{"id":4540,"date":"2026-08-28T13:24:46","date_gmt":"2026-08-28T13:24:46","guid":{"rendered":"https:\/\/cosmalore.com\/ar\/?p=4540"},"modified":"2026-08-28T13:24:46","modified_gmt":"2026-08-28T13:24:46","slug":"prime-numbers","status":"publish","type":"post","link":"https:\/\/cosmalore.com\/ar\/2026\/08\/28\/prime-numbers\/","title":{"rendered":"\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629"},"content":{"rendered":"<article>\n<p>\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0647\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0627\u0644\u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u0648\u0627\u062d\u062f \u0627\u0644\u062a\u064a \u0644\u0627 \u062a\u0642\u0628\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u062f\u0648\u0646 \u0628\u0627\u0642\u064d \u0625\u0644\u0627 \u0639\u0644\u0649 \u0627\u0644\u0639\u062f\u062f 1 \u0648\u0639\u0644\u0649 \u0646\u0641\u0633\u0647\u0627. \u0648\u062a\u062d\u062a\u0644 \u0645\u0643\u0627\u0646\u0629 \u0645\u0631\u0643\u0632\u064a\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0644\u0623\u0646 \u0643\u0644 \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u0648\u0627\u062d\u062f \u064a\u0645\u0643\u0646 \u062a\u062d\u0644\u064a\u0644\u0647 \u0625\u0644\u0649 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0623\u0639\u062f\u0627\u062f \u0623\u0648\u0644\u064a\u0629 \u0628\u0637\u0631\u064a\u0642\u0629 \u0648\u062d\u064a\u062f\u0629\u060c \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0639\u0648\u0627\u0645\u0644. \u0648\u0644\u0647\u0630\u0627 \u062a\u064f\u0639\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0628\u0645\u062b\u0627\u0628\u0629 \u00ab\u0627\u0644\u0644\u0628\u0646\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\u00bb \u0644\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629. \u0648\u0642\u062f \u0639\u064f\u0631\u0641\u062a \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0645\u0646\u0630 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a\u0629 \u0627\u0644\u0642\u062f\u064a\u0645\u0629\u061b \u0641\u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u062a\u0627\u0633\u0639 \u0645\u0646 <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u0644\u0625\u0642\u0644\u064a\u062f\u0633 \u064a\u0638\u0647\u0631 \u0628\u0631\u0647\u0627\u0646 \u0634\u0647\u064a\u0631 \u0639\u0644\u0649 \u0639\u062f\u0645 \u0627\u0646\u062a\u0647\u0627\u0621 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0643\u0645\u0627 \u062a\u062a\u0636\u0645\u0646 \u0627\u0644\u0643\u062a\u0628 \u0646\u0641\u0633\u0647\u0627 \u0646\u062a\u0627\u0626\u062c \u062a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644 \u0623\u0648\u0644\u064a\u0629 \u0648\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"1|Prime numbers|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[1]<\/a><\/sup><\/p>\n<div class=\"infobox\">\n<table>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0627\u0633\u0645<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0628\u0627\u0644\u0625\u0646\u062c\u0644\u064a\u0632\u064a\u0629<\/td>\n<td class=\"ib-val\">Prime Numbers<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0645\u062c\u0627\u0644<\/td>\n<td class=\"ib-val\">\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062a\u0639\u0631\u064a\u0641<\/td>\n<td class=\"ib-val\">\u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0637\u0628\u064a\u0639\u064a \u0623\u0643\u0628\u0631 \u0645\u0646 1 \u0644\u0627 \u064a\u0642\u0628\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0625\u0644\u0627 \u0639\u0644\u0649 1 \u0648\u0639\u0644\u0649 \u0646\u0641\u0633\u0647<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0623\u0635\u063a\u0631 \u0639\u062f\u062f \u0623\u0648\u0644\u064a<\/td>\n<td class=\"ib-val\">2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0623\u0635\u063a\u0631 \u0639\u062f\u062f \u0623\u0648\u0644\u064a \u0641\u0631\u062f\u064a<\/td>\n<td class=\"ib-val\">3<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u0627\u0644\u0632\u0648\u062c\u064a \u0627\u0644\u0648\u062d\u064a\u062f<\/td>\n<td class=\"ib-val\">2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0639\u062f\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0644\u0627 \u0646\u0647\u0627\u0626\u064a<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0645\u0628\u0631\u0647\u0646\u0629 \u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0645\u0628\u0631\u0647\u0646\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0645\u0628\u0631\u0647\u0646\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u062d\u0648\u0644 \u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0645\u0646\u062e\u0644 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0646\u062a\u064a\u062c\u0629 \u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0631\u0626\u064a\u0633\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0623\u0648\u0644 \u0639\u062f\u062f \u0623\u0648\u0644\u064a<\/td>\n<td class=\"ib-val\">2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0623\u0645\u062b\u0644\u0629<\/td>\n<td class=\"ib-val\">2\u060c 3\u060c 5\u060c 7\u060c 11\u060c 13\u060c 17\u060c 19\u060c 23\u060c 29\u060c 31\u060c 37<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0623\u0647\u0645 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644\u060c \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629\u060c \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u0639\u0642\u064a\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062a\u0634\u0641\u064a\u0631<\/td>\n<td class=\"ib-val\">\u0628\u0646\u0627\u0621 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0634\u0641\u064a\u0631 \u0628\u0627\u0644\u0645\u0641\u062a\u0627\u062d \u0627\u0644\u0639\u0627\u0645<\/td>\n<\/tr>\n<\/table>\n<div class=\"ib-foot\">COSMALORE \u00b7 \u0627\u0644\u0645\u0648\u0633\u0648\u0639\u0629 \u0627\u0644\u0639\u0631\u0628\u064a\u0629<\/div>\n<\/div>\n<h2>\u0645\u0627\u0647\u064a\u0629 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a<\/h2>\n<p>\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u0647\u0648 \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0637\u0628\u064a\u0639\u064a \u0623\u0643\u0628\u0631 \u0645\u0646 1 \u0644\u0627 \u064a\u0645\u062a\u0644\u0643 \u0625\u0644\u0627 \u0642\u0627\u0633\u0645\u064a\u0646 \u0645\u0648\u062c\u0628\u064a\u0646 \u0647\u0645\u0627 1 \u0648\u0627\u0644\u0639\u062f\u062f \u0646\u0641\u0633\u0647. \u0648\u0628\u0630\u0644\u0643 \u062a\u0643\u0648\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f 2 \u06483 \u06485 \u06487 \u064811 \u064813 \u0623\u0648\u0644\u064a\u0629\u060c \u0641\u064a \u062d\u064a\u0646 \u0623\u0646 4 \u0644\u064a\u0633 \u0623\u0648\u0644\u064a\u064b\u0627 \u0644\u0623\u0646\u0647 \u064a\u0642\u0628\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 1 \u06482 \u06484\u060c \u0648\u0627\u0644\u0639\u062f\u062f 15 \u0644\u064a\u0633 \u0623\u0648\u0644\u064a\u064b\u0627 \u0644\u0623\u0646\u0647 \u064a\u0642\u0628\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 1 \u06483 \u06485 \u064815. \u0623\u0645\u0627 \u0627\u0644\u0639\u062f\u062f 1 \u0641\u0644\u0627 \u064a\u064f\u0639\u062f \u0639\u062f\u062f\u064b\u0627 \u0623\u0648\u0644\u064a\u064b\u0627\u060c \u0644\u0623\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u064a\u062a\u0637\u0644\u0628 \u0648\u062c\u0648\u062f \u0642\u0627\u0633\u0645\u064a\u0646 \u0645\u0648\u062c\u0628\u064a\u0646 \u0645\u062a\u0645\u064a\u0632\u064a\u0646. \u0648\u064a\u0639\u062f \u0627\u0644\u0639\u062f\u062f 2 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629\u061b \u0641\u0647\u0648 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u0627\u0644\u0632\u0648\u062c\u064a \u0627\u0644\u0648\u062d\u064a\u062f\u060c \u0644\u0623\u0646 \u0643\u0644 \u0639\u062f\u062f \u0632\u0648\u062c\u064a \u0623\u0643\u0628\u0631 \u0645\u0646 2 \u064a\u0642\u0628\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 2.<\/p>\n<p>\u0648\u064a\u0638\u0647\u0631 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 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\u064a\u062f \u062c\u0627\u0643 \u0623\u062f\u0627\u0645\u0627\u0631 \u0648\u0634\u0627\u0631\u0644-\u062c\u0627\u0646 \u062f\u0648 \u0644\u0627 \u0641\u0627\u0644\u064a\u0647 \u0628\u0648\u0633\u0627\u0646\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u062f\u0648\u0627\u062a \u0645\u0646 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u0642\u062f\u064a. \u0648\u062a\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0645\u0646 \u0627\u0644\u0625\u0646\u062c\u0627\u0632\u0627\u062a \u0627\u0644\u0643\u0628\u0631\u0649 \u0627\u0644\u062a\u064a \u0631\u0628\u0637\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0628\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a.<\/p>\n<h2>\u0625\u0642\u0644\u064a\u062f\u0633 \u0648\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u0645\u0646 \u0623\u0642\u062f\u0645 \u0648\u0623\u0634\u0647\u0631 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0644\u0627 \u062a\u0646\u062a\u0647\u064a. \u0648\u0642\u062f \u0638\u0647\u0631 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u062a\u0627\u0633\u0639 \u0645\u0646 <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u0627\u0644\u062a\u064a \u064a\u0631\u062c\u0639 \u062a\u0623\u0644\u064a\u0641\u0647\u0627 \u0625\u0644\u0649 \u0646\u062d\u0648 300 \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f. \u0648\u062a\u0648\u0636\u062d \u0627\u0644\u0645\u0635\u0627\u062f\u0631 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0623\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0644\u0645 \u064a\u0635\u063a \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0628\u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062d\u062f\u064a\u062b \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u0629 \u0643\u0645\u0627 \u0646\u0633\u062a\u062e\u062f\u0645\u0647 \u0627\u0644\u064a\u0648\u0645\u060c \u0628\u0644 \u0623\u062b\u0628\u062a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646\u060c \u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0623\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062d\u062f\u062f\u0629 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0639\u062f\u062f \u0623\u0648\u0644\u064a \u0622\u062e\u0631 \u062e\u0627\u0631\u062c\u0647\u0627. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"2|Prime numbers and Euclid|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[2]<\/a><\/sup><\/p>\n<p>\u062a\u0642\u0648\u0645 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0628\u0631\u0647\u0627\u0646 \u0639\u0644\u0649 \u0627\u0641\u062a\u0631\u0627\u0636 \u0648\u062c\u0648\u062f \u0642\u0627\u0626\u0645\u0629 \u0645\u0646\u062a\u0647\u064a\u0629 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u062b\u0645 \u0636\u0631\u0628 \u062c\u0645\u064a\u0639 \u0639\u0646\u0627\u0635\u0631\u0647\u0627 \u0648\u0625\u0636\u0627\u0641\u0629 1. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0646\u0627\u062a\u062c \u0623\u0648\u0644\u064a\u064b\u0627\u060c \u0641\u0642\u062f \u0638\u0647\u0631 \u0639\u062f\u062f \u0623\u0648\u0644\u064a \u062c\u062f\u064a\u062f. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0631\u0643\u0628\u064b\u0627\u060c \u0641\u0625\u0646 \u0644\u0647 \u0639\u0627\u0645\u0644\u064b\u0627 \u0623\u0648\u0644\u064a\u064b\u0627 \u0644\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0648\u0627\u062d\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0627\u0644\u0642\u0627\u0626\u0645\u0629\u061b \u0644\u0623\u0646 \u0642\u0633\u0645\u0629 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u062c\u062f\u064a\u062f \u0639\u0644\u0649 \u0623\u064a \u0639\u0627\u0645\u0644 \u0645\u0646 \u0639\u0648\u0627\u0645\u0644 \u062d\u0627\u0635\u0644 \u0627\u0644\u0636\u0631\u0628 \u062a\u062a\u0631\u0643 \u0628\u0627\u0642\u064a\u064b\u0627 \u0645\u0642\u062f\u0627\u0631\u0647 1. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0644\u0627 \u064a\u0645\u0643\u0646 \u0644\u0623\u064a \u0642\u0627\u0626\u0645\u0629 \u0645\u0646\u062a\u0647\u064a\u0629 \u0623\u0646 \u062a\u062d\u062a\u0648\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/p>\n<blockquote><p>\n\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0623\u064a \u0639\u062f\u062f \u0645\u062d\u062f\u062f \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<br \/>\n<strong>\u2014 \u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0643\u062a\u0627\u0628 \u0627\u0644\u0639\u0646\u0627\u0635\u0631\u060c \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u062a\u0627\u0633\u0639\u060c \u0646\u062d\u0648 300 \u0642.\u0645.<\/strong>\n<\/p><\/blockquote>\n<p>\u0648\u062a\u064f\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u062d\u062c\u0629 \u0645\u0646 \u0627\u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0644\u0644\u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0644\u062e\u0644\u0641\u060c \u0643\u0645\u0627 \u0623\u0646\u0647\u0627 \u062a\u0643\u0634\u0641 \u0625\u062d\u062f\u0649 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0639\u0645\u064a\u0642\u0629 \u0644\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629: \u0645\u0647\u0645\u0627 \u0627\u0645\u062a\u062f \u0627\u0644\u0628\u062d\u062b \u0641\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0641\u0644\u0627 \u062a\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u0646\u0647\u0627\u0626\u064a\u0629 \u0644\u0647\u0627.<\/p>\n<h2>\u0645\u0646\u062e\u0644 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633<\/h2>\n<p>\u0645\u0646 \u0623\u0642\u062f\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u00ab\u0645\u0646\u062e\u0644 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633\u00bb\u060c \u0627\u0644\u0630\u064a \u0627\u0631\u062a\u0628\u0637 \u0628\u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f \u062a\u0642\u0631\u064a\u0628\u064b\u0627. \u062a\u0642\u0648\u0645 \u0627\u0644\u0641\u0643\u0631\u0629 \u0639\u0644\u0649 \u0643\u062a\u0627\u0628\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u062d\u062a\u0649 \u062d\u062f \u0645\u0639\u064a\u0646\u060c \u062b\u0645 \u062d\u0630\u0641 \u0645\u0636\u0627\u0639\u0641\u0627\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0628\u062a\u062f\u0627\u0621\u064b \u0645\u0646 2\u060c \u062b\u0645 3\u060c \u062b\u0645 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0648\u0644\u064a \u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0648\u0647\u0643\u0630\u0627. \u0648\u0645\u0627 \u064a\u0628\u0642\u0649 \u0628\u0639\u062f \u0625\u0632\u0627\u0644\u0629 \u0627\u0644\u0645\u0631\u0643\u0628\u0627\u062a \u064a\u0643\u0648\u0646 \u0623\u0639\u062f\u0627\u062f\u064b\u0627 \u0623\u0648\u0644\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"3|Sieve of Eratosthenes|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[3]<\/a><\/sup><\/p>\n<p>\u0648\u062a\u0643\u0645\u0646 \u0642\u0648\u0629 \u0627\u0644\u0645\u0646\u062e\u0644 \u0641\u064a \u0628\u0633\u0627\u0637\u062a\u0647: \u0641\u0628\u062f\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0644 \u0639\u062f\u062f \u0628\u0635\u0648\u0631\u0629 \u0645\u0633\u062a\u0642\u0644\u0629\u060c \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0644\u0645\u0643\u062a\u0634\u0641\u0629 \u0644\u0625\u0632\u0627\u0644\u0629 \u0645\u0636\u0627\u0639\u0641\u0627\u062a\u0647\u0627 \u0645\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u0629. \u0648\u0642\u062f \u0623\u0635\u0628\u062d\u062a \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u0623\u0633\u0627\u0633\u064b\u0627 \u062a\u0627\u0631\u064a\u062e\u064a\u064b\u0627 \u0645\u0647\u0645\u064b\u0627 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062a\u0648\u0644\u064a\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/p>\n<h2>\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629<\/h2>\n<p>\u062a\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0639\u0644\u0649 \u0623\u0646 \u0643\u0644 \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0623\u0643\u0628\u0631 \u0645\u0646 1 \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u062a\u0647 \u0639\u0644\u0649 \u0635\u0648\u0631\u0629 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0623\u0639\u062f\u0627\u062f \u0623\u0648\u0644\u064a\u0629\u060c \u0648\u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0648\u062d\u064a\u062f \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0639\u0648\u0627\u0645\u0644. \u0648\u0642\u062f \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0645\u0639\u0631\u0648\u0641\u0629 \u0641\u064a \u0635\u0648\u0631\u0629 \u0645\u0628\u0643\u0631\u0629 \u0636\u0645\u0646 <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u0644\u0625\u0642\u0644\u064a\u062f\u0633\u060c \u062d\u064a\u062b \u062a\u0638\u0647\u0631 \u0646\u062a\u0627\u0626\u062c \u062a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0648\u0627\u0644\u0642\u0633\u0645\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"4|Euclid and the Fundamental Theorem of Arithmetic|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[4]<\/a><\/sup><\/p>\n<p>\u0641\u0645\u062b\u0644\u064b\u0627:<\/p>\n<p><em>360 = 2\u00b3 \u00d7 3\u00b2 \u00d7 5<\/em><\/p>\n<p>\u0648\u0644\u0627 \u062a\u0648\u062c\u062f \u0637\u0631\u064a\u0642\u0629 \u0623\u062e\u0631\u0649 \u0644\u062a\u062d\u0644\u064a\u0644 360 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644 \u0623\u0648\u0644\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629 \u0639\u0646 \u0647\u0630\u0647 \u0625\u0644\u0627 \u0628\u062a\u063a\u064a\u064a\u0631 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0639\u0648\u0627\u0645\u0644. \u0648\u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u062a\u062c\u0639\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0634\u0628\u064a\u0647\u0629 \u0628\u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0628\u0646\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629\u061b \u0641\u0627\u0644\u0636\u0631\u0628 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0628\u0646\u064a \u0645\u0646\u0647\u0627 \u062c\u0645\u064a\u0639 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\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0645\u0646 \u0623\u0639\u0638\u0645 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629. \u0648\u0647\u064a \u0644\u0627 \u062a\u0639\u0637\u064a \u0642\u0627\u0626\u0645\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0628\u0644 \u062a\u0635\u0641 \u0639\u062f\u062f\u0647\u0627 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a \u062d\u062a\u0649 \u062d\u062f \u0645\u0639\u064a\u0646. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <em>\u03c0(x)<\/em> \u062a\u0645\u062b\u0644 \u0639\u062f\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0644\u0623\u0635\u063a\u0631 \u0645\u0646 \u0623\u0648 \u0627\u0644\u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u0640<em>x<\/em>\u060c \u0641\u0625\u0646:<\/p>\n<p><em>\u03c0(x) ~ x \/ ln x<\/em><\/p>\n<p>\u0648\u064a\u0631\u0645\u0632 \u0627\u0644\u0631\u0645\u0632 <em>~<\/em> \u0647\u0646\u0627 \u0625\u0644\u0649 \u0623\u0646 \u0646\u0633\u0628\u0629 \u0627\u0644\u0637\u0631\u0641\u064a\u0646 \u062a\u0642\u062a\u0631\u0628 \u0645\u0646 1 \u0639\u0646\u062f\u0645\u0627 \u064a\u0642\u062a\u0631\u0628 <em>x<\/em> \u0645\u0646 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u0648\u062a\u0643\u0634\u0641 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0623\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u062a\u0635\u0628\u062d \u0623\u0642\u0644 \u0643\u062b\u0627\u0641\u0629 \u0646\u0633\u0628\u064a\u064b\u0627 \u0643\u0644\u0645\u0627 \u0643\u0628\u0631\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0645\u0639 \u0627\u0633\u062a\u0645\u0631\u0627\u0631 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\u0648\u0642\u062f \u0634\u0643\u0644\u062a \u0623\u0639\u0645\u0627\u0644\u0647\u0645\u0627 \u0645\u0631\u062d\u0644\u0629 \u062d\u0627\u0633\u0645\u0629 \u0641\u064a \u062a\u0637\u0648\u0631 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629.<\/p>\n<h2>\u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u0644\u0631\u064a\u0645\u0627\u0646<\/h2>\n<p>\u062a\u062d\u062a\u0644 \u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u0644\u0631\u064a\u0645\u0627\u0646 \u0645\u0643\u0627\u0646\u0629 \u0645\u062d\u0648\u0631\u064a\u0629 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629. \u0648\u062a\u064f\u0639\u0631\u0651\u0641 \u0641\u064a \u0646\u0637\u0627\u0642\u0647\u0627 \u0627\u0644\u0623\u0648\u0644\u064a \u0628\u0627\u0644\u062a\u0639\u0628\u064a\u0631:<\/p>\n<p><em>\u03b6(s) = \u03a3 1\/n<sup>s<\/sup><\/em><\/p>\n<p>\u0643\u0645\u0627 \u062a\u0631\u062a\u0628\u0637 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0639\u0628\u0631 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0623\u0648\u064a\u0644\u0631:<\/p>\n<p><em>\u03b6(s) = \u220f<sub>p prime<\/sub> (1 \u2212 p<sup>\u2212s<\/sup>)<sup>\u22121<\/sup><\/em><\/p>\n<p>\u0648\u062a\u0648\u0636\u062d \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0623\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u0648\u0632\u0639\u0629 \u0639\u0634\u0648\u0627\u0626\u064a\u064b\u0627 \u0628\u0627\u0644\u0643\u0627\u0645\u0644\u060c \u0628\u0644 \u062a\u0631\u062a\u0628\u0637 \u0628\u0628\u0646\u064a\u0629 \u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0639\u0645\u064a\u0642\u0629. \u0648\u0642\u062f \u062c\u0639\u0644 \u0631\u064a\u0645\u0627\u0646 \u0645\u0646 \u062f\u0631\u0627\u0633\u0629 \u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u0648\u0627\u0644\u0623\u0635\u0641\u0627\u0631 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0644\u0647\u0627 \u0623\u062f\u0627\u0629 \u0645\u0631\u0643\u0632\u064a\u0629 \u0644\u0641\u0647\u0645 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/p>\n<h2>\u0641\u0631\u0636\u064a\u0629 \u0631\u064a\u0645\u0627\u0646<\/h2>\n<p>\u0641\u0631\u0636\u064a\u0629 \u0631\u064a\u0645\u0627\u0646 \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u0641\u062a\u0648\u062d\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a. \u0627\u0642\u062a\u0631\u062d \u0628\u0631\u0646\u0627\u0631\u062f \u0631\u064a\u0645\u0627\u0646 \u0633\u0646\u0629 1859 \u0623\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0635\u0641\u0627\u0631 \u063a\u064a\u0631 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 \u0644\u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u062a\u0642\u0639 \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0630\u064a \u064a\u0643\u0648\u0646 \u0641\u064a\u0647 \u0627\u0644\u062c\u0632\u0621 \u0627\u0644\u062d\u0642\u064a\u0642\u064a \u0644\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0631\u0643\u0628 \u0645\u0633\u0627\u0648\u064a\u064b\u0627 \u0644\u06401\/2. \u0648\u062a\u0648\u062c\u062f \u0635\u0644\u0629 \u0639\u0645\u064a\u0642\u0629 \u0628\u064a\u0646 \u0645\u0648\u0642\u0639 \u0647\u0630\u0647 \u0627\u0644\u0623\u0635\u0641\u0627\u0631 \u0648\u062f\u0642\u0629 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/p>\n<p>\u0644\u0627 \u062a\u0639\u0646\u064a \u0641\u0631\u0636\u064a\u0629 \u0631\u064a\u0645\u0627\u0646 \u0623\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0646\u0641\u0633\u0647\u0627 \u062a\u062a\u0628\u0639 \u0646\u0645\u0637\u064b\u0627 \u0628\u0633\u064a\u0637\u064b\u0627\u060c \u0648\u0625\u0646\u0645\u0627 \u062a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u062f\u0642\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0628\u0647\u0627 \u0648\u0635\u0641 \u0627\u0646\u062d\u0631\u0627\u0641 \u062a\u0648\u0632\u064a\u0639\u0647\u0627 \u0639\u0646 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0630\u064a \u062a\u062d\u062f\u062f\u0647 \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629. \u0648\u0642\u062f \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u062c\u0632\u0621\u064b\u0627 \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0644\u0641\u064a\u0629 \u0627\u0644\u062a\u064a \u062e\u0635\u0635 \u0644\u0647\u0627 \u0645\u0639\u0647\u062f \u0643\u0644\u0627\u064a \u0644\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u062c\u0627\u0626\u0632\u0629 \u0642\u062f\u0631\u0647\u0627 \u0645\u0644\u064a\u0648\u0646 \u062f\u0648\u0644\u0627\u0631 \u0644\u0643\u0644 \u0645\u0633\u0623\u0644\u0629 \u062a\u064f\u062d\u0644 \u0648\u0641\u0642 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0644\u0644\u0645\u0633\u0627\u0628\u0642\u0629. <sup class=\"ref\"><a href=\"https:\/\/www.claymath.org\/millennium-problems\/riemann-hypothesis\/\" title=\"5|Riemann Hypothesis|Clay Mathematics Institute|2026\" target=\"_blank\" rel=\"noopener\">[5]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629<\/h2>\n<p>\u062a\u0644\u0639\u0628 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u062f\u0648\u0631\u064b\u0627 \u0645\u0647\u0645\u064b\u0627 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629\u060c \u0648\u0647\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0639\u062f\u062f \u0645\u0639\u064a\u0646. \u0648\u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0642\u0633\u0648\u0645 \u0639\u0644\u064a\u0647 \u0639\u062f\u062f\u064b\u0627 \u0623\u0648\u0644\u064a\u064b\u0627 <em>p<\/em>\u060c \u062a\u0635\u0628\u062d \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0644\u0644\u0628\u0648\u0627\u0642\u064a \u0623\u0643\u062b\u0631 \u0627\u0646\u062a\u0638\u0627\u0645\u064b\u0627\u060c \u0625\u0630 \u062a\u0634\u0643\u0644 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u063a\u064a\u0631 \u0627\u0644\u0635\u0641\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a \u0628\u062a\u0631\u062f\u064a\u062f <em>p<\/em> \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0636\u0631\u0648\u0628\u064a\u0629.<\/p>\n<p>\u0648\u0645\u0646 \u0647\u0646\u0627 \u0638\u0647\u0631\u062a \u0646\u062a\u0627\u0626\u062c \u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u064a\u0631\u0645\u0627 \u0627\u0644\u0635\u063a\u0631\u0649\u060c \u0627\u0644\u062a\u064a \u062a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 <em>p<\/em> \u0639\u062f\u062f\u064b\u0627 \u0623\u0648\u0644\u064a\u064b\u0627 \u0648\u0644\u0627 \u064a\u0642\u0633\u0645 <em>a<\/em>\u060c \u0641\u0625\u0646:<\/p>\n<p><em>a<sup>p\u22121<\/sup> \u2261 1 (mod p)<\/em><\/p>\n<p>\u0648\u0642\u062f \u0623\u0635\u0628\u062d\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u062c\u0632\u0621\u064b\u0627 \u0623\u0633\u0627\u0633\u064a\u064b\u0627 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0648\u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629.<\/p>\n<h2>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u064a\u0631\u0645\u0627 \u0627\u0644\u0635\u063a\u0631\u0649<\/h2>\n<p>\u062a\u0639\u062f \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u064a\u0631\u0645\u0627 \u0627\u0644\u0635\u063a\u0631\u0649 \u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646 <em>p<\/em> \u0639\u062f\u062f\u064b\u0627 \u0623\u0648\u0644\u064a\u064b\u0627 \u0648\u0643\u0627\u0646 <em>a<\/em> \u063a\u064a\u0631 \u0642\u0627\u0628\u0644 \u0644\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 <em>p<\/em>\u060c \u0641\u0625\u0646 \u0631\u0641\u0639 <em>a<\/em> \u0625\u0644\u0649 \u0627\u0644\u0642\u0648\u0629 <em>p\u22121<\/em> \u064a\u0639\u0637\u064a \u0628\u0627\u0642\u064a\u064b\u0627 \u0645\u0642\u062f\u0627\u0631\u0647 1 \u0639\u0646\u062f \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 <em>p<\/em>. \u0648\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0641\u064a \u0628\u0639\u0636 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0641\u064a \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629.<\/p>\n<p>\u0644\u0643\u0646 \u0627\u0644\u0639\u0643\u0633 \u0644\u064a\u0633 \u0635\u062d\u064a\u062d\u064b\u0627 \u0628\u0635\u0648\u0631\u0629 \u0639\u0627\u0645\u0629: \u0646\u062c\u0627\u062d \u0627\u062e\u062a\u0628\u0627\u0631 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u064a\u0631\u0645\u0627 \u0644\u0627 \u064a\u0636\u0645\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0623\u0646 \u0627\u0644\u0639\u062f\u062f \u0623\u0648\u0644\u064a\u060c \u0644\u0623\u0646 \u0647\u0646\u0627\u0643 \u0623\u0639\u062f\u0627\u062f\u064b\u0627 \u0645\u0631\u0643\u0628\u0629 \u0642\u062f \u062a\u062a\u0635\u0631\u0641 \u0641\u064a \u0628\u0639\u0636 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0641\u064a\u0631\u0645\u0627 \u0643\u0645\u0627 \u0644\u0648 \u0643\u0627\u0646\u062a \u0623\u0648\u0644\u064a\u0629. \u0648\u0644\u0647\u0630\u0627 \u0637\u064f\u0648\u0631\u062a \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0623\u0643\u062b\u0631 \u0642\u0648\u0629.