{"id":7652,"date":"2022-06-13T15:50:03","date_gmt":"2022-06-13T13:50:03","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=7652"},"modified":"2022-06-13T15:50:03","modified_gmt":"2022-06-13T13:50:03","slug":"comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2022\/06\/13\/comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire\/","title":{"rendered":"Comment calculer la cl\u00e9 d&rsquo;un num\u00e9ro (s\u00e9curit\u00e9 sociale, compte bancaire,&#8230;)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Comment calculer la cl\u00e9 du num\u00e9ro qui compose votre compte bancaire ou votre num\u00e9ro de s\u00e9curit\u00e9 sociale ? Vous allez voir que la notion de nombres premiers n&rsquo;est pas \u00e9trang\u00e8re \u00e0 cette question&#8230;<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><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><\/span><\/a><\/span><\/div>\n<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:\/\/www.mathweb.fr\/euclide\/2022\/06\/13\/comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire\/#Comment_calculer_la_cle_dun_numero_securite_sociale_compte_bancaire%E2%80%A6_rappels_sur_les_nombres_premiers\" >Comment calculer la cl\u00e9 d&rsquo;un num\u00e9ro (s\u00e9curit\u00e9 sociale, compte bancaire,&#8230;): rappels sur les nombres premiers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/06\/13\/comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire\/#Calculer_la_cle_dun_numero_de_securite_sociale_avec_une_division_euclidienne\" >Calculer la cl\u00e9 d&rsquo;un num\u00e9ro de s\u00e9curit\u00e9 sociale avec une division euclidienne<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/06\/13\/comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire\/#Calculer_la_cle_dun_numero_de_compte_francais_avec_une_division_euclidienne\" >Calculer la cl\u00e9 d&rsquo;un num\u00e9ro de compte fran\u00e7ais avec une division euclidienne<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2022\/06\/13\/comment-calculer-la-cle-dun-numero-securite-sociale-compte-bancaire\/#Pourquoi_ces_calculs\" >Pourquoi ces calculs ?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Comment_calculer_la_cle_dun_numero_securite_sociale_compte_bancaire%E2%80%A6_rappels_sur_les_nombres_premiers\"><\/span>Comment calculer la cl\u00e9 d&rsquo;un num\u00e9ro (s\u00e9curit\u00e9 sociale, compte bancaire,&#8230;): rappels sur les nombres premiers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Un nombre est dit <em>premier<\/em> s&rsquo;il n&rsquo;est divisible que par lui-m\u00eame et 1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c0 ce titre, \u00ab\u00a01\u00a0\u00bb n&rsquo;est pas un nombre premier.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pour avoir la liste des premiers nombres premiers, on peut par exemple utiliser le <a href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/24\/le-crible-deratosthene-en-python\/\" target=\"_blank\" rel=\"noreferrer noopener\">crible d&rsquo;Eratosth\u00e8ne<\/a> en Python (pourquoi pas ?)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Les cents premiers nombres premiers sont :<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Remarquez que le dernier nombre premier inf\u00e9rieur \u00e0 100 est 97. Je dis \u00e7a, je dis rien&#8230;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculer_la_cle_dun_numero_de_securite_sociale_avec_une_division_euclidienne\"><\/span>Calculer la cl\u00e9 d&rsquo;un num\u00e9ro de s\u00e9curit\u00e9 sociale avec une division euclidienne<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Je vais prendre un num\u00e9ro de s\u00e9curit\u00e9 sociale au hasard:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Comment calculer sa cl\u00e9 ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Avant tout, effectuons la division euclidienne de ce nombre par&#8230; 97 !<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"563\" height=\"358\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-2.png\" alt=\"\" class=\"wp-image-7653\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-2.png 563w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-2-300x191.png 300w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\\documentclass{article}\n\\usepackage{xlop}\n\\begin{document}\n\\opidiv{1891275125012}{97}\n\\end{document}<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Je ne me suis pas emb\u00eat\u00e9, et ai fait cela en \\(\\LaTeX\\). Pas folle la gu\u00eape!