{"id":14218,"date":"2013-10-11T09:54:04","date_gmt":"2013-10-11T01:54:04","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=14218"},"modified":"2017-07-27T11:09:31","modified_gmt":"2017-07-27T03:09:31","slug":"%e3%80%90%e6%8e%a2%e7%b4%a210-%e3%80%91%e6%95%b8%e5%ad%b8%e6%98%af%e7%99%bc%e7%8f%be%ef%bc%8c%e9%82%84%e6%98%af%e7%99%bc%e6%98%8e%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=14218","title":{"rendered":"\u3010\u63a2\u7d2210 \u3011\u6578\u5b78\u662f\u767c\u73fe\uff0c\u9084\u662f\u767c\u660e\uff1f"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">\u7b2c\u4e00\u8b1b\u2027\u7279\u7a3f<\/span><\/strong><\/h2>\n<p><strong><strong><span style=\"color: #333399;\">\u25a0 \u82f1\u570b\u6578\u5b78\u5bb6Keith Devlin\u8a8d\u70ba\uff1a\u300c\u6578\u5b78\u8b93\u4e0d\u53ef\u898b\u8b8a\u6210\u53ef\u898b\u3002\u300d<\/span><\/strong><\/strong><\/p>\n<figure id=\"attachment_14244\" aria-describedby=\"caption-attachment-14244\" style=\"width: 693px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?attachment_id=14244\" rel=\"attachment wp-att-14244\"><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-14244\" title=\"\u6d2a\u842c\u751f\u6559\u6388\u8207\u5b78\u5b50\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1.png\" alt=\"\" width=\"693\" height=\"462\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1.png 866w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1-300x199.png 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1-800x533.png 800w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1-600x400.png 600w\" sizes=\"(max-width: 693px) 100vw, 693px\" \/><\/a><figcaption id=\"caption-attachment-14244\" class=\"wp-caption-text\">\u651d\u5f71\u2502\u8d99\u63da\u5149<\/figcaption><\/figure>\n<p><strong>\u64b0\u6587<\/strong>\u2502\u5f35\u601d\u9060<\/p>\n<p>\u611b\u65af\u57fa\u6469\u8a9e\u4e2d\u5f62\u5bb9\u96ea\u7684\u8a5e\u8a9e\u5c31\u4e0a\u767e\u4e0a\u5343\u7a2e\uff0c\u5982\u679c\u8aaa\u54ea\u4e00\u7a2e\u8a9e\u8a00\u6700\u7c21\u6f54\u7cbe\u78ba\u5730\u63cf\u8ff0\u771f\u5be6\u73fe\u8c61\uff1f\u90a3\u5c31\u975e\u6578\u5b78\u83ab\u5c6c\u4e86\u3002\u6578\u5b78\u662f\u79d1\u5b78\u7684\u8a9e\u8a00\uff0c\u8af8\u5982\u842c\u6709\u5f15\u529b\u5b9a\u5f8b\u3001\u71b1\u529b\u5b78\u5b9a\u8ad6\u6216\u8005\u76f8\u5c0d\u8ad6\uff0c\u751a\u81f3\u65e5\u5e38\u751f\u6d3b\u7684\u8a08\u7b97\u6e2c\u91cf\uff0c\u6240\u4f7f\u7528\u7684\u6a21\u578b\u5de5\u5177\u90fd\u662f\u6578\u5b78\u3002<\/p>\n<p>\u65e5\u672c\u4f5c\u5bb6\u5c0f\u5ddd\u6d0b\u5b50\u95dc\u65bc\u6578\u5b78\u984c\u6750\u7684\u5c0f\u8aaa\u300a\u535a\u58eb\u71b1\u611b\u7684\u7b97\u5f0f\u300b\u4e2d\u6545\u4e8b\u4e3b\u89d2\u535a\u58eb\u662f\u4f4d\u67cf\u62c9\u5716\u4e3b\u7fa9\u8005(Platonist)\uff0c\u5805\u4fe1\u6578\u5b78\u662f\u767c\u73fe\u771f\u7406\uff0c\u7576\u4e2d\u91dd\u5c0d\u7ba1\u5bb6\u554f\u5230\u6578\u8ad6\u7814\u7a76\u662f\u5426\u5c31\u662f\u767c\u73fe\u6b63\u6574\u6578\u4e4b\u9593\u95dc\u4fc2\uff0c\u6709\u5982\u4e0b\u7684\u56de\u7b54\uff1a\u300c\u6c92\u932f\u662f\u767c\u73fe\uff0c\u4e0d\u662f\u767c\u660e\uff0c\u6211\u8981\u627e\u51fa\u5728\u6211\u9084\u6c92\u6709\u51fa\u4e16\u7684\u9059\u9060\u904e\u53bb\uff0c\u5c31\u5df2\u7d93\u4e0d\u70ba\u4eba\u77e5\u5728\u67d0\u500b\u5730\u65b9\u5b58\u5728\u7684\u5b9a\u7406\uff0c\u5c31\u597d\u50cf\u4e00\u5b57\u4e00\u53e5\u5730\u6284\u4e0b\u8a18\u9304\u5728\u4e0a\u5e1d\u7b46\u8a18\u672c\u4e2d\u771f\u7406\u4e00\u6a23\uff0c\u8ab0\u90fd\u6c92\u6709\u8fa6\u6cd5\u9810\u77e5\u9019\u672c\u7b46\u8a18\u672c\u5230\u5e95\u5728\u54ea\u88e1\uff0c\u751a\u9ebc\u6642\u5019\u6703\u6253\u958b\u3002\u300d<!