{"id":847,"date":"2022-11-01T23:25:00","date_gmt":"2022-11-01T20:25:00","guid":{"rendered":"https:\/\/kriptogram.net\/?p=847"},"modified":"2022-12-08T12:42:09","modified_gmt":"2022-12-08T09:42:09","slug":"asallik-testi","status":"publish","type":"post","link":"https:\/\/kriptogram.net\/blog\/asallik-testi\/","title":{"rendered":"Asall\u0131k Testi"},"content":{"rendered":"\n<p>Bir\u00e7ok \u015fifreleme algoritmas\u0131 bir veya daha fazla asal say\u0131ya ihtiya\u00e7 duymaktad\u0131r. Peki b\u00fcy\u00fck bir asal say\u0131s\u0131 nas\u0131l se\u00e7ebiliriz? B\u00fcy\u00fck bir say\u0131n\u0131n asal  olup olmad\u0131\u011f\u0131 gibi zor bir soruya nas\u0131l cevap verebiliriz? Bu soruya cevap veren baz\u0131 alogirtmalardan biri olan <strong>Miller-Rabin<\/strong> algoritmas\u0131n\u0131 hep beraber inceleyelim. Bu algoritman\u0131n bir asal say\u0131 d\u00f6nebilece\u011fi gibi, asal say\u0131 d\u00f6nmesine gerek olmad\u0131\u011f\u0131n\u0131 da belirtmek gerekir. \u0130nceleyelim.<\/p>\n\n\n\n<p>Miller-Robin algoritmas\u0131 b\u00fcy\u00fck bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 test eder. Algoritmay\u0131 a\u00e7\u0131klamadan \u00f6nce \u00f6n bilgi olarak mod\u00fcler aritmetik bilginizin oldu\u011funu varsay\u0131yorum.<\/p>\n\n\n\n<p>\u00d6ncelikle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-85846dbc2b39c94e2b2d65f7c4009218_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#62;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -2px;\"\/> pozitif bir  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> tek  say\u0131s\u0131  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-619091c421168a0a94925f612458c344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#107;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"102\" style=\"vertical-align: -4px;\"\/> \u015feklinde ifade edilebilir. Burada  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-49575e90f347c887bf3ecb7c0acc4347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#62;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -2px;\"\/> ve  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d964c413961af510c6c44f2659558d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -4px;\"\/>  tek bir say\u0131d\u0131r. \u00d6rnek olarak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-3307aeb7ac97b69171d15ef9af628bda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#61;&#32;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: 0px;\"\/> i\u00e7in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-5038da82e2b4249da5f3e78ff9b3f974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#57;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: 0px;\"\/> verilebilir. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-f6cef83035607741c50c5489911ef54e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#61;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: 0px;\"\/> i\u00e7in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-b0088419b59a178d1203e5c673fd7f7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: 0px;\"\/> vs.. Buradan, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-405c98f7936e42101d9a1ac165ed66b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"45\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131n\u0131 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6e21e30f2152ddddf1063438768bb712_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"10\" style=\"vertical-align: 0px;\"\/> defa <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-2add0e5568c24573820b2e070e80f173_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"9\" style=\"vertical-align: 0px;\"\/> ile b\u00f6lersek, b\u00f6l\u00fcm olarak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d964c413961af510c6c44f2659558d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -4px;\"\/> say\u0131s\u0131n\u0131 elde edece\u011fimiz a\u00e7\u0131kt\u0131r. E\u011fer 28 say\u0131s\u0131n\u0131 binary olarak ele al\u0131rsak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-75e06aff3ed74a34885f92f13cf745f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#49;&#49;&#49;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: 0px;\"\/>, en sa\u011fdaki bit 1 oluncaya kadar sa\u011fa do\u011fru <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6e21e30f2152ddddf1063438768bb712_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"10\" style=\"vertical-align: 0px;\"\/> defa <strong><em>shift<\/em><\/strong> yaparsak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-381db04585222e993515714553bdf9aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#32;&#61;&#32;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"46\" style=\"vertical-align: -4px;\"\/> say\u0131s\u0131n\u0131 binary olarak(<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d72e68562687b24630bf5db3a493d4de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#48;&#48;&#49;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: 0px;\"\/>) elde ederiz. <\/p>\n\n\n\n<p>As\u0131l konuya ge\u00e7meden \u00f6nce bize yard\u0131mc\u0131 olacak bir teoremden bahsetmek gerekiyor. <strong>Fermat Teoremine<\/strong> g\u00f6re, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-7ec558bdcb80163781b4880daeacb77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#123;&#112;&#45;&#49;&#125;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#49;&#92;&#58;&#32;&#109;&#111;&#100;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"132\" style=\"vertical-align: -4px;\"\/>&#8216;dir, e\u011fer <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> bir asal say\u0131 ve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6ef92b953e3aaabcd83bb3d457f50922_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> taraf\u0131ndan b\u00f6l\u00fcnemeyen bir tamsay\u0131 oldu\u011fu \u015fartlar\u0131 sa\u011flan\u0131yorsa(devrik c\u00fcmle maalesef). Konumuzla devam edelim..<\/p>\n\n\n\n<p>Asal say\u0131lar\u0131n \u00f6zelliklerinden birini \u015fu \u015fekilde a\u00e7\u0131klayabiliriz: E\u011fer <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> bir asal say\u0131 ve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6ef92b953e3aaabcd83bb3d457f50922_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/>  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/>&#8216;den k\u00fc\u00e7\u00fck pozitif bir tamsay\u0131 ise, a\u015fa\u011f\u0131daki \u015fartlardan herhangi biri do\u011fru ise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-be6e474e708091b3e3888b6732806533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"112\" style=\"vertical-align: -4px;\"\/> olur.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-7e6f768ace1c4a7d5c374348b2cb1b3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"103\" style=\"vertical-align: -4px;\"\/> veya,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-730138c8e92297a5a11a584f8cda948f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#32;&#61;&#32;&#45;&#49;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#32;&#61;&#32;&#112;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"246\" style=\"vertical-align: -4px;\"\/>. Mod\u00fcler aritmetik kurallar\u0131na g\u00f6re, (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-54a22783e5a76a21ce47c48ab3e80458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\"\/>) (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-54a22783e5a76a21ce47c48ab3e80458_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -4px;\"\/> ) = <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6f5abb46985e162c98df09939ccfee34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"76\" style=\"vertical-align: -4px;\"\/> &#8216;dir. Buna g\u00f6re <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-b4f7f610fbc3245d48b0979b0b0cd4d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;&#32;&#61;&#32;&#49;&#92;&#58;&#32;&#118;&#101;&#121;&#97;&#32;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"183\" style=\"vertical-align: -4px;\"\/> olsa da, sonu\u00e7 olarak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-be6e474e708091b3e3888b6732806533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#50;&#32;&#92;&#58;&#109;&#111;&#100;&#32;&#92;&#58;&#112;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"112\" style=\"vertical-align: -4px;\"\/> olur.<\/li>\n<\/ul>\n\n\n\n<p>Asal say\u0131lar\u0131n di\u011fer bir \u00f6zelli\u011fini \u015fu \u015fekilde a\u00e7\u0131klayabiliriz: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-2add0e5568c24573820b2e070e80f173_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"9\" style=\"vertical-align: 0px;\"\/>&#8216;den b\u00fcy\u00fck bir asal say\u0131 ise, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-49a43710d5765e90c47269b3fd5f5889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#107;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"101\" style=\"vertical-align: -4px;\"\/> \u015feklinde ifade edilebilir. Burada  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-49575e90f347c887bf3ecb7c0acc4347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#62;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -2px;\"\/> ve  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d964c413961af510c6c44f2659558d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -4px;\"\/>  tek bir say\u0131d\u0131r (3. paragrafta de\u011fi\u015fnmi\u015ftik).  