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u00a0<strong>GIMPS<\/strong>\u00a0(Great Internet Mersenne Prime Search) \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03c3\u03c5\u03bd\u03b4\u03ad\u03b5\u03b9 \u03c7\u03b9\u03bb\u03b9\u03ac\u03b4\u03b5\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ad\u03c2 \u03c3\u03c4\u03bf\u03bd \u03ba\u03cc\u03c3\u03bc\u03bf \u03c8\u03ac\u03c7\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2.<\/p>\n<p>\u0388\u03bd\u03b1\u03c2 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03c4\u03ae\u03c2 (\u03c4\u03bf\u03c5 \u03b4\u03b9\u03ba\u03c4\u03cd\u03bf\u03c5 GIMPS) \u03c3\u03c4\u03bf \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03c4\u03bf\u03c5 \u039c\u03b9\u03c3\u03bf\u03cd\u03c1\u03b9 \u03c3\u03c4\u03b9\u03c2\u00a0\u0397\u03a0\u0391 \u03ba\u03b1\u03c4\u03ad\u03b3\u03c1\u03b1\u03c8\u03b5\u00a0\u03c4\u03bf\u03bd \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03c0\u03c1\u03ce\u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc, \u03c0\u03bf\u03c5 \u03b3\u03c1\u03ac\u03c6\u03b5\u03c4\u03b1\u03b9 \u03c9\u03c2:<br \/>\n<strong>\u00a02<sup>74,207,281<\/sup>-1<\/strong> \u03ba\u03b1\u03b9 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 <strong>M74207281<\/strong>. \u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf 49\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03c4\u03bf\u03c5\u00a0Mersenne.<\/p>\n<p>\u039f \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b1\u03c5\u03c4\u03cc\u03c2 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc <strong>22 338 618<\/strong> \u03c8\u03b7\u03c6\u03af\u03b1 \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac <strong>5 \u03b5\u03ba\u03b1\u03c4\u03bf\u03bc\u03bc\u03cd\u03c1\u03b9\u03b1 \u03c8\u03b7\u03c6\u03af\u03b1<\/strong>\u03c0\u03b5\u03c1\u03af\u03c0\u03bf\u03c5 \u03bc\u03b1\u03ba\u03c1\u03cd\u03c4\u03b5\u03c1\u03bf\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd <a href=\"https:\/\/physicsgg.me\/2013\/02\/05\/%CE%BF-%CE%BC%CE%B5%CE%B3%CE%B1%CE%BB%CF%8D%CF%84%CE%B5%CF%81%CE%BF%CF%82-%CF%80%CF%81%CF%8E%CF%84%CE%BF%CF%82-%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CE%BF%CF%82-%CE%AD%CF%87%CE%B5%CE%B9-17-%CE%B5%CE%BA%CE%B1\/\" target=\"_blank\">\u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03c0\u03c1\u03ce\u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc<\/a> 2<sup>57,885,161<\/sup>-1.<\/p>\n<p>To Gimps \u03be\u03b5\u03ba\u03af\u03bd\u03b7\u03c3\u03b5 \u03c0\u03c1\u03b9\u03bd \u03b1\u03c0\u03cc 20 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03ba\u03b1\u03b9 (\u03c0\u03b1\u03c1\u03ac \u03c4\u03bf\u00a0\u00ab\u03b1\u03c4\u03c5\u03c7\u03ad\u03c2\u00bb\u00a0\u03cc\u03bd\u03bf\u03bc\u03ac\u00a0\u03c4\u03bf\u03c5) \u03ba\u03b1\u03c4\u03ac\u03c6\u03b5\u03c1\u03b5 \u03bd\u03b1 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9 \u03c4\u03bf\u03c5\u03c2 15 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03c5\u03c2 \u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03cd\u03c2 \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd\u03c2.<\/p>\n<p>\u0395\u03c0\u03cc\u03bc\u03b5\u03bd\u03bf\u03c2 \u03c3\u03c4\u03cc\u03c7\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c1\u03b5\u03c5\u03bd\u03b7\u03c4\u03ce\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b2\u03c1\u03b1\u03b2\u03b5\u03af\u03bf \u03c4\u03c9\u03bd<span style=\"text-decoration: underline;\"><strong> 150 000<\/strong><\/span> \u03b4\u03bf\u03bb\u03b1\u03c1\u03af\u03c9\u03bd \u03c0\u03bf\u03c5 \u03c0\u03c1\u03bf\u03c3\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c4\u03bf Electronic Frontier Foundation \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b5\u03cd\u03c1\u03b5\u03c3\u03b7 \u03c0\u03c1\u03ce\u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd \u03bc\u03b5 100 \u03b5\u03ba\u03b1\u03c4\u03bf\u03bc\u03bc\u03cd\u03c1\u03b9\u03b1 \u03c8\u03b7\u03c6\u03af\u03b1.<\/p>\n<p>\u03c0\u03b7\u03b3\u03ae:\u00a0<a href=\"https:\/\/www.mersenne.org\/\" target=\"_blank\">https:\/\/www.mersenne.org<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2026. \u03ad\u03c7\u03b5\u03b9 22 338 618 \u03c8\u03b7\u03c6\u03af\u03b1 \u03a0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c6\u03c5\u03c3\u03b9\u03ba\u03bf\u03af \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af (\u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf\u03b9 \u03c4\u03bf\u03c5 1) \u03c0\u03bf\u03c5 \u03b4\u03b9\u03b1\u03b9\u03c1\u03bf\u03cd\u03bd\u03c4\u03b1\u03b9 \u03bc\u03cc\u03bd\u03bf \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b5\u03b1\u03c5\u03c4\u03cc \u03c4\u03bf\u03c5\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7 \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1, \u03cc\u03c0\u03c9\u03c2 \u03bf\u03b9 2, 3, 5, 7, 11, 13, \u03ba.\u03bf.\u03ba. \u039f\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u03c0\u03bf\u03c5 \u03b3\u03c1\u03ac\u03c6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03bc\u03bf\u03c1\u03c6\u03ae 2\u03bd-1, \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c0\u03c1\u03ce\u03c4\u03bf\u03b9 \u03c4\u03bf\u03c5 Mersenne, \u03b1\u03c0\u03cc \u03c4\u03bf \u03cc\u03bd\u03bf\u03bc\u03b1 \u03c4\u03bf\u03c5 \u0393\u03ac\u03bb\u03bb\u03bf\u03c5 \u03bc\u03bf\u03bd\u03b1\u03c7\u03bf\u03cd Marin Mersenne, \u03c4\u03bf\u03bd\u00a0\u03c0\u03c1\u03ce\u03c4\u03bf [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-606","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=\/wp\/v2\/posts\/606","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=606"}],"version-history":[{"count":0,"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=\/wp\/v2\/posts\/606\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=606"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=606"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.mousoulides.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}