{"id":4568,"date":"2017-06-28T10:11:00","date_gmt":"2017-06-28T10:11:00","guid":{"rendered":"http:\/\/club.informatix.co.jp\/?p=4568"},"modified":"2024-04-30T05:48:14","modified_gmt":"2024-04-30T05:48:14","slug":"%e4%ba%ba%e3%81%a8%e6%98%9f%e3%81%a8%e3%81%a8%e3%82%82%e3%81%ab%e3%81%82%e3%82%8b%e6%95%b0%e5%ad%a6%e3%80%80%e7%ac%ac18%e5%9b%9e","status":"publish","type":"post","link":"https:\/\/club.informatix.co.jp\/?p=4568","title":{"rendered":"\u7d20\u6570\u306e\u7a2e\u985e\uff5c\u540d\u79f0\u306b\u4eba\u540d\u304c\u4ed8\u3044\u305f\u7d20\u6570"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u76ee\u6b21<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a109f58cc1d0\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a109f58cc1d0\" checked aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%81%AF%E3%81%98%E3%82%81%E3%81%AB\" >\u306f\u3058\u3081\u306b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%83%A1%E3%83%AB%E3%82%BB%E3%83%B3%E3%83%8C%E7%B4%A0%E6%95%B0\" >\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%82%BD%E3%83%95%E3%82%A3%E3%83%BC%E3%83%BB%E3%82%B8%E3%82%A7%E3%83%AB%E3%83%9E%E3%83%B3%E7%B4%A0%E6%95%B0\" >\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%83%97%E3%83%AD%E3%82%B9%E7%B4%A0%E6%95%B0\" >\u30d7\u30ed\u30b9\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%82%AB%E3%83%AC%E3%83%B3%E7%B4%A0%E6%95%B0\" >\u30ab\u30ec\u30f3\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%82%A6%E3%82%A9%E3%83%BC%E3%83%AB-%E3%82%B5%E3%83%B3-%E3%82%B5%E3%83%B3%E7%B4%A0%E6%95%B0\" >\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%83%B4%E3%82%A3%E3%83%BC%E3%83%95%E3%82%A7%E3%83%AA%E3%83%83%E3%83%92%E7%B4%A0%E6%95%B0\" >\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%82%A6%E3%82%A3%E3%83%AB%E3%82%BD%E3%83%B3%E7%B4%A0%E6%95%B0\" >\u30a6\u30a3\u30eb\u30bd\u30f3\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E3%82%A6%E3%82%A9%E3%83%AB%E3%82%B9%E3%83%86%E3%83%B3%E3%83%9B%E3%83%AB%E3%83%A0%E7%B4%A0%E6%95%B0\" >\u30a6\u30a9\u30eb\u30b9\u30c6\u30f3\u30db\u30eb\u30e0\u7d20\u6570<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/club.informatix.co.jp\/?p=4568\/#%E6%9C%AA%E7%9F%A5%E3%81%AE%E7%B4%A0%E6%95%B0%E3%81%AE%E6%AD%A3%E4%BD%93%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6\" >\u672a\u77e5\u306e\u7d20\u6570\u306e\u6b63\u4f53\u3092\u6c42\u3081\u3066<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%AF%E3%81%98%E3%82%81%E3%81%AB\"><\/span>\u306f\u3058\u3081\u306b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7d00\u5143\u524d300\u5e74\u3001\u53e4\u4ee3\u30ae\u30ea\u30b7\u30e3\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306f\u3001<a href=\"https:\/\/club.informatix.co.jp\/?p=4737\" target=\"_blank\" rel=\"noopener\">\u7d20\u6570<\/a>\u304c\u7121\u9650\u500b\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u3066\u307f\u305b\u307e\u3057\u305f\u3002<\/p>\n<p>\u7121\u9650\u500b\u3042\u308b\u81ea\u7136\u6570\u306e\u4e2d\u306b\u7121\u9650\u500b\u3042\u308b\u7d20\u6570\u3001\u305d\u306e\u5206\u5e03\u3092\u30c6\u30fc\u30de\u306b\u3059\u308b\u306e\u304c\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3067\u3059\u3002<\/p>\n<p>\u300c<a