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e8280ada6de4d8009500937f98b535af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#60;&#97;&#60;&#112;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\"\/> \u015feklinde herhangi bir <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6ef92b953e3aaabcd83bb3d457f50922_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/>  tamsay\u0131s\u0131n\u0131 ele ald\u0131\u011f\u0131m\u0131zda a\u015fa\u011f\u0131daki \u015fartlardan biri do\u011frudur.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-864e9b68a7435218da8946b39d80c37f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#113;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#49;&#32;&#40;&#109;&#111;&#100;&#92;&#58;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"121\" style=\"vertical-align: -5px;\"\/>, di\u011fer ifadeyle <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e5e591cb7cbadf0397160f97580027c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#113;&#32;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\"\/><\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-c1dfd862ee63a18db1c88b6173b23708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#113;&#44;&#92;&#58;&#97;&#94;&#123;&#50;&#113;&#125;&#44;&#92;&#58;&#97;&#94;&#123;&#52;&#113;&#125;&#46;&#46;&#46;&#97;&#94;&#123;&#50;&#94;&#123;&#107;&#45;&#49;&#125;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"167\" style=\"vertical-align: -4px;\"\/> say\u0131lar\u0131ndan biri <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d542a67ef024a4f17871fa85c2b8a5bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#45;&#49;&#32;&#40;&#109;&#111;&#100;&#92;&#58;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"112\" style=\"vertical-align: -5px;\"\/>. Burada <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6599b6586a509112e8a4f3214b2aa8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#60;&#61;&#106;&#60;&#61;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"114\" style=\"vertical-align: -4px;\"\/> \u015feklinde baz\u0131 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-ff3cb7d4724588e376ea27563508f03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#106;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"9\" style=\"vertical-align: -4px;\"\/> say\u0131lar\u0131 vard\u0131r ve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-1b0170b178611ae702b8cc9dad0ca5ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#123;&#50;&#94;&#123;&#106;&#45;&#49;&#125;&#113;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#45;&#49;&#92;&#58;&#32;&#109;&#111;&#100;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"160\" style=\"vertical-align: -4px;\"\/>&#8216;dir. Fermat teoremine g\u00f6re <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-7ec558bdcb80163781b4880daeacb77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#123;&#112;&#45;&#49;&#125;&#125;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#49;&#92;&#58;&#32;&#109;&#111;&#100;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"132\" style=\"vertical-align: -4px;\"\/>&#8216;dir, e\u011fer <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> bir asal say\u0131 ise, \u015feklinde belirtmi\u015ftik. Elimizde <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-49a43710d5765e90c47269b3fd5f5889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#107;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"101\" style=\"vertical-align: -4px;\"\/> oldu\u011funa g\u00f6re,\n\n<ul class=\"wp-block-list\">\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e1658aca0ad02d9d723c6941ea9e1b21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#113;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#44;&#92;&#58;&#97;&#94;&#123;&#50;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#44;&#92;&#58;&#97;&#94;&#123;&#52;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#92;&#58;&#46;&#46;&#46;&#92;&#58;&#97;&#94;&#123;&#50;&#94;&#123;&#107;&#45;&#49;&#125;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#44;&#92;&#58;&#97;&#94;&#123;&#50;&#94;&#123;&#107;&#125;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"508\" style=\"vertical-align: -4px;\"\/> dizisinin son eleman\u0131n\u0131n de\u011feri  1&#8217;dir. Her dizi eleman\u0131 bir \u00f6ncekinin karesidir ayn\u0131 zamanda. Bundan dolay\u0131 a\u015fa\u011f\u0131daki olas\u0131l\u0131klar mevcuttur.\n\n<ol class=\"wp-block-list\">\n\n<li>Dizinin ilk eleman\u0131 ve dolay\u0131s\u0131yla kareleri olan di\u011fer elemanlar\u0131n de\u011feri 1&#8217;dir.<\/li>\n\n\n<li>Dizideki baz\u0131 say\u0131lar 1de\u011fildir ancak kareleri <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-02766803bc6b9d5d82cabbb6d1ea99c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#111;&#100;&#92;&#58;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\"\/>&#8216;de 1&#8217;dir.