--more--><\/p>\n<p>\u6578\u5b78\u5bb6Godfrey H. Hardy\u5728\u5176\u8457\u4f5c\u300a\u4e00\u500b\u6578\u5b78\u5bb6\u7684\u8faf\u767d\u300b\u4e2d\u63d0\u5230\uff1a\u300c\u6211\u76f8\u4fe1\u6578\u5b78\u5be6\u5728\u5b58\u5728\u65bc\u6211\u5011\u4e4b\u5916\uff0c\u800c\u6211\u5011\u7684\u8077\u8cac\u662f\u767c\u73fe\u5b83\u3001\u89c0\u5bdf\u5b83\uff0c\u800c\u6211\u5011\u767c\u660e\u7684\u5b9a\u7406\uff0c\u6211\u5011\u5927\u8a00\u4e0d\u615a\u5730\u5ba3\u7a31\u70ba\u6211\u5011\u7684\u300e\u5275\u4f5c\u300f\u5b9a\u7406\uff0c\u90fd\u53ea\u662f\u6211\u5011\u89c0\u5bdf\u7684\u7d00\u9304\u7f77\u4e86\u3002\u300d1960\u8afe\u8c9d\u723e\u7269\u7406\u734e\u5f97\u4e3b\u9b4f\u683c\u7d0d(Eugene Wigner)\u5c0d\u6578\u5b78\u9019\u7a2e\u300c\u4e0d\u5408\u7406\u7684\u6709\u6548\u6027\u300d(unreasonable effectiveness of mathematics)\u4ea6\u66fe\u8b9a\u5606\u4e0d\u5df2\u3002<\/p>\n<p>\u7136\u800c\uff0c\u82f1\u570b\u6578\u5b78\u5bb6Micheal Atiyah\u8a8d\u70ba\uff1a\u300c\u5982\u679c\u6211\u5011\u89c0\u5bdf\u5927\u8166\u7684\u6f14\u5316\u8108\u7d61\uff0c\u90a3\u9ebc\uff0c\u6578\u5b78\u5728\u7269\u7406\u79d1\u5b78\u4e2d\u7684\u795e\u79d8\u6210\u5c31\uff0c\u81f3\u5c11\u53ef\u4ee5\u8aaa\u660e\u5927\u8166\u6f14\u5316\u5c31\u662f\u70ba\u4e86\u8655\u7406\u7269\u7406\u4e16\u754c\uff0c\u56e0\u6b64\u767c\u660e\u6578\u5b78\u9019\u7a2e\u8a9e\u8a00\u4e5f\u6c92\u6709\u751a\u9ebc\u597d\u5947\u602a\u7684\u4e86\u3002\u300d\u6b64\u5916\uff0c\u9ea5\u91d1\u5854\u8a08\u5283\u5275\u8fa6\u4ebaJeff Raskin\u63d0\u5230\uff1a\u300c\u4eba\u985e\u908f\u8f2f\u662f\u88ab\u7269\u7406\u4e16\u754c\u5f37\u52a0\u5728\u81ea\u5df1\u8eab\u4e0a\uff0c\u8207\u4e16\u754c\u7684\u904b\u884c\u8da8\u5411\u4e00\u81f4\uff0c\u6578\u5b78\u884d\u751f\u81ea\u908f\u8f2f\uff0c\u81ea\u7136\u6703\u8ddf\u7269\u7406\u4e16\u754c\u4e00\u81f4\uff0c\u9019\u6c92\u6709\u751a\u9ebc\u597d\u9a5a\u8a1d\u7684\u3002\u300d\u611b\u56e0\u65af\u5766\u4e5f\u66fe\u7d93\u8aaa\u904e\uff1a\u300c\u6578\u5b78\u4f5c\u70ba\u4eba\u985e\u601d\u60f3\u7684\u7522\u7269\uff0c\u7368\u7acb\u65bc\u7d93\u9a57\u4e4b\u5916\uff0c\u600e\u9ebc\u53ef\u80fd\u548c\u73fe\u5be6\u4e16\u754c\u914d\u5408\u5f97\u5982\u6b64\u5929\u8863\u7121\u7e2b\uff1f\u300d<\/p>\n<p>\u6578\u5b78\u7a76\u7adf\u662f\u4eba\u985e\u667a\u6167\u7684\u7d50\u6676\u9084\u662f\u7368\u7acb\u65bc\u7d93\u9a57\u4e4b\u5916\u7684\u771f\u7406\u7b49\u5f85\u4eba\u985e\u53bb\u63a2\u7d22\uff0c\u81ea\u6709\u6578\u5b78\u958b\u59cb\u5c31\u722d\u8ad6\u4e0d\u65b7\u3002<\/p>\n<p><strong>\u96e3\u4ee5\u6349\u6478\u537b\u53c8\u4ee4\u4eba\u8457\u8ff7\u7684\u8cea\u6578<\/strong><\/p>\n<p>\u51fa\u81ea\u5c0f\u8aaa\u300a\u535a\u58eb\u71b1\u611b\u7684\u7b97\u5f0f\u300b\u4e2d\u7ba1\u5bb6\u7684\u4e00\u6bb5\u8a71\uff1a\u300c\u6211\u8a8d\u70