<\/p>\n<h2>\u0623\u0639\u062f\u0627\u062f \u0645\u064a\u0631\u0633\u064a\u0646 \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u0623\u0639\u062f\u0627\u062f \u0645\u064a\u0631\u0633\u064a\u0646 \u0647\u064a \u0623\u0639\u062f\u0627\u062f \u0645\u0646 \u0627\u0644\u0634\u0643\u0644:<\/p>\n<p><em>M<sub>p<\/sub> = 2<sup>p<\/sup> \u2212 1<\/em><\/p>\n<p>\u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 <em>M<sub>p<\/sub><\/em> \u0623\u0648\u0644\u064a\u064b\u0627\u060c \u064a\u0633\u0645\u0649 \u00ab\u0639\u062f\u062f \u0645\u064a\u0631\u0633\u064a\u0646 \u0623\u0648\u0644\u064a\u064b\u0627\u00bb. \u0648\u0645\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0623\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 <em>2<sup>p<\/sup> \u2212 1<\/em> \u0623\u0648\u0644\u064a\u064b\u0627\u060c \u0641\u0644\u0627 \u0628\u062f \u0623\u0646 \u064a\u0643\u0648\u0646 <em>p<\/em> \u0646\u0641\u0633\u0647 \u0623\u0648\u0644\u064a\u064b\u0627. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0644\u064a\u0633 \u0643\u0644 \u0623\u0633 \u0623\u0648\u0644\u064a \u064a\u0646\u062a\u062c \u0639\u062f\u062f \u0645\u064a\u0631\u0633\u064a\u0646 \u0623\u0648\u0644\u064a\u064b\u0627.<\/p>\n<p>\u0648\u062a\u0631\u062a\u0628\u0637 \u0623\u0639\u062f\u0627\u062f \u0645\u064a\u0631\u0633\u064a\u0646 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629 \u0627\u0644\u0632\u0648\u062c\u064a\u0629. \u0641\u0642\u062f \u0623\u062b\u0628\u062a \u0625\u0642\u0644\u064a\u062f\u0633 \u0641\u064a <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u0635\u064a\u063a\u0629 \u062a\u0631\u0628\u0637 \u0639\u062f\u062f\u064b\u0627 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629\u060c \u062b\u0645 \u0623\u062b\u0628\u062a \u0623\u0648\u064a\u0644\u0631 \u0628\u0639\u062f \u0623\u0643\u062b\u0631 \u0645\u0646 \u0623\u0644\u0641\u064a \u0639\u0627\u0645 \u0623\u0646 \u0643\u0644 \u0639\u062f\u062f \u0645\u062b\u0627\u0644\u064a \u0632\u0648\u062c\u064a \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0645\u0646 \u0635\u064a\u063a\u0629 \u0645\u0646 \u0646\u0645\u0637 \u0645\u064a\u0631\u0633\u064a\u0646 \u0627\u0644\u0645\u0646\u0627\u0633\u0628. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"6|Prime numbers and Mersenne primes|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[6]<\/a><\/sup><\/p>\n<h2>\u0623\u0639\u062f\u0627\u062f \u0641\u064a\u0631\u0645\u0627<\/h2>\n<p>\u0627\u0642\u062a\u0631\u062d \u0628\u064a\u064a\u0631 \u062f\u0648 \u0641\u064a\u0631\u0645\u0627 \u0623\u0639\u062f\u0627\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0634\u0643\u0644:<\/p>\n<p><em>F<sub>n<\/sub> = 2<sup>2<sup>n<\/sup><\/sup> + 1<\/em><\/p>\n<p>\u0648\u0643\u0627\u0646\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u0649 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0645\u062b\u0627\u0631 \u0627\u0647\u062a\u0645\u0627\u0645 \u0643\u0628\u064a\u0631 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f. \u0648\u0642\u062f \u0623\u062b\u0628\u062a \u0641\u064a\u0631\u0645\u0627 \u0623\u0646 \u0628\u0639\u0636 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u0649 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0623\u0648\u0644\u064a\u0629\u060c \u0644\u0643\u0646 \u0627\u062a\u0636\u062d \u0644\u0627\u062d\u0642\u064b\u0627 \u0623\u0646 \u0643\u062b\u064a\u0631\u064b\u0627 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0631\u0643\u0628\u0629. \u0648\u062a\u0642\u062f\u0645 \u0623\u0639\u062f\u0627\u062f \u0641\u064a\u0631\u0645\u0627 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\u0627\u0644\u062a\u0627\u0633\u0639 \u0645\u0646 <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u062a\u0636\u0645\u0646\u062a \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0645\u0646\u0647\u0627 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0648\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/SH\/euclid_sh.pdf\" title=\"7|Euclid and Number Theory|University of St Andrews, MacTutor History of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[7]<\/a><\/sup><\/p>\n<h2>\u062a\u0627\u0631\u064a\u062e \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u0628\u062f\u0623 \u0627\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0627\u0644\u0645\u0646\u0647\u062c\u064a \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a\u0629 \u0627\u0644\u0642\u062f\u064a\u0645\u0629. \u0648\u0642\u062f \u062a\u0646\u0627\u0648\u0644\u062a \u0645\u062f\u0631\u0633\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u062e\u0635\u0627\u0626\u0635 \u0639\u062f\u062f\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u062b\u0645 \u062c\u0627\u0621\u062a \u0623\u0639\u0645\u0627\u0644 \u0625\u0642\u0644\u064a\u062f\u0633 \u0644\u062a\u0642\u062f\u0645 \u0639\u062f\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629. \u0648\u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0627\u0631\u062a\u0628\u0637 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633 \u0628\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0645\u0646\u062e\u0644 \u0627\u0644\u062a\u064a \u062a\u0633\u0645\u062d \u0628\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u062d\u062a\u0649 \u062d\u062f \u0645\u0639\u064a\u0646. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"8|History of Prime Numbers|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[8]<\/a><\/sup><\/p>\n<p>\u0648\u0641\u064a \u0627\u0644\u0639\u0635\u0631 \u0627\u0644\u062d\u062f\u064a\u062b \u062a\u0637\u0648\u0631\u062a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0643\u0628\u064a\u0631\u0629 \u0645\u0639 \u0641\u064a\u0631\u0645\u0627 \u0648\u0623\u0648\u064a\u0644\u0631 \u0648\u063a\u0648\u0633 \u0648\u0644\u064a\u062c\u0627\u0646\u062f\u0631 \u0648\u063a\u064a\u0631\u0647\u0645. \u062b\u0645 \u0623\u062f\u0649 \u0638\u0647\u0648\u0631 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062a\u0627\u0633\u0639 \u0639\u0634\u0631 \u0625\u0644\u0649 \u0646\u0634\u0648\u0621 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0648\u0628\u0644\u063a\u062a \u062f\u0631\u0627\u0633\u0629 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0645\u0631\u062d\u0644\u0629 \u062d\u0627\u0633\u0645\u0629 \u0645\u0639 \u0631\u064a\u0645\u0627\u0646 \u0648\u0623\u062f\u0627\u0645\u0627\u0631 \u0648\u062f\u0648 \u0644\u0627 \u0641\u0627\u0644\u064a\u0647 \u0628\u0648\u0633\u0627\u0646.