<\/li>\n\n<\/ol>\n\n<\/li>\n\n<\/ul>\n\n<\/li>\n<\/ul>\n\n\n\n<p>Sonu\u00e7 olarak <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> bir asal say\u0131 ise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-4c89e73c53f85be62bb51afd4ae1443e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#97;&#94;&#113;&#44;&#92;&#58;&#97;&#94;&#123;&#50;&#113;&#125;&#44;&#92;&#58;&#97;&#94;&#123;&#52;&#113;&#125;&#46;&#46;&#46;&#97;&#94;&#123;&#50;&#94;&#123;&#107;&#45;&#49;&#125;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#44;&#97;&#94;&#123;&#50;&#94;&#123;&#107;&#125;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#58;&#112;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"338\" style=\"vertical-align: -5px;\"\/> dizideki say\u0131lar 1 de\u011ferindedir, veya dizideki baz\u0131 say\u0131lar <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-1b3afb0c041bd2ba0830999eaf66a1a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\"\/>&#8216;e e\u015fittir.  Aksi durumda <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> asal de\u011fildir. Bu \u015fartlar\u0131 sa\u011flamas\u0131 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> say\u0131s\u0131n\u0131 asal olarak se\u00e7memizi sa\u011flar ancak bu <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-158dfaffe1aaf0609fa00363e2fd5d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"11\" style=\"vertical-align: -4px;\"\/> say\u0131s\u0131n\u0131n kesin olarak asal oldu\u011fu anlam\u0131na gelmez.<\/p>\n\n\n\n<p>Bir <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131n\u0131n asall\u0131k testi i\u00e7in izlememiz gereken algoritman\u0131n ad\u0131mlar\u0131 \u015fu  \u015fekildedir:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-49575e90f347c887bf3ecb7c0acc4347_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#62;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -2px;\"\/> ve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d964c413961af510c6c44f2659558d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -4px;\"\/> tek say\u0131 olacak \u015fekilde <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6e21e30f2152ddddf1063438768bb712_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"10\" style=\"vertical-align: 0px;\"\/> ve <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-d964c413961af510c6c44f2659558d9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -4px;\"\/> say\u0131lar\u0131n\u0131 bul, (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-619091c421168a0a94925f612458c344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#45;&#49;&#32;&#61;&#32;&#50;&#94;&#107;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"102\" style=\"vertical-align: -4px;\"\/>)<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-638fb74b453aa3ad6d21c30f49918e28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#60;&#97;&#60;&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -2px;\"\/> olacak \u015fekilde rastgele bir <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6ef92b953e3aaabcd83bb3d457f50922_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131 se\u00e7,<\/li>\n\n\n\n<li>E\u011fer <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-ed2558e2defbee69cd4b2a3f65e3a6d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#113;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#49;&#32;&#40;&#109;&#111;&#100;&#92;&#58;&#110;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"\/> ise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-73ffc674b267e96ef552312db0cf97fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#101;&#116;&#117;&#114;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\"\/>  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131 asal olabilir,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6c5fc6632a068c6cb321b53f6a3e3244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#106;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\"\/>&#8216;dan <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-713960fb1f4e44442830b50ca83aadaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"43\" style=\"vertical-align: 0px;\"\/>&#8216;e bir for d\u00f6ng\u00fcs\u00fc kur,<\/li>\n\n\n\n<li>E\u011fer <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-1791e04a570d4d51b172777c56552394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#94;&#123;&#50;&#94;&#123;&#106;&#45;&#49;&#125;&#113;&#125;&#92;&#58;&#109;&#111;&#100;&#92;&#110;&#61;&#110;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"165\" style=\"vertical-align: 0px;\"\/> ise <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-73ffc674b267e96ef552312db0cf97fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#101;&#116;&#117;&#114;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\"\/>  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131 asal olabilir,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-73ffc674b267e96ef552312db0cf97fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#101;&#116;&#117;&#114;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131 asal de\u011fildir.