href=\"https:\/\/club.informatix.co.jp\/?p=3830\">\u8d85\u5165\u9580\u3000\u30ea\u30fc\u30de\u30f3\u4e88\u60f3<\/a>\u300d\u51684\u56de\u3067\u306f\u3001\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u304c\u6559\u3048\u308b\u6570\u306e\u4e16\u754c\u306e\u6df1\u6df5\u3055\u3092\u8997\u3044\u3066\u307f\u307e\u3057\u305f\u3002\u898b\u3048\u3066\u304f\u308b\u98a8\u666f\u306f\u3001\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u3067\u3042\u308b\u7d20\u6570\u306e\u96e3\u3057\u3055\u3067\u3059\u3002<\/p>\n<p>\u4eca\u56de\u306f\u8da3\u5411\u3092\u5909\u3048\u3066\u4eba\u985e\u304c\u7d20\u6570\u306b\u6311\u3093\u3067\u304d\u305f\u8ecc\u8de1\u3092\u632f\u308a\u8fd4\u3063\u3066\u307f\u3088\u3046\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u7d20\u6570\u306e\u7a2e\u985e\u306e\u591a\u3055\u304c\u3001\u3044\u304b\u306b\u7d20\u6570\u304c\u63a2\u7a76\u3055\u308c\u3066\u304d\u305f\u306e\u304b\u3092\u5982\u5b9f\u306b\u7269\u8a9e\u308a\u307e\u3059\u3002<a title=\"\u4eba\u3068\u661f\u3068\u3068\u3082\u306b\u3042\u308b\u6570\u5b66\u3000\u7b2c17\u56de\" href=\"http:\/\/club.informatix.co.jp\/?p=4529\" target=\"_blank\" rel=\"noopener noreferrer\">\u300c\u9055\u6cd5\u306a\u7d20\u6570\u300d<\/a>\u3082\u305d\u306e\u4e00\u4f8b\u3067\u3059\u304c\u3001\u4eca\u56de\u306f\u4eba\u306e\u540d\u524d\u304c\u4ed8\u3044\u305f\u7d20\u6570\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%83%A1%E3%83%AB%E3%82%BB%E3%83%B3%E3%83%8C%E7%B4%A0%E6%95%B0\"><\/span>\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>17\u4e16\u7d00\u3001\u30d5\u30e9\u30f3\u30b9\u306e\u4fee\u9053\u50e7\u30de\u30e9\u30f3\u30fb\u30e1\u30eb\u30bb\u30f3\u30cc\uff081588-1648\uff09\u306f\u30012<sup>n<\/sup>-1\u304c\u7d20\u6570\u306b\u306a\u308b\u5834\u5408\u304c\u3001257\u4ee5\u4e0b\u306en\u3067\u306f\u3001n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257 \u3060\u3051\u3067\u3042\u308b\u3068\u4e3b\u5f35\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u3053\u306e\u3053\u3068\u304b\u30892<sup>n-<\/sup>1\u306e\u5f62\u3092\u3057\u305f\u6570\u3092\u30e1\u30eb\u30bb\u30f3\u30cc\u6570\u3001\u305d\u3057\u3066\u305d\u308c\u304c\u7d20\u6570\u306e\u5834\u5408\u306f<a href=\"https:\/\/club.informatix.co.jp\/?p=3956\" target=\"_blank\" rel=\"noopener\">\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570<\/a>\u3068\u547c\u3076\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u3061\u306a\u307f\u306b\u3001\u3053\u306e\u30de\u30e9\u30f3\u30fb\u30e1\u30eb\u30bb\u30f3\u30cc\u306f\u73fe\u5728\u306e\u97f3\u697d\u306b\u4f7f\u308f\u308c\u3066\u3044\u308b\u97f3\u5f8b\u300112\u5e73\u5747\u5f8b\u306e\u307b\u307c\u5b8c\u74a7\u306a\u8a08\u7b97\u3092\u884c\u3063\u305f\u4eba\u7269\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570\u306f\u53e4\u304f\u304b\u3089\u7814\u7a76\u3055\u308c\u3066\u304d\u305f\u7d20\u6570\u3067\u3059\u3002<\/p>\n<p>\u53e4\u4ee3\u30ae\u30ea\u30b7\u30e3\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306f\u3001\u5b8c\u5168\u6570\uff08\u305d\u306e\u6570\u81ea\u8eab\u3092\u9664\u304f\u7d04\u6570\u306e\u548c\u304c\u305d\u306e\u6570\u3068\u7b49\u3057\u3044\u81ea\u7136\u6570\uff09\u3068\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570\u306e\u95a2\u4fc2\u3092\u767a\u898b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u65702<sup>p<\/sup>\u22121\u306b\u5bfe\u3057\u3066\u30012