<\/p>\n<h2>\u0623\u0648\u064a\u0644\u0631 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u0643\u0627\u0646 \u0644\u064a\u0648\u0646\u0647\u0627\u0631\u062a \u0623\u0648\u064a\u0644\u0631 \u0645\u0646 \u0623\u0643\u062b\u0631 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u064a\u0646 \u062a\u0623\u062b\u064a\u0631\u064b\u0627 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f. \u0648\u0642\u062f \u062f\u0631\u0633 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0639\u0644\u0627\u0642\u0627\u062a\u0647\u0627 \u0628\u0627\u0644\u0645\u062a\u0633\u0644\u0633\u0644\u0627\u062a \u0648\u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u0623\u0633\u0647\u0645 \u0628\u0635\u0648\u0631\u0629 \u0645\u0647\u0645\u0629 \u0641\u064a \u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u0635\u064a\u0627\u063a\u0627\u062a \u0627\u0644\u062a\u064a \u0623\u0635\u0628\u062d\u062a \u0644\u0627\u062d\u0642\u064b\u0627 \u062c\u0632\u0621\u064b\u0627 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629. \u0648\u062a\u0639\u062f \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0623\u0648\u064a\u0644\u0631 \u0644\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u0645\u0646 \u0623\u0647\u0645 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u064a \u062a\u0648\u0636\u062d \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0645\u0636\u0627\u0639\u0641\u0629 \u0644\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629.<\/p>\n<p>\u0643\u0645\u0627 \u0623\u062b\u0628\u062a \u0623\u0648\u064a\u0644\u0631 \u0646\u062a\u064a\u062c\u0629 \u0645\u0647\u0645\u0629 \u062d\u0648\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629 \u0627\u0644\u0632\u0648\u062c\u064a\u0629\u060c \u0645\u0648\u0636\u062d\u064b\u0627 \u0623\u0646 \u0643\u0644 \u0639\u062f\u062f \u0645\u062b\u0627\u0644\u064a \u0632\u0648\u062c\u064a \u064a\u0631\u062a\u0628\u0637 \u0628\u0639\u062f\u062f \u0623\u0648\u0644\u064a \u0645\u0646 \u0646\u0648\u0639 \u0645\u064a\u0631\u0633\u064a\u0646 \u0648\u0641\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629. \u0648\u0642\u062f \u0631\u0628\u0637 \u0630\u0644\u0643 \u0628\u064a\u0646 \u0645\u0648\u0636\u0648\u0639\u064a\u0646 \u0642\u062f \u064a\u0628\u062f\u0648\u0627\u0646 \u0645\u0646\u0641\u0635\u0644\u064a\u0646: \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0628\u0646\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u062b\u0627\u0644\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"9|Euler and Prime Numbers|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[9]<\/a><\/sup><\/p>\n<h2>\u063a\u0627\u0648\u0633 \u0648\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u0627\u0631\u062a\u0628\u0637 \u0643\u0627\u0631\u0644 \u0641\u0631\u064a\u062f\u0631\u064a\u0634 \u063a\u0627\u0648\u0633 \u0628\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0628\u0627\u0644\u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0628\u0643\u0631\u0629 \u0644\u0639\u062f\u062f\u0647\u0627. \u0648\u0642\u062f \u0644\u0627\u062d\u0638\u060c \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u062d\u0633\u0627\u0628\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u0648\u0627\u0633\u0639\u0629\u060c \u0623\u0646 \u0639\u062f\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u062d\u062a\u0649 \u062d\u062f \u0645\u0639\u064a\u0646 \u064a\u0631\u062a\u0628\u0637 \u0628\u0635\u0648\u0631\u0629 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0628\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a. \u0648\u0623\u0633\u0647\u0645\u062a \u0647\u0630\u0647 \u0627\u0644\u0623\u0641\u0643\u0627\u0631 \u0641\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0630\u064a \u0627\u0646\u062a\u0647\u0649 \u0625\u0644\u0649 \u0627\u0644\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 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\u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u062a\u0648\u0632\u064a\u0639\u0647\u0627 \u0648\u0641\u062c\u0648\u0627\u062a\u0647\u0627 \u0648\u0639\u0644\u0627\u0642\u062a\u0647\u0627 \u0628\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u062a\u0642\u0648\u062f \u0625\u0644\u0649 \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0645\u062a\u0642\u062f\u0645\u0629 \u062c\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.<\/p>\n<p>\u0641\u0645\u0646 \u062c\u0647\u0629\u060c \u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0628\u062d\u062c\u0629 \u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0642\u0635\u064a\u0631\u0629. \u0648\u0645\u0646 \u062c\u0647\u0629 \u0623\u062e\u0631\u0649\u060c \u0645\u0627 \u062a\u0632\u0627\u0644 \u0645\u0633\u0627\u0626\u0644 \u0639\u0645\u064a\u0642\u0629 \u0645\u062b\u0644 \u0641\u0631\u0636\u064a\u0629 \u0631\u064a\u0645\u0627\u0646 \u0648\u062d\u062f\u0633\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0644\u062a\u0648\u0623\u0645 \u0645\u0641\u062a\u0648\u062d\u0629. \u0648\u0647\u0630\u0627 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0628\u064a\u0646 \u0633\u0647\u0648\u0644\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0648\u0639\u0645\u0642 \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u062a\u064a \u064a\u0648\u0644\u062f\u0647\u0627 \u0647\u0648 \u0623\u062d\u062f \u0627\u0644\u0623\u0633\u0628\u0627\u0628 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062c\u0639\u0644\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0645\u0648\u0636\u0648\u0639\u064b\u0627 \u0645\u0631\u0643\u0632\u064a\u064b\u0627 \u0648\u0645\u0633\u062a\u0645\u0631\u064b\u0627 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.