ba\u8cea\u6578\u7684\u9b45\u529b\u5728\u65bc\u7121\u6cd5\u8aaa\u660e\u5b83\u51fa\u73fe\u7684\u79e9\u5e8f\u3002\u6bcf\u4e00\u500b\u8cea\u6578\u90fd\u6c92\u6709\u56e0\u6578\uff0c\u96a8\u610f\u5730\u51fa\u73fe\u5728\u6578\u5217\u4e2d\u3002\u96d6\u7136\u6578\u5b57\u8d8a\u5927\u5c31\u8d8a\u4e0d\u5bb9\u6613\u627e\u5230\u8cea\u6578\uff0c\u537b\u7121\u6cd5\u6839\u64da\u4e00\u5b9a\u7684\u898f\u5247\u9810\u6e2c\u8cea\u6578\u7684\u51fa\u73fe\u3002\u9019\u7a2e\u60f1\u4eba\u7684\u53cd\u8986\u7121\u5e38\uff0c\u4f7f\u8ffd\u6c42\u5b8c\u7f8e\u7684\u535a\u58eb\u5b8c\u5168\u62dc\u5012\u5728\u5b83\u7684\u77f3\u69b4\u88d9\u4e0b\u3002\u300d\u6b63\u6b63\u9053\u51fa\u4e86\u8cea\u6578\u9019\u7a2e\u4ee4\u4eba\u6b32\u7f77\u4e0d\u80fd\u7684\u7279\u6027\u3002<\/p>\n<p>\u300a\u81ea\u7531\u6642\u5831\u300b\u5831\u5c0e\u4e86\u7f8e\u570b\u4e2d\u592e\u5bc6\u8607\u91cc\u5927\u5b78\u6578\u5b78\u5bb6\u5eab\u67cf\u767c\u73fe\u76ee\u524d\u70ba\u6b62\u6700\u5927\u7684\u8cea\u6578\u70ba2\u768457,885,161\u6b21\u65b9\u518d\u6e1b\u53bb1\uff0c\u5f88\u62b1\u6b49\u7684\u662f\u6c92\u8fa6\u6cd5\u7d66\u8b80\u8005\u5c55\u793a\u9019\u500b\u76ee\u524d\u6700\u5927\u8cea\u6578\u7684\u5168\u8c8c\uff0c\u56e0\u70ba\u9019\u500b\u8cea\u6578\u5171\u670917425170\u4f4d\u6578\uff0c\u6bd4\u4e4b\u524d\u66fe\u7d93\u6700\u5927\u7684\u8cea\u6578\u591a\u4e86400\u591a\u842c\u4f4d\u6578\uff0c\u5982\u679c\u7528Courier New 11\u865f\u7684\u5b57\u9ad4\u5217\u5370\uff0c\u4f30\u8a08\u9700\u8981\u8017\u75285319\u5f35A4\u7d19\u3002<\/p>\n<p>\u8cea\u6578\u7684\u500b\u6578\u7121\u7aae\u7121\u76e1\uff0c\u9019\u65e9\u5728\u53e4\u5e0c\u81d8\u6578\u5b78\u5bb6\u6b50\u5e7e\u91cc\u5f97\u7684\u300a\u5e7e\u4f55\u539f\u672c\u300b\u5df2\u7d93\u5f97\u5230\u8b49\u660e\u3002\u6839\u64da\u8cea\u6578\u5b9a\u7406\uff0c\u57281\u5104\u4ee5\u5167\u5171\u67095,761,455\u500b\u8cea\u6578\uff0c\u5bc6\u5ea6\u70ba0.06\uff0c\u5e73\u5747\u8ddd\u96e2\u70ba17.4\uff0c\u7576\u7bc4\u570d\u64f4\u5927\u52301\u5146\u5247\u670937,607,912,018\u500b\u8cea\u6578\uff0c\u5bc6\u5ea6\u537b\u53ea\u67090.038\uff0c\u5e73\u5747\u8ddd\u96e2\u62c9\u5927\u523026.6\uff0c\u53ef\u898b\u96a8\u8457\u6578\u503c\u4e0d\u65b7\u8b8a\u5927\uff0c\u8cea\u6578\u4e4b\u9593\u6703\u6f38\u96e2\u6f38\u9060\uff0c\u8d8a\u4f86\u8d8a\u300c\u5b64\u7368\u300d\u3002<\/p>\n<p>\u50cf3\u548c5\u30015\u548c7\u9019\u6a23\u7684\u4e00\u5c0d\u8cea\u6578\u53ea\u662f\u76f8\u5dee2\uff0c\u7a31\u70ba\u5b7f\u751f\u8cea\u6578(twin primes)\uff0c\u7576\u6578\u503c\u8b8a\u5927\uff0c\u8cea\u6578\u6703\u8d8a\u898b\u7a00\u5c11\u800c\u4e14\u5404\u81ea\u9593\u5dee\u8ddd\u4e5f\u6703\u62c9\u5927\uff0c\u4f46\u9019\u500b\u7f88\u7d46\u4e26\u6c92\u6709\u88ab\u78e8\u6ec5\uff0c\u6700\u5927\u7684\u5b7f\u751f\u8cea\u6578\u4e0d\u65b7\u88ab\u5237\u65b0\uff0c\u5df2\u7d93\u8b49\u660e\u8cea\u6578\u6709\u7121\u7aae\u591a\u500b\uff0c\u90a3\u9ebc\u7121\u7aae\u591a\u5c0d\u5b7f\u751f\u8cea\u6578\u662f\u5426\u5b58\u5728\uff1f\u9019\u5c31\u662f\u5b7f\u751f\u8cea\u6578\u731c\u60f3\u3002\u5f35\u76ca\u5510\u535a\u58eb\u904e\u53bb\u4e0d\u8ad6\u5728\u6c42\u5b78\u9084\u662f\u8b00\u8077\u7d93\u6b77\u4e0a\u90fd\u6ce2\u6298\u91cd\u91cd<a