<sup>p\u22121<\/sup>\u3092\u4e57\u3058\u305f\u6570\u304c\u5b8c\u5168\u6570\u306b\u306a\u308b\u3068\u3044\u3046\u6cd5\u5247\u3067\u3059\u3002<\/p>\n<p>\u305d\u3057\u3066\u3001\u73fe\u5728\u77e5\u3089\u308c\u3066\u3044\u308b\u6700\u5927\u306e\u7d20\u6570\u306f\u30012016\u5e741\u6708\u306b\u767a\u898b\u3055\u308c\u305f49\u756a\u76ee\u306e\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u6570\u30012<sup>74207281<\/sup>-1\u3067\u3059\u30022233\u4e078618\u6841\u306b\u53ca\u3076\u5de8\u5927\u306a\u6570\u3067\u3059\u3002<\/p>\n<p>\u30e1\u30eb\u30bb\u30f3\u30cc\u7d20\u65702<sup>p\u2212<\/sup>1\u306e\u6307\u6570p\u306f\u7d20\u6570\u3067\u3059\u3002\u3057\u304b\u3057\u30012<sup>p<\/sup>\u22121\uff08p\u306f\u7d20\u6570\uff09\u306e\u5f62\u306e\u6570\u306f\u5fc5\u305a\u3057\u3082\u7d20\u6570\u3067\u306f\u306a\u304f\u305d\u306e\u6570\u306f\u5c11\u306a\u3044\u306e\u3067\u3001\u63a2\u7d22\u306f\u5bb9\u6613\u3067\u306f\u306a\u304f\u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%BD%E3%83%95%E3%82%A3%E3%83%BC%E3%83%BB%E3%82%B8%E3%82%A7%E3%83%AB%E3%83%9E%E3%83%B3%E7%B4%A0%E6%95%B0\"><\/span>\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30d5\u30e9\u30f3\u30b9\u306e\u5973\u6027\u6570\u5b66\u8005\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\uff081776-1831\uff09\u306f\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u306e\u7814\u7a76\u3092\u884c\u3046\u4e2d\u3067\u30012p+1\u304c\u7d20\u6570\u3067\u3042\u308b\u3088\u3046\u306a\u7d20\u6570p\u3092\u8003\u3048\u307e\u3057\u305f\u3002<\/p>\n<p>\u3059\u306a\u308f\u3061\u3001p\u30682p+1\u306e\u4e21\u65b9\u304c\u7d20\u6570\u3067\u3042\u308b\u3068\u304d\u3001p\u3092\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570\u3067\u3042\u308b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p style=\"text-align: center;\">2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, \u2026<br \/>\n\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570<\/p>\n<p>2016\u5e74\u6642\u70b9\u3067\u77e5\u3089\u308c\u3066\u3044\u308b\u6700\u5927\u306e\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570\u306f<\/p>\n<p style=\"text-align: center;\">2618163402417 \u00d7 2<sup>1290000<\/sup> \u2212 1<\/p>\n<p>\u3067\u3042\u308a388342 \u6841\u306e\u6570\u3067\u3059\u3002<\/p>\n<p>\u5f53\u6642\u306f\u5973\u6027\u304c\u5927\u5b66\u306b\u5165\u5b66\u3067\u304d\u305a\u3001\u6570\u5b66\u7814\u7a76\u3092\u884c\u3046\u3053\u3068\u304c\u56f0\u96e3\u306a\u4e2d\u3001\u30bd\u30d5\u30a3\u30fc\u306f\u72ec\u5b66\u3067\u6570\u5b66\u3092\u30de\u30b9\u30bf\u30fc\u3057\u3001\u7537\u6027\u540d\u3092\u4f7f\u3063\u3066\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\uff081736-1813\uff09\u3084\u30ac\u30a6\u30b9\uff081777-1855\uff09\u3068\u3044\u3063\u305f\u5927\u7269\u6570\u5b66\u8005\u306b\u8ad6\u6587\u3092\u9001\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u3068\u30ac\u30a6\u30b9\u306f\u5171\u306b\u30bd\u30d5\u30a3\u30fc\u306e\u5b9f\u529b\u3092\u8a8d\u3081\u8cde\u8cdb\u3057\u3001\u5e83\u304f\u4e16\u306b\u77e5\u308c\u6e21\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u30bd\u30d5\u30a3\u30fc\u306f\u6570\u5b66\u306e\u696d\u7e3e\u304c\u6709\u540d\u3067\u3059\u304c\u3001\u7269\u7406\u5b66\uff08\u5f3e\u6027\u7406\u8ad6\uff09\u3001\u5316\u5b66\u3001\u