<\/li>\n<\/ul>\n\n\n\n<p>Birden fazla <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-6ef92b953e3aaabcd83bb3d457f50922_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131 se\u00e7ilerek <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/kriptogram.net\/blog\/wp-content\/ql-cache\/quicklatex.com-e884c91d8f698b5b6b456f5bfa094652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"12\" style=\"vertical-align: 0px;\"\/> say\u0131s\u0131n\u0131n test edilmesi asal olma ihtimalini g\u00fc\u00e7lendirir. <\/p>\n\n\n\n<p>A\u015fa\u011f\u0131da \u00f6rnek kodlar verilmi\u015ftir. Kodlar \u00f6rnek ama\u00e7l\u0131d\u0131r. Herhangi bir \u00fcr\u00fcnde kullan\u0131lmak i\u00e7in tamamen haz\u0131r halde (production-ready) de\u011fildir.<\/p>\n\n\n\n<p>Bir sonraki yaz\u0131m\u0131zda g\u00f6r\u00fc\u015fmek \u00fczere..<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"csharp\" class=\"language-csharp\">using System.Numerics;\nusing System.Security.Cryptography;\n\nConsole.WriteLine(\"***Miller-Rabin Primality Test***\");\nConsole.WriteLine();\nstring isGameOver = \"\";\nwhile (isGameOver.ToLower() != \"y\")\n{\n    Console.Write(\"Please write a number for primality test: \");\n    if (!BigInteger.TryParse(Console.ReadLine(), out BigInteger n))\n    {\n        Console.WriteLine(\"This is not a Number!\");\n        continue;\n    }\n    Console.Write(\"How many times do you want to test this number? : \");\n    if (!int.TryParse(Console.ReadLine(), out int numberOfTest))\n    {\n        Console.WriteLine(\"This is not a Number!\");\n        continue;\n    } \n    Console.WriteLine($\"Is {n} prime? : {IsPrime(n, numberOfTest)}\");\n    Console.Write(\"Is game over? (Quit?) [y] [n]: \");\n    isGameOver = Console.ReadLine();\n}\nstatic bool IsPrime(BigInteger n, int numberOfTest)\n{\n    if ((n &lt; 3) || (n % 2 == 0))\n    {\n        return false;\n    }\n    BigInteger q = n - 1;\n    int k = 0;\n    while (q % 2 == 0)\n    {\n        q &gt;&gt;= 1;\n        k++;\n    }\n    Console.WriteLine($\"k: {k}\");\n    Console.WriteLine($\"q: {q}\");\n\n    RandomNumberGenerator rng = RandomNumberGenerator.Create();\n    byte[] bytes = new byte[n.ToByteArray().LongLength];\n    BigInteger a;\n    for (int i = 0; i &lt; numberOfTest; i++)\n    {\n        do\n        {\n            rng.GetBytes(bytes);\n            a = new BigInteger(bytes);\n        }\n        while (a &lt; 2 || a &gt;= n - 2);\n        if (BigInteger.ModPow(a, q, n) == 1)\n        {\n            return true;\n        }\n        for (int j = 0; j &lt; k; j++)\n        {\n            if (BigInteger.ModPow(a, BigInteger.Pow(2, j) * q, n) == n - 1)\n            {\n                return true;\n            }\n        }\n    }\n    return false;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Bir\u00e7ok \u015fifreleme algoritmas\u0131 bir veya daha fazla asal say\u0131ya ihtiya\u00e7 duymaktad\u0131r. Peki b\u00fcy\u00fck bir asal say\u0131s\u0131 nas\u0131l se\u00e7ebiliriz? B\u00fcy\u00fck bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131 gibi zor bir soruya nas\u0131l cevap verebiliriz? Bu soruya cevap&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":1131,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"ngg_post_thumbnail":0,"footnotes":""},"categories":[25],"tags":[],"class_list":["post-847","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sayilar-teorisi"],"_links":{"self":[{"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/posts\/847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/comments?post=847"}],"version-history":[{"count":75,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/posts\/847\/revisions"}],"predecessor-version":[{"id":1323,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/posts\/847\/revisions\/1323"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/media\/1131"}],"wp:attachment":[{"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/media?parent=847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/categories?post=847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kriptogram.net\/blog\/wp-json\/wp\/v2\/tags?post=847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}