href=\"#1\"><sup>[1]<\/sup><\/a>\uff0c\u5373\u4f7f\u6839\u64da\u7d71\u8a08\u4ee5\u53ca\u904e\u5f80\u7d93\u9a57\uff0c\u4e00\u500b\u5b78\u8005\u5982\u679c\u904e\u4e86\u4eba\u751f\u4e2d\u6700\u5177\u5275\u610f\u624d\u83ef\u7684\u9ec3\u91d1\u6642\u671f\uff0c\u5c31\u96e3\u4ee5\u671f\u5f85\u5728\u5b78\u8853\u4e0a\u6703\u6709\u751a\u9ebc\u91cd\u5927\u8ca2\u737b\uff0c\u4f46\u4ed6\u4e26\u6c92\u6709\u56e0\u6b64\u81ea\u66b4\u81ea\u68c4\u5411\u73fe\u5be6\u59a5\u5354\uff0c\u800c\u662f\u81f4\u529b\u7814\u7a76\u9577\u4e45\u4ee5\u4f86\u6578\u5b78\u754c\u672a\u89e3\u7684\u96e3\u984c\uff0c\u5b7f\u751f\u8cea\u6578\u731c\u60f3\u5c31\u662f\u5176\u4e2d\u4e4b\u4e00\uff0c\u7d50\u679c\u5728\u5e74\u904e\u767e\u534a\u81e8\u8fd1\u9000\u4f11\u4e4b\u9f61\uff0c\u767c\u8868\u8ad6\u6587\u300aBounded gaps between primes\u300b<a href=\"#2\"><sup>[2] <\/sup><\/a>\u8b49\u660e\u5b58\u5728\u7121\u7aae\u591a\u5c0d\u8cea\u6578\u7684\u5dee\u5c0f\u65bc7000\u842c\uff0c\u5118\u7ba1\u76f8\u5c0d\u65bc\u8b49\u660e\u300c\u5b58\u5728\u7121\u7aae\u591a\u5c0d\u8cea\u6578\u7684\u5dee\u7b49\u65bc2\u300d\u4ecd\u6709\u76f8\u7576\u8ddd\u96e2\uff0c\u4f46\u5f35\u76ca\u5510\u535a\u58eb\u7684\u8b49\u660e\u5df2\u7d93\u628a\u7bc4\u570d\u5f9e\u7121\u9650\u5927\u7e2e\u5c0f\u52307000\u842c\u4ee5\u5167\uff0c\u88ab\u8996\u70ba\u662f\u8fd1\u767e\u5e74\u4f86\u6578\u5b78\u754c\u7684\u91cd\u5927\u7a81\u7834\u3002<\/p>\n<p><strong>\u8cea\u6578\u7121\u7528\u4e4b\u70ba\u5927\u7528<\/strong><\/p>\n<p>\u8cea\u6578\u7406\u8ad6\u5728\u904e\u53bb\u6578\u5343\u5e74\u6b72\u6708\u88e1\u53ea\u662f\u4fb7\u9650\u65bc\u7d14\u7cb9\u6578\u5b78\u7684\u7bc4\u7587\uff0c\u67af\u71e5\u53c8\u96e3\u641e\u7684\u500b\u6027\u66fe\u7d93\u8b93\u591a\u5c11\u7814\u7a76\u8005\u671b\u4e4b\u537b\u6b65\uff0c\u76f4\u52301977\u5e74\u7531\u7f8e\u570b\u9ebb\u7701\u7406\u5de5\u5b78\u9662Ron Rivest, Adi Shamir\u548cLeonard Adleman\u6240\u767c\u8868\u7684\"A Method for Obtaining Digital Signatures and Public-Key Cryptosystems\"<a href=\"#3\"><sup>[3]<\/sup><\/a>\u8ad6\u6587\u4e2d\u63d0\u51fa\u4ee5\u4e09\u4eba\u59d3\u6c0f\u7684\u958b\u982d\u5b57\u6bcd\u7d44\u5408\u547d\u540d\u7684RSA\u5bc6\u78bc\u6f14\u7b97\u6cd5\uff0c\u9996\u6b21\u628a\u8cea\u6578\u7406\u8ad6\u5f15\u9032\u5bc6\u78bc\u5b78\u3002\u6f14\u7b97\u6703\u5f97\u5230\u4e00\u5bc6\u9470\u5c0d\uff0c\u5206\u5225\u662f\u5c0d\u5916\u516c\u958b\u7684\u516c\u9470\u4ee5\u53ca\u7528\u6236\u4fdd\u5b58\u7684\u79c1\u9470\uff0c\u516c\u9470\u7684\u5169\u500b\u53c3\u6578N\u548ce\uff0cp\u8ddfq\u5206\u5225\u70ba\u5927\u6578\u503c\u7684\u8cea\u6578\uff0cN\u7b49\u65bcp\u8ddfq\u7684\u4e58\u7a4d\uff0c\u53e6\u5916e\u5247\u8207(p-1)(q-1)\u4e92\u8cea\uff0c\u9280\u884c\u6703\u5c0d\u5ba2\u6236\u516c\u958bN\u8ddfe\u7684\u6578\u503c\uff0c\u4f46\u8a08\u7b97\u904e\u7a0b\u4e2d\u4f7f\u7528\u7684p\u8ddfq\u5c31\u7121\u5f9e\u5f97\u77e5\u3002RSA\u5bc6\u78bc\u7684\u64cd\u4f5c\u539f\u7406\u5c31\u662f\u57fa\u65bc\u5c0d\u5169\u500b\u5927\u6578\u503c\u7684\u8cea\u6578\u76f8\u4e58\u6240\u5f97\u5230\u7684\u975e\u8cea\u6578\u9032\u884c\u56e0\u5f0f\u5206\u89e3\u5728\u8a08\u7b97\u4e0a\u5e7e\u8fd1\u4e0d\u53ef\u80fd\u7684\u4e8b\u5be6\uff0c\u8cea\u6578\u9019\u7a2e\u67af\u71e5\u53c8\u96e3\u641e\u7684\u500b\u6027\u53cd\u5