5730\u7406\u5b66\u3001\u6b74\u53f2\u306e\u7814\u7a76\u306b\u304a\u3044\u3066\u3082\u4e26\u3005\u306a\u3089\u306c\u624d\u80fd\u3092\u767a\u63ee\u3057\u307e\u3057\u305f\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%83%97%E3%83%AD%E3%82%B9%E7%B4%A0%E6%95%B0\"><\/span>\u30d7\u30ed\u30b9\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30bd\u30d5\u30a3\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u3068\u540c\u3058\u304f\u72ec\u5b66\u3067\u6570\u5b66\u3092\u30de\u30b9\u30bf\u30fc\u3057\u305f\u30d5\u30e9\u30f3\u30b9\u306e\u6570\u5b66\u8005\u30d5\u30e9\u30f3\u30bd\u30ef\u30fb\u30d7\u30ed\u30b9\uff08Proth\u30011852-1879\uff09\u306f\u6b21\u306e\u5b9a\u7406\u3092\u5f97\u307e\u3057\u305f\u3002<\/p>\n<p>Proth\u306e\u5b9a\u7406<br \/>\nN\uff1dk\u00d72<sup>n<\/sup>+1\u3068\u3059\u308b\u3002\u3053\u3053\u3067\u3001k\u306f\u5947\u6570\u30012<sup>n<\/sup>&gt;k\u3002<br \/>\n\u30e4\u30b3\u30d3\u8a18\u53f7(a\/N)\uff1d-1\u3068\u306a\u308b\u6574\u6570a\u306b\u5bfe\u3057\u3066\u3001<\/p>\n<p style=\"text-align: center;\">a<sup>(N-1)\/2<\/sup>\u2261-1 \uff08mod N\uff09<\/p>\n<p>\u304c\u6210\u308a\u7acb\u3064\u3068\u304d\u3001\u304b\u3064\u305d\u306e\u3068\u304d\u306b\u9650\u308aN\u306f\u7d20\u6570\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u306b\u767b\u5834\u3059\u308bk\u00d72<sup>n<\/sup>+1\uff082<sup>n<\/sup>&gt;k\uff09\u306e\u5f62\u3092\u3057\u305f\u7d20\u6570\u3092\u30d7\u30ed\u30b9\u7d20\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u524d\u8ff0\u3057\u305f\u30ab\u30ec\u30f3\u7d20\u6570n\u00d72<sup>n<\/sup>-1\u306f\u30d7\u30ed\u30b9\u7d20\u6570\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002<\/p>\n<p style=\"text-align: center;\">3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145,\u2026<br \/>\n\u30d7\u30ed\u30b9\u7d20\u6570<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%AB%E3%83%AC%E3%83%B3%E7%B4%A0%E6%95%B0\"><\/span>\u30ab\u30ec\u30f3\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>20\u4e16\u7d00\u521d\u3081\u3001\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u306e\u6570\u5b66\u8005\u30b8\u30a7\u30fc\u30e0\u30ba\u30fb\u30ab\u30ec\u30f3\uff08Cullen\u30011867-1933\uff09\u306fn\u00d72<sup>n<\/sup>-1\u306e\u5f62\u306e\u6570\u306b\u8208\u5473\u3092\u6301\u3061\u307e\u3057\u305f\u3002\u3053\u308c\u3092\u30ab\u30ec\u30f3\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u307b\u3068\u3093\u3069\u3059\u3079\u3066\u306e\u30ab\u30ec\u30f3\u6570\u306f\u5408\u6210\u6570\uff081\u3067\u306a\u30442\u3064\u306e\u6b63\u306e\u6574\u6570ab\u306b\u5206\u89e3\u3067\u304d\u308b\u6570\u30024\u30016\u30018\u30019\u300110\u300112\u3001\u2026\uff09\u3067\u3042\u308b\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u7d20\u6570\u306b\u306a\u308b\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u304c\u30ab\u30ec\u30f3\u7d20\u6570\u3067\u3059\u3002<\/p>\n<p>2009\u5e74\u306b\u300116\u756a\u76ee\u306e\u30ab\u30ec\u30f3\u7d20\u6570<br \/>\n6679881 \u00d7 2<sup>6679881<\/sup> + 1\uff08\u7d04201\u4e07\u6841\uff09<br \/>\n\u304c\u5206\u6563\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u3067\u3042\u308bPrimeGrid\u306b\u3088\u3063\u3066\u767a\u898b\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%A6%E3%82%A9%E3%83%BC%E3%83%AB-%E3%82%B5%E3%83%B3-%E3%82%B5%E3%83%B3%E7%B4%A0%E6%95%B0\"><\/span>\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>p\u304c5\u3088\u308a\u5927\u304d\u3044\u7d20\u6570\u306a\u3089\u3070\u3001p\u306fF(p-(p\/5))\u3092\u5272\u308a\u5207\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001F(n)\u306fn\u756a\u76ee\u306e<a href=\"https:\/\/club.informatix.co.jp\/?p=11714\" target=\"_blank\" rel=\"noopener\">\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570<\/a>\u3067\u3001(p\/5)\u306f\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u8a18\u53f7\u3067\u3059\u3002<\/p>\n<p style=\"text-align: center;\">0,1,1,2,3,5,8,13,21,34,\u2026<br \/>\n\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570F(n)<\/p>\n<p>0\u30681\u304b\u3089\u59cb\u3081\u30660+1=1\u30011+1=2\u30011+2=3\u30012+3=5\u30013+5=8\u3068\u3044\u3046\u3088\u3046\u306b\u5b9a\u307e\u308b\u6570\u304c\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u3067\u3059\u3002<\/p>\n<p>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u8a18\u53f7(p\/5)\u3068\u306f\u3001p\u304c5\u306e\u500d\u6570\u306b\uff11\u307e\u305f\u306f4\u3092\u52a0\u3048\u305f\u6570\u306e\u3068\u304d(p\/5)=1\u3067\u3001p\u304c5\u306e\u500d\u6570\u306b2\u307e\u305f\u306f3\u3092\u52a0\u3048\u305f\u6570\u306e\u3068\u304d(p\/5)=-1\u3068\u306a\u308b\u8a18\u53f7\u3067\u3059\u3002<\/p>\n<p>\u3053\u308c\u306b\u5bfe\u3057\u3066\u3001p<sup>2<\/sup>\u304cF(p-(p\/5))\u3092\u5272\u308a\u5207\u308b\u7d20\u6570p&gt;5\u3092\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e2d\u56fd\u306e\u6570\u5b66\u8005\u30a6\u30a9\u30fc\u30eb\uff08Wall\u30011921-2000\uff09\u3068\u53cc\u5b50\u306e\u30bd\u30f3\uff08Zhi-Wei Sun\u30011965-\uff09\u3068\u30bd\u30f3\uff08Zhi-Hong Sun\u30011965-\uff09\u3089\u306f\u3001\u30bd\u30d5\u30a3\u30fc\u30fb\u30b8\u30a7\u30eb\u30de\u30f3\u7d20\u6570\u306e\u5834\u5408\u3068\u540c\u3058\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u306e\u4e2d\u3067\u4e0a\u8a18\u306e\u7d20\u6570\u3092\u8003\u3048\u307e\u3057\u305f\u3002<\/p>\n<p>\u53cc\u5b50\u306e\u30bd\u30f3\u306f1992\u5e74\u306b\u3001\u3082\u3057\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u306e\u7b2c1\u306e\u5834\u5408\u304c\u3001\u7d20\u6570p\u306e\u6307\u6570\u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u305f\u306a\u3044\u306a\u3089\u3070\u3001p\u306f\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u306f\u305f\u3057\u3066\u3001\u73fe\u5728\u307e\u3067\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570\u306f\u767a\u898b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u3042\u308b\u3068\u3059\u308c\u30702\u00d710<sup>14<\/sup>\u3088\u308a\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30ab\u30ec\u30f3\u7d20\u6570\u540c\u69d8\u306bPrimeGrid\u306b\u304a\u3044\u3066\u30a6\u30a9\u30fc\u30eb-\u30b5\u30f3-\u30b5\u30f3\u7d20\u6570\u306e\u63a2\u7d22\u304c\u7d9a\u3051\u3066\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%83%B4%E3%82%A3%E3%83%BC%E3%83%95%E3%82%A7%E3%83%AA%E3%83%83%E3%83%92%E7%B4%A0%E6%95%B0\"><\/span>\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u308c\u3082\u307e\u305f\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u306b\u95a2\u4fc2\u3057\u305f\u7d20\u6570\u3067\u3059\u3002p<sup>2<\/sup>\u304c2<sup>P-1<\/sup>-1\u3092\u5272\u308a\u5