{"id":20342140,"url":"https://github.com/briandfoy/excellent_numbers","last_synced_at":"2025-04-11T23:40:47.446Z","repository":{"id":54704713,"uuid":"43576387","full_name":"briandfoy/excellent_numbers","owner":"briandfoy","description":"Compute excellent numbers","archived":false,"fork":false,"pushed_at":"2024-05-05T20:42:25.000Z","size":52456,"stargazers_count":9,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-03-25T19:36:59.537Z","etag":null,"topics":["bignum","c","julia","math","perl","python"],"latest_commit_sha":null,"homepage":null,"language":"Perl","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/briandfoy.png","metadata":{"files":{"readme":"README.pod","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2015-10-02T21:07:07.000Z","updated_at":"2021-09-02T19:19:18.000Z","dependencies_parsed_at":"2024-11-14T21:42:26.077Z","dependency_job_id":null,"html_url":"https://github.com/briandfoy/excellent_numbers","commit_stats":null,"previous_names":[],"tags_count":1,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/briandfoy%2Fexcellent_numbers","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/briandfoy%2Fexcellent_numbers/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/briandfoy%2Fexcellent_numbers/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/briandfoy%2Fexcellent_numbers/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/briandfoy","download_url":"https://codeload.github.com/briandfoy/excellent_numbers/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248497885,"owners_count":21113982,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["bignum","c","julia","math","perl","python"],"created_at":"2024-11-14T21:31:22.513Z","updated_at":"2025-04-11T23:40:47.420Z","avatar_url":"https://github.com/briandfoy.png","language":"Perl","funding_links":[],"categories":[],"sub_categories":[],"readme":"=encoding utf8\n\n=head1 Excellent Numbers\n\nA seemingly useless number theory problem wastes so much time, but\nis too much fun to put that time to good use. I want to compute very\nlarge \"Excellent Numbers\".\n\nA number I\u003cab\u003e is excellent if I\u003cb²\u003e - I\u003ca²\u003e is the number I\u003cab\u003e,\nwhere I\u003ca\u003e and I\u003cb\u003e have an equal number of digits. For instance, 48\nis 8² - 4².\n\n=head2 The Numbers\n\nI'm currently working on the 32-digit numbers. So far:\n\n\t[2 digits]\n\t48\n\n\t[4 digits]\n\t3468\n\n\t[6 digits]\n\t140400\n\t190476\n\t216513\n\t300625\n\t334668\n\t416768\n\t484848\n\t530901\n\n\t[8 digits]\n\t16604400\n\t33346668\n\t59809776\n\n\t[10 digits]\n\t3333466668\n\t4848484848\n\t4989086476\n\n\t[12 digits]\n\t101420334225\n\t181090462476\n\t238580543600\n\t243970550901\n\t268234583253\n\t274016590848\n\t320166650133\n\t333334666668\n\t346834683468\n\t400084748433\n\t440750796876\n\t502016868353\n\t569466945388\n\n\t[14 digits]\n\t33333346666668\n\t48484848484848\n\n\t[16 digits]\n\t1045751633986928\n\t1140820035650625\n\t3333333466666668\n\n\t[18 digits]\n\t103495840337945601\n\t115220484358463728\n\t134171310390093900\n\t139601140398860400\n\t140400140400140400\n\t146198830409356725\n\t168654484443958128\n\t189525190474810476\n\t190476190476190476\n\t215488216511784513\n\t216513216513216513\n\t225789700526090001\n\t241951680548171776\n\t271851166588008693\n\t299376300623700625\n\t300625300625300625\n\t332001666665001333\n\t333333334666666668\n\t334668334668334668\n\t344329484680361873\n\t415233416766584768\n\t416768416768416768\n\t468197520829099776\n\t483153484846516848\n\t484848484848484848\n\t529100530899470901\n\t530901530901530901\n\t572945416949321793\n\n\t[20 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Contributors\n\n=over 4\n\n=item * Mark Jason Dominus presented the problem and same the initial optimization I came up with\n\n=item * Joe Zbiciak contributed the modulus congruence optimization\n\n=item * Phil Doroff from ServerCentral provided a fat box with 80 CPUs so I could run the 30 digit list in a reasonable time.\n\n=item * Sinan Ünür made everything really fast by using int128 math\n\n=item * Matthew Arcus\n\n=back\n\n=head2 Other Readings\n\n=over 4\n\n=item * L\u003cExcellent Numbers|https://matthewarcus.wordpress.com/2016/01/16/excellent-numbers/\u003e\n\nMatthew Arcus re-uses what we already know about factors of 10^k-1 to make the process much faster.\n\n=item * L\u003cComputing excellent numbers|http://www.masteringperl.org/2015/05/computing-excellent-numbers/\u003e\n\n=item * L\u003cDoing less work to compute excellent numbers|http://www.masteringperl.org/2015/10/doing-less-work-to-compute-excellent-numbers/\u003e\n\n=item * L\u003cExcellent Numbers|http://blog.plover.com/math/excellent.html\u003e\n\n=item * L\u003cThe \"excellent numbers\" tag at Mastering Perl|http://www.masteringperl.org/tag/excellent-numbers/\u003e\n\n=item * L\u003c484848 is excellent|http://blog.plover.com/math/484848.html\u003e\n\n=item * L\u003cThe Online Encyclopedia of Integer Sequences, A162700|https://oeis.org/A162700\u003e\n\nThey only have 25 entries. I would add more but they don't like my\nname. If someone wants to add them, you can do that.\n\n=back\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbriandfoy%2Fexcellent_numbers","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fbriandfoy%2Fexcellent_numbers","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbriandfoy%2Fexcellent_numbers/lists"}