012\u6210\u70ba\u5bc6\u78bc\u7834\u8b6f\u8005\u7684\u5669\u5922\u3002<\/p>\n<p><strong>\u7f8e\u9e97\u7684\u80cc\u5f8c\u539f\u4f86\u6709\u300c\u6578\u300d\u53ef\u5faa<\/strong><\/p>\n<p>\u82b1\u7684\u7a2e\u985e\u6210\u5343\u4e0a\u842c\uff0c\u67092\u679a\u82b1\u74e3\u7684\u6d77\u68e0\u82b1\u30013\u679a\u82b1\u74e3\u7684\u9435\u862d\u82b1\u30015\u679a\u82b1\u74e3\u7684\u6cb9\u6850\u82b1\u30018\u679a\u82b1\u74e3\u7684\u6ce2\u65af\u83ca\u4ee5\u53ca13\u679a\u82b1\u74e3\u7684\u74dc\u8449\u83ca\uff0c\u82b1\u74e3\u6578\u76ee\u5404\u4e0d\u76f8\u540c\uff0c\u770b\u4f3c\u53ea\u662f\u96a8\u6a5f\u4e82\u5e8f\u7684\u751f\u7269\u6f14\u5316\uff0c\u80cc\u5f8c\u537b\u6709\u898f\u5f8b\u53ef\u5faa\uff01\u610f\u5927\u5229\u6578\u5b78\u5bb6\u8cbb\u6ce2\u90a3\u5951\u767c\u73fe2\u52a03\u7b49\u65bc5\uff0c\u800c5\u52a0\u4e0a8\u7b49\u65bc13\uff0c\u5982\u6b64\u985e\u63a8\uff0c\u9019\u5c31\u662f\u8457\u540d\u7684\u8cbb\u6c0f\u6578\u5217\uff0c\u6709\u8da3\u7684\u662f\uff0c\u81ea\u7136\u754c\u5e7e\u4e4e\u6240\u6709\u82b1\u90fd\u7b26\u5408\u6578\u5217\u7684\u898f\u5f8b\u3002<\/p>\n<p>\u958b\u666e\u6566\u767c\u73fe\u5982\u679c\u6578\u5217\u7684\u5f8c\u9805\u9664\u4ee5\u524d\u9805\uff0c\u5c31\u50cf3\u9664\u4ee52\uff0c5\u9664\u4ee53\uff0c8\u9664\u4ee55\u7136\u5f8c13\u9664\u4ee58\uff0c\u4ee5\u6b64\u985e\u63a8\uff0c\u5f97\u5230\u7684\u6bd4\u503c\u6703\u8da8\u8fd11.618\uff0c\u4e5f\u5c31\u662f\u9ec3\u91d1\u6bd4\u4f8b\uff0c\u6240\u4ee5\u8cbb\u6c0f\u6578\u5217\u53c8\u7a31\u70ba\u9ec3\u91d1\u5206\u5272\u6578\u5217\u3002\u53e4\u5e0c\u81d8\u7562\u9054\u54e5\u62c9\u65af\u5b78\u6d3e\u5c31\u9032\u884c\u904e\u6b63\u4e94\u908a\u5f62\u7684\u4f5c\u5716\uff0c\u9019\u53ef\u80fd\u662f\u4eba\u985e\u6700\u65e9\u5c0d\u9ec3\u91d1\u5206\u5272\u7684\u7814\u7a76\uff0c\u5927\u81ea\u7136\u7f8e\u4f96\u7f8e\u5950\u7684\u7522\u7269\u5e7e\u4e4e\u90fd\u5408\u65bc\u9ec3\u91d1\u6bd4\u4f8b\uff0c\u6bd4\u5982\u9e1a\u9d61\u87ba\u548c\u6d77\u99ac\uff0c\u7531\u65bc\u9ec3\u91d1\u5206\u5272\u5177\u6709\u7f8e\u5b78\u4e0a\u50f9\u503c\uff0c\u5927\u591a\u6578\u5efa\u7bc9\u7269\u4ee5\u53ca3C\u7522\u54c1\u87a2\u5e55\u5728\u8a2d\u8a08\u4e0a\u90fd\u4f9d\u5faa\u8457\u9ec3\u91d1\u6bd4\u4f8b\uff0c\u4eba\u985e\u628a\u9ec3\u91d1\u5206\u5272\u61c9\u7528\u5230\u65e5\u5e38\u751f\u6d3b\u4e0a\u7684\u5404\u500b\u5c64\u9762\u3002<\/p>\n<figure id=\"attachment_14273\" aria-describedby=\"caption-attachment-14273\" style=\"width: 350px\" class=\"wp-caption alignright\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?attachment_id=14273\" rel=\"attachment wp-att-14273\"><img decoding=\"async\" class=\"size-full wp-image-14273 \" title=\"\u6d77\u738b\u661f\u904b\u884c\u8ecc\u9053\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p2.png\" alt=\"\" width=\"350\" height=\"453\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p2.png 759w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p2-231x300.png 231w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p2-600x776.png 600w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/a><figcaption