207\u308b\u5834\u5408\u3001\u7d20\u6570p\u3092\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\u7d20\u6570\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>1909\u5e74\u3001\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\uff08Wieferich\u30011884-1954\uff09\u306f\u3001\u3082\u3057\u30d5\u30a7\u30eb\u30de\u30fc\u306e\u6700\u7d42\u5b9a\u7406\u306e\u7b2c1\u306e\u5834\u5408\u304c\u7d20\u6570p\u306e\u6307\u6570\u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u305f\u306a\u3044\u306a\u3089\u3070\u3001p\u306f\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\u7d20\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u30f4\u30a3\u30fc\u30d5\u30a7\u30ea\u30c3\u30d2\u7d20\u6570\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\u306e\u306f1093\u30683511\u3060\u3051\u3067\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%A6%E3%82%A3%E3%83%AB%E3%82%BD%E3%83%B3%E7%B4%A0%E6%95%B0\"><\/span>\u30a6\u30a3\u30eb\u30bd\u30f3\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>p<sup>2<\/sup>\u304c(p-1)!+1\u3092\u5272\u308a\u5207\u308b\u3068\u304d\u3001p\u3092\u30a6\u30a3\u30eb\u30bd\u30f3\u7d20\u6570\u3068\u3044\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3001n!\u306f\u968e\u4e57\u3068\u3044\u3044\u3001n\u4ee5\u4e0b\u306e\u81ea\u7136\u6570\u3059\u3079\u3066\u306e\u7a4d\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u30014!\uff1d4\u00d73\u00d72\u00d71\uff1d24\u3067\u3059\u30021970\u5e74\u3001\u30a4\u30ae\u30ea\u30b9\u306e\u6570\u5b66\u8005\u30a6\u30a3\u30eb\u30bd\u30f3\uff08Wilson\u30011741-1793\uff09\u306f\u6b21\u306e\u5b9a\u7406\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u30a6\u30a3\u30eb\u30bd\u30f3\u306e\u5b9a\u7406<br \/>\np\u30921\u3088\u308a\u5927\u304d\u3044\u6574\u6570\u3068\u3059\u308b\u3002<\/p>\n<p style=\"text-align: center;\">(p-1)!\u2261-1 (mod p)<\/p>\n<p>\u306e\u3068\u304d\u3001\u304b\u3064\u305d\u306e\u3068\u304d\u306b\u9650\u308ap\u306f\u7d20\u6570\u3067\u3042\u308b\u3002<\/p>\n<p>5<sup>2<\/sup>=25\u306f(5-1)!+1=25\u3092\u5272\u308a\u5207\u308b\u304b\u30895\u306f\u30a6\u30a3\u30eb\u30bd\u30f3\u7d20\u6570\u3067\u3059\u3002\u73fe\u5728\u307e\u3067\u77e5\u3089\u308c\u3066\u3044\u308b\u30a6\u30a3\u30eb\u30bd\u30f3\u7d20\u6570\u306f5\u300113\u3001563\u3060\u3051\u3067\u3059\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%A6%E3%82%A9%E3%83%AB%E3%82%B9%E3%83%86%E3%83%B3%E3%83%9B%E3%83%AB%E3%83%A0%E7%B4%A0%E6%95%B0\"><\/span>\u30a6\u30a9\u30eb\u30b9\u30c6\u30f3\u30db\u30eb\u30e0\u7d20\u6570<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>n\u500b\u306e\u3082\u306e\u304b\u3089k\u500b\u306e\u3082\u306e\u3092\u9078\u3076\u7d44\u5408\u305b\u306e\u6570\u3092\u4e8c\u9805\u4fc2\u6570\u3068\u3044\u3044\u3001\u9ad8\u6821\u6570\u5b66\u3067\u306f<sub>n<\/sub>C<sub>k<\/sub>\u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<p>1819\u5e74\u306b\u30d0\u30d9\u30c3\u30b8\uff081791-1871\uff09\u306f\u6b21\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002<\/p>\n<p style=\"text-align: center;\"><sub>2p-1<\/sub>C<sub>p-1<\/sub>\u22611 (mod p<sup>2<\/sup>)<\/p>\n<p>1862\u5e74\u3001\u30a4\u30ae\u30ea\u30b9\u306e\u6570\u5b66\u8005\u30a6\u30a9\u30eb\u30b9\u30c6\u30f3\u30db\u30eb\u30e0\uff081829-1891\uff09\u306f\u30d0\u30d9\u30c3\u30b8\u306e\u7d50\u679c\u3092\u6539\u826f\u3057\u3001\u6b21\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u30a6\u30a9\u30eb\u30b9\u30c6\u30f3\u30db\u30eb\u30e0\u306e\u5b9a\u7406<br 