<\/p>\n<h2>\u0627\u0644\u0645\u0631\u0627\u062c\u0639 \u0627\u0644\u0623\u0643\u0627\u062f\u064a\u0645\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629<\/h2>\n<p>\u062a\u064f\u0639\u062f <em>Elements<\/em> \u0644\u0625\u0642\u0644\u064a\u062f\u0633 \u0627\u0644\u0645\u0635\u062f\u0631 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0644\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u0628\u0643\u0631\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0648\u0644\u0627 \u0633\u064a\u0645\u0627 \u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0639 \u0648\u0627\u0644\u062a\u0627\u0633\u0639\u060c \u062d\u064a\u062b \u062a\u0638\u0647\u0631 \u0646\u062a\u0627\u0626\u062c \u062d\u0648\u0644 \u0627\u0644\u0642\u0633\u0645\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644. \u0648\u062a\u0624\u0643\u062f \u0627\u0644\u062f\u0631\u0627\u0633\u0627\u062a \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0623\u0646 <em>\u0627\u0644\u0639\u0646\u0627\u0635\u0631<\/em> \u062a\u0636\u0645\u0646\u062a \u0628\u0627\u0644\u0641\u0639\u0644 \u0623\u062c\u0632\u0627\u0621 \u0645\u0647\u0645\u0629 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0625\u0644\u0649 \u062c\u0627\u0646\u0628 \u0627\u0644\u0647\u0646\u062f\u0633\u0629. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"10|Prime numbers in Euclid&amp;apos;s Elements|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[10]<\/a><\/sup><\/p>\n<p>Bernhard Riemann\u060c \u00ab\u00dcber die Anzahl der Primzahlen unter einer gegebenen Gr\u00f6sse\u00bb\u060c 1859\u060c \u0648\u0647\u0648 \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a \u0627\u0644\u0630\u064a \u0648\u0636\u0639 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u062f\u0627\u0644\u0629 \u0632\u064a\u062a\u0627 \u0641\u064a \u0645\u0631\u0643\u0632 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629. \u0648\u0642\u062f \u0634\u0643\u0644 \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0623\u0633\u0627\u0633\u064b\u0627 \u0644\u0645\u0633\u0627\u0631 \u0643\u0627\u0645\u0644 \u0645\u0646 \u0627\u0644\u0623\u0628\u062d\u0627\u062b \u062d\u0648\u0644 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/p>\n<p>Harald Davenport\u060c <em>Multiplicative Number Theory<\/em>\u060c Springer\u060c \u0648\u0647\u0648 \u0645\u0631\u062c\u0639 \u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0636\u0631\u0628\u064a\u0629\u060c \u064a\u062a\u0646\u0627\u0648\u0644 \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0639\u0645\u064a\u0642\u0629 \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629.<\/p>\n<p>G. H. Hardy \u0648E. M. Wright\u060c <em>An Introduction to the Theory of Numbers<\/em>\u060c Oxford University Press\u060c \u0648\u0647\u0648 \u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u0645\u0631\u0627\u062c\u0639 \u0627\u0644\u062c\u0627\u0645\u0639\u064a\u0629 \u0648\u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0648\u064a\u063a\u0637\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u5408\u540c\u0627\u062a \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0648\u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0639\u062f\u064a\u062f\u0629 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f.<\/p>\n<p>Tom M. Apostol\u060c <em>Introduction to Analytic Number Theory<\/em>\u060c Springer\u060c \u0648\u0647\u0648 \u0645\u0631\u062c\u0639 \u062c\u0627\u0645\u0639\u064a \u0645\u0639\u0631\u0648\u0641 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0648\u064a\u0642\u062f\u0645 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u0633\u0644\u0633\u0644\u0627\u062a \u0648\u062f\u0648\u0627\u0644 \u0632\u064a\u062a\u0627.<\/p>\n<p>\u0648\u0642\u062f \u062d\u0641\u0638\u062a \u0627\u0644\u0645\u0635\u0627\u062f\u0631 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0644\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0645\u0643\u0627\u0646\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0648\u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633 \u0648\u0641\u064a\u0631\u0645\u0627 \u0648\u0623\u0648\u064a\u0644\u0631 \u0648\u063a\u0627\u0648\u0633 \u0648\u0631\u064a\u0645\u0627\u0646 \u0648\u063a\u064a\u0631\u0647\u0645 \u0641\u064a \u062a\u0637\u0648\u0631 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u0623\u0635\u0628\u062d\u062a \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062a\u0627\u0633\u0639 \u0639\u0634\u0631 \u0648\u0627\u0644\u0639\u0634\u0631\u064a\u0646 \u0623\u0633\u0627\u0633\u064b\u0627 \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629. <sup class=\"ref\"><a href=\"https:\/\/mathshistory.st-andrews.ac.uk\/HistTopics\/Prime_numbers\/\" title=\"11|Historical development of prime number theory|University of St Andrews, MacTutor History of Mathematics|2018\" target=\"_blank\" rel=\"noopener\">[11]<\/a><\/sup><\/p>\n<\/article>\n","protected":false},"excerpt":{"rendered":"<p>\u0644\u0628\u0646\u0627\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629<\/p>\n","protected":false},"author":1,"featured_media":4539,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[],"class_list":["post-4540","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-basic-sciences"],"_links":{"self":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4540","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/comments?post=4540"}],"version-history":[{"count":1,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4540\/revisions"}],"predecessor-version":[{"id":4541,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4540\/revisions\/4541"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media\/4539"}],"wp:attachment":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media?parent=4540"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/categories?post=4540"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/tags?post=4540"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}