id=\"caption-attachment-14273\" class=\"wp-caption-text\">\u6d77\u738b\u661f\u7684\u904b\u884c\u8ecc\u9053\uff0c\u662f\u592a\u967d\u7cfb\u516b\u5927\u884c\u661f\u4e2d\u60df\u4e00\u4e0d\u662f\u900f\u904e\u5929\u6587\u89c0\u6e2c\u6240\u767c\u73fe\u7684\u3002(\u5716\u7247\u4f86\u6e90\uff1aSolar system\u2502Getty Images)<\/figcaption><\/figure>\n<p><strong>\u56e0\u70ba\u9700\u8981\uff0c\u6240\u4ee5\u767c\u660e <\/strong><\/p>\n<p>\u5982\u679c\u8981\u628a2\u7247\u9eb5\u5305\u5e73\u5747\u5206\u7d663\u500b\u4eba\uff0c\u53ef\u4ee5\u628a\u5169\u7247\u9eb5\u5305\u5207\u62103\u7b49\u5206\uff0c\u6bcf\u4eba\u5206\u7d662\/3\u7247\uff0c\u7406\u8ad6\u53ef\u884c\u4f46\u57f7\u884c\u4e0a\u6709\u56f0\u96e3\uff1b\u5982\u679c\u7528\u53e4\u57c3\u53ca\u5206\u6578\u7684\u65b9\u5f0f\uff0c\u628a2\/3\u62c6\u89e3\u70ba1\/2\u82071\/6\u7684\u548c\uff0c\u57f7\u884c\u6642\u5c31\u5148\u5206\u7d66\u4e09\u4eba\u5404\u81ea\u534a\u7247\u9eb5\u5305\uff0c\u6700\u5f8c\u7684\u534a\u7247\u9eb5\u5305\u5e73\u52063\u5206\uff0c\u5404\u53d61\/2\u7247\u52a0\u4e0a1\/6\u7247\u7684\u9eb5\u5305\uff0c\u540c\u6a23\u662f\u6bcf\u4eba2\/3\u7247\u9eb5\u5305\uff0c\u4f46\u64cd\u4f5c\u4e0a\u8f03\u70ba\u7c21\u6613\u800c\u4e14\u53ef\u80fd\u51fa\u73fe\u7684\u8aa4\u5dee\u8f03\u5c11\u3002<\/p>\n<p>\u6cd5\u570b\u5929\u6587\u5b78\u5bb6Le Verrier\u5229\u7528\u6578\u5b78\u63a8\u7b97\u51fa\u6d77\u738b\u661f\u7684\u904b\u884c\u8ecc\u9053\uff0c\u662f\u592a\u967d\u7cfb\u516b\u5927\u884c\u661f\u4e2d\u60df\u4e00\u4e0d\u662f\u900f\u904e\u5929\u6587\u89c0\u6e2c\u6240\u767c\u73fe\u7684\u3002\u5357\u975e\u7269\u7406\u5b78\u5bb6Allen Cormack\u767c\u8868\u4e86\u96fb\u8166\u65b7\u5c64\u651d\u5f71(computer tomography, \u7c21\u7a31CT)\u6280\u8853\u53ef\u884c\u6027\u7684\u8ad6\u6587\u300a\u51fd\u6578\u7684\u7dda\u7a4d\u5206\u53ca\u5176\u653e\u5c04\u5b78\u61c9\u7528\u300b\uff0c\u7576\u4e2d\u7684\u6578\u5b78\u69cb\u60f3\u5176\u5be6\u662f\u4f86\u81ea\u5967\u5730\u5229\u6578\u5b78\u5bb6Johann Radon\u6240\u63d0\u51fa\u7684Randon transform\u3002\u5c31\u9019\u6a23\uff0c\u4e00\u9580\u62bd\u8c61\u7684\u6578\u5b78\u6210\u70ba\u65e5\u5f8cCT\u5be6\u969b\u61c9\u7528\u7684\u7406\u8ad6\u57fa\u790e\u3002<\/p>\n<p><strong>\u767c\u660e\u8207\u767c\u73fe\u4e0d\u662f\u622a\u7136\u4e8c\u5206<\/strong><\/p>\n<p>\u4f5c\u5bb6Philip J. Davis\u548cReuben Hersh\u5728\u300a\u6578\u5b78\u7d93\u9a57\u300b\u4e00\u66f8\u4e2d\u63d0\u5230\uff1a\u300c\u5178\u578b\u7684\u5c08\u696d\u6578\u5b78\u5bb6\u5728\u5e73\u65e5\u4fe1\u5949\u67cf\u62c9\u5716\u4e3b\u7fa9\uff0c\u8a8d\u70ba\u6578\u5b78\u662f\u767c\u73fe\uff0c\u5230\u5047\u65e5\u5c31\u6416\u8eab\u4e00\u8b8a\u6210\u70ba\u5f62\u5f0f\u4e3b\u7fa9(formalist)\u8005\uff0c\u89ba\u5f97\u6578\u5b78\u662f\u767c\u660e\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u7576\u6578\u5b78\u5bb6\u5f9e\u4e8b\u6578\u5b78\u7814\u7a76\u6642\u6703\u76f8\u4fe1\u81ea\u5df1\u6b63\u5728\u8a66\u5716\u5224\u5b9a\u5176\u6027\u8cea\u7684\u5ba2\u89c0\u4e8b\u5be6\uff0c\u4f46\u7dca\u63a5\u8457\u88ab\u8981\u6c42\u8ce6\u4e88\u9019\u500b\u4e8b\u5be6\u7684\u4e00\u500b\u54f2\u5b78\u89e3\u8aaa\u6642\uff0c\u6578\u5b78\u5bb6\u53c8\u6703\u767c\u89ba\u300e\u5047\u88dd\u4e0d\u76f8\u4fe1\u300f\u662f\u6700\u7c21\u55ae\u7684\u8aaa\u6cd5\u3002\u300d<\/p>\n<p>Mario