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id=\"%E6%9C%AA%E7%9F%A5%E3%81%AE%E7%B4%A0%E6%95%B0%E3%81%AE%E6%AD%A3%E4%BD%93%E3%82%92%E6%B1%82%E3%82%81%E3%81%A6\"><\/span>\u672a\u77e5\u306e\u7d20\u6570\u306e\u6b63\u4f53\u3092\u6c42\u3081\u3066<span 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style=\"list-style-type: disc;\">\n<li><a href=\"http:\/\/www.mersenne.org\" target=\"_blank\" rel=\"noopener noreferrer\">GIMPS\uff08Great Internet Mersenne Prime Search\uff09<\/a><\/li>\n<li><a href=\"http:\/\/www.primegrid.com\" target=\"_blank\" rel=\"noopener noreferrer\">PrimeGrid<\/a><\/li>\n<\/ul>\n<p>\u30c7\u30a3\u30fc\u30d7\u306a\u7d20\u6570\u306e\u4e16\u754c\u3068\u7d20\u6570\u63a2\u7d22\u306e\u8ecc\u8de1\u3092\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u65b0\u7a2e\u306e\u751f\u7269\u3084\u661f\u304c\u767a\u898b\u3055\u308c\u308b\u3068\u767a\u898b\u8005\u306e\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u308b\u3088\u3046\u306b\u3001\u65b0\u7a2e\u306e\u7d20\u6570\u306e\u767a\u898b\u306b\u306f\u767a\u898b\u8005\u306e\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u5b87\u5b99\u306e\u63a2\u67fb\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u3001\u5b87\u5b99\u304c1\u3064\u306e\u751f\u547d\u4f53\u3067\u3042\u308b\u767a\u60f3\u304c\u751f\u307e\u308c\u3066\u304d\u305f\u3088\u3046\u306b\u3001\u6570\u306e\u4e16\u754c\u306e\u63a2\u67fb\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u3001\u6570\u3082\u751f\u547d\u4f53\u306e\u3088\u3046\u306b\u601d\u3048\u3066\u304d\u307e\u3059\u3002<\/p>\n<p>\u5b87\u5b99\u3001\u751f\u547d\u306e\u6839\u6e90\u304c\u8b0e\u306b\u6e80\u3061\u3066\u3044\u308b\u3088\u3046\u306b\u6570\u306e\u4e16\u754c\u306e\u6839\u6e90\u2500\u2500\u7d20\u6570\u3082\u307e\u305f\u8b0e\u3060\u3089\u3051\u3067\u3059\u3002<\/p>\n<p>\u3053\u308c\u304b\u3089\u3082\u65b0\u305f\u306a\u300c\u4eba\u540d\uff0b\u7d20\u6570\u300d\u304c\u767a\u898b\u3055\u308c\u3066\u3044\u304f\u3053\u3068\u3067\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b 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<\/p>\n","protected":false},"author":4,"featured_media":16840,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,464,526],"tags":[380],"class_list":["post-4568","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-4","category-hito-star-mathmatics","category-526","tag-380"],"jetpack_featured_media_url":"https:\/\/club.informatix.co.jp\/wp-content\/uploads\/2017\/06\/20170628-1.jpg","_links":{"self":[{"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/posts\/4568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4568"}],"version-history":[{"count":22,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/posts\/4568\/revisions"}],"predecessor-version":[{"id":19946,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/posts\/4568\/revisions\/19946"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=\/wp\/v2\/media\/16840"}],"wp:attachment":[{"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/club.informatix.co.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}