Livio\u5728\u300a\u4e0a\u5e1d\u662f\u6578\u5b78\u5bb6\uff1f\u300b\u4e2d\u63d0\u5230\uff1a\u300c\u6211\u5011\u7684\u6578\u5b78\u662f\u767c\u660e\u548c\u767c\u73fe\u7684\u7d50\u5408\u3002\u6b50\u5e7e\u91cc\u5f97\u5b9a\u7406\u9019\u7a2e\u6982\u5ff5\u662f\u767c\u660e\uff0c\u5c31\u50cf\u4e0b\u897f\u6d0b\u68cb\u7684\u898f\u5247\u662f\u767c\u660e\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6b50\u5e7e\u91cc\u5f97\u5e7e\u4f55\u5b78\u7684\u5b9a\u7406\uff0c\u5927\u81f4\u8aaa\u4f86\u5c31\u662f\u767c\u73fe\uff0c\u5b83\u5011\u662f\u9023\u63a5\u4e0d\u540c\u6982\u5ff5\u7684\u8def\u5f91\u3002\u57fa\u672c\u4e0a\uff0c\u6982\u5ff5\u5c31\u662f\u767c\u660e\uff0c\u8cea\u6578\u9019\u7a2e\u6982\u5ff5\u662f\u767c\u660e\uff0c\u4f46\u6240\u6709\u95dc\u4e4e\u8cea\u6578\u7684\u5b9a\u7406\u90fd\u662f\u767c\u73fe\u3002\u6578\u5b78\u77e5\u8b58\u5177\u6709\u975e\u5e38\u8c50\u5bcc\u7684\u6587\u5316\u8108\u7d61\uff0c\u60f3\u8981\u6df1\u5165\u7406\u89e3\u6578\u5b78\uff0c\u5f9e\u300e\u767c\u73fe\uff0b\u767c\u660e\u300f\u9762\u5411\u5207\u5165\uff0c\u6216\u8a31\u503c\u5f97\u6211\u5011\u5617\u8a66\uff01\u300d<\/p>\n<p>\u5176\u5be6\u4e0d\u7ba1\u662f\u767c\u660e\u9084\u662f\u767c\u73fe\uff0c\u7d14\u7cb9\u7684\u4e8c\u5206\u6cd5\u5230\u5f8c\u4f86\u90fd\u4e0d\u514d\u6703\u7522\u751f\u77db\u76fe\u3002<\/p>\n<p>\u53e4\u4ee3\u6578\u5b78\u4f5c\u70ba\u65e5\u5e38\u751f\u6d3b\u6240\u9700\u8655\u7406\u7c21\u55ae\u6578\u76ee\u53ca\u5e7e\u4f55\u5f62\u72c0\u7684\u5b78\u554f\uff0c\u5230\u4e86\u5341\u4e03\u4e16\u7d00\u4e2d\u8449\u96a8\u8457\u5fae\u7a4d\u5206\u5b78\u7684\u6210\u719f\uff0c\u6578\u5b78\u6210\u70ba\u7814\u7a76\u8b8a\u5316\u7684\u5b78\u554f\uff0c\u4e0d\u518d\u4fb7\u9650\u65bc\u7d14\u7cb9\u6578\u5b78\uff0c\u66f4\u591a\u5730\u64f4\u53ca\u5230\u61c9\u7528\u65b9\u9762\u3002\u6642\u81f3\u4eca\u65e5\uff0c\u6578\u5b78\u7814\u7a76\u767c\u5c55\u5927\u653e\u7570\u5f69\uff0c\u4f5c\u70ba\u62d3\u6a38\u5b78\u3001\u908f\u8f2f\u5b78\u3001\u7d71\u8a08\u5b78\u3001\u5bc6\u78bc\u5b78\u3001\u7269\u7406\u5b78\u3001\u5316\u5b78\u7b49\u591a\u500b\u5b78\u79d1\u7684\u7406\u8ad6\u6a21\u578b\u5de5\u5177\u3002\u5982\u679c\u8aaa\u5343\u5e74\u4f86\u7684\u6578\u5b78\u767c\u5c55\u90fd\u53ea\u662f\u66f4\u9032\u4e00\u6b65\u5730\u767c\u73fe\u771f\u76f8\uff0c\u5168\u76e4\u5426\u5b9a\u904e\u53bb\u4eba\u985e\u667a\u6167\u7684\u6210\u679c\u986f\u7136\u662f\u4e0d\u5408\u7406\u7684\uff1b\u53cd\u4e4b\u4ea6\u7136\uff0c\u7121\u53ef\u5426\u8a8d\u7684\u662f\uff0c\u67d0\u4e9b\u6578\u5b78\u5de5\u5177\u78ba\u5be6\u662f\u70ba\u4e86\u89e3\u91cb\u73fe\u8c61\u800c\u91cf\u8eab\u6253\u9020\uff1a\u6bd4\u5982\u61c9\u7528\u5fae\u7a4d\u5206\u4f86\u9a57\u8b49\u7d93\u6fdf\u76f4\u89ba\uff1b\u53e6\u5916\u4e00\u4e9b\u6578\u5b78\u5b9a\u7406\u5c31\u50cf\u592a\u967d\u6771\u5347\u897f\u843d\uff0c\u662f\u9435\u4e00\u822c\u7684\u4e8b\u5be6\u53ea\u80fd\u63cf\u8ff0\u800c\u7121\u6cd5\u66f4\u52d5\u7684\uff0c\u4f8b\u5982\u8cea\u6578\u5b9a\u7406\uff0c\u4f3c\u4e4e\u767c\u73fe\u8207\u767c\u660e\u540c\u5728\u7684\u8aaa\u6cd5\u8f03\u70ba\u4e2d\u80af\u3002<\/p>\n<p>\u5982\u679c\u4f60\u70ba\u89e3\u6c7a\u6578\u5b78\u672c\u8cea\u7684\u554f\u984c\u611f\u5230\u56f0\u9813\u4e0d\u5df2\uff0c\u4e0d\u59a8\u53c3\u8003\u82f1\u570b\u6578\u5b78\u5bb6Keith Devlin\u7684\u898b\u89e3\uff1a\u300c\u6578\u5b78\u8b93\u4e0d\u53ef\u898b\u8b8a\u6210\u53ef\u898b\u3002\u300d<\/p>\n<hr size=\"1\" \/>\n<p><a name=\"1\"><\/a><sup>[1]<\/sup>\u5f35\u76ca\u5510\u5ef6\u4f38\u50b3\u8a18<br \/>\n<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=13917\">http:\/\/case.ntu.edu.tw\/blog\/?p=13917<br \/>\n<\/a><a style=\"font-size: 13px;\" href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=13966\">http:\/\/case.ntu.edu.tw\/blog\/?p=13966<br \/>\n<\/a><a style=\"font-size: 13px;\" href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=14046\">http:\/\/case.ntu.edu.tw\/blog\/?p=14046<\/a><\/p>\n<p><a name=\"2\"><\/a><sup>[2] <\/sup><span style=\"font-size: 13px;\">\u300aBounded gaps between primes\u300b\u8ad6\u6587\u767c\u8868\uff1a<\/span><a style=\"font-size: 13px;\" href=\"http:\/\/www.nature.com\/news\/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989\">http:\/\/www.nature.com\/news\/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989<\/a><\/p>\n<p><a name=\"3\"><\/a><sup>[3]<\/sup>\u300aA Method for Obtaining Digital Signatures and Public-Key Cryptosystems\u300b\u8ad6\u6587\u767c\u8868\uff1a<span style=\"text-decoration: underline;\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p120-rivest.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u8acb\u9ede\u6b64<\/a><\/span><\/p>\n<p>--<\/p>\n<pre><span style=\"color: #333333;\"> \u672c\u6587\u6574\u7406\u81ea\uff1a102\/09\/28\u4e0b\u5348\u7531\u6d2a\u842c\u751f\u6559\u6388\u5728\u81fa\u5927\u61c9\u529b\u6240\u570b\u969b\u6f14\u8b1b\u5ef3\u6240\u4e3b\u8b1b\u4e4b\u300c\u6578\u5b78\u662f\u767c\u73fe\uff0c\u9084\u662f\u767c\u660e\uff1f\u300d\u7684\u6f14\u8b1b\u5167\u5bb9<\/span><\/pre>\n<pre><span style=\"color: #333333;\"> \u5ef6\u4f38\u95b1\u8b80\uff1a\u81fa\u5927\u79d1\u5b78\u6559\u80b2\u767c\u5c55\u4e2d\u5fc3\u63a2\u7d22\u57fa\u790e\u79d1\u5b78\u8b1b\u5ea72013\u5e749\u670828\u65e5\u7b2c\u4e00\u8b1b\u3008\u6578\u5b78\u662f\u767c\u73fe\uff0c\u9084\u662f\u767c\u660e\uff1f\u3009<\/span><a href=\"https:\/\/case.ntu.edu.tw\/CASTUDIO\/course.php?speech_ID=3341#video_top\" target=\"_blank\" rel=\"noopener noreferrer\"><span style=\"color: #333333;\">\u5168\u7a0b\u5f71\u97f3<\/span><\/a><\/pre>\n<p><strong><span style=\"color: #333399;\">\u8cac\u4efb\u7de8\u8f2f\uff1aVita Chen<\/span><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c\u4e00\u8b1b\u2027\u7279\u7a3f \u25a0 \u82f1\u570b\u6578\u5b78\u5bb6Keith <\/p>\n","protected":false},"author":20,"featured_media":14244,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,892],"tags":[896,897,2251,899,898,900],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/10\/p1.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/14218"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14218"}],"version-history":[{"count":62,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/14218\/revisions"}],"predecessor-version":[{"id":28944,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/14218\/revisions\/28944"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/14244"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}