<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Maintenant, on soustrait \u00e0 97 le reste de cette division euclidienne:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">97 &#8211; 15 = 82<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La cl\u00e9 de contr\u00f4le de ce num\u00e9ro de s\u00e9curit\u00e9 sociale est donc 82.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculer_la_cle_dun_numero_de_compte_francais_avec_une_division_euclidienne\"><\/span>Calculer la cl\u00e9 d&rsquo;un num\u00e9ro de compte fran\u00e7ais avec une division euclidienne<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Un num\u00e9ro de compte bancaire est compos\u00e9 de 3 parties:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>le code \u00e9tablissement (que l&rsquo;on va noter A),<\/li><li>le code guichet (not\u00e9 B),<\/li><li>le num\u00e9ro de compte dans la banque (not\u00e9 C).<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Nous allons effectuer la division euclidienne de 89A+15B+3C par 97 (encore lui sacr\u00e9 vin diou!).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Une fois trouv\u00e9 le reste de cette division, on le soustraira \u00e0 97, comme pr\u00e9c\u00e9demment.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Prenons par exemple le compte (fictif):<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">13335<\/td><td class=\"has-text-align-center\" data-align=\"center\">00301<\/td><td class=\"has-text-align-center\" data-align=\"center\">04123456789<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">A<\/td><td class=\"has-text-align-center\" data-align=\"center\">B<\/td><td class=\"has-text-align-center\" data-align=\"center\">C<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">89A+15B+3C = 12371561697<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"316\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-4.png\" alt=\"calculer cl\u00e9 num\u00e9ro\" class=\"wp-image-7656\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-4.png 469w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2022\/06\/image-4-300x202.png 300w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">97 &#8211; 16 = 81<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La cl\u00e9 est donc \u00e9gale \u00e0 81. Bien jou\u00e9 Barnab\u00e9 !<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il arrive cependant que des compte poss\u00e8dent des lettres. Dans ce cas, il faut les remplacer par un nombre comme indiqu\u00e9 dans le tableau suivant:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">1<\/th><th class=\"has-text-align-center\" data-align=\"center\">2<\/th><th class=\"has-text-align-center\" data-align=\"center\">3<\/th><th class=\"has-text-align-center\" data-align=\"center\">4<\/th><th class=\"has-text-align-center\" data-align=\"center\">5<\/th><th class=\"has-text-align-center\" data-align=\"center\">6<\/th><th class=\"has-text-align-center\" data-align=\"center\">7<\/th><th class=\"has-text-align-center\" data-align=\"center\">8<\/th><th class=\"has-text-align-center\" data-align=\"center\">9<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">A<\/td><td class=\"has-text-align-center\" data-align=\"center\">B<\/td><td class=\"has-text-align-center\" data-align=\"center\">C<\/td><td class=\"has-text-align-center\" data-align=\"center\">D<\/td><td class=\"has-text-align-center\" data-align=\"center\">E<\/td><td class=\"has-text-align-center\" data-align=\"center\">F<\/td><td class=\"has-text-align-center\" data-align=\"center\">G<\/td><td class=\"has-text-align-center\" data-align=\"center\">H<\/td><td class=\"has-text-align-center\" data-align=\"center\">I<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">J<\/td><td class=\"has-text-align-center\" data-align=\"center\">K<\/td><td class=\"has-text-align-center\" data-align=\"center\">L<\/td><td class=\"has-text-align-center\" data-align=\"center\">M<\/td><td class=\"has-text-align-center\" data-align=\"center\">N<\/td><td class=\"has-text-align-center\" data-align=\"center\">O<\/td><td class=\"has-text-align-center\" data-align=\"center\">P<\/td><td class=\"has-text-align-center\" data-align=\"center\">Q<\/td><td class=\"has-text-align-center\" data-align=\"center\">R<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><\/td><td class=\"has-text-align-center\" data-align=\"center\">S<\/td><td class=\"has-text-align-center\" data-align=\"center\">T<\/td><td class=\"has-text-align-center\" data-align=\"center\">U<\/td><td class=\"has-text-align-center\" data-align=\"center\">V<\/td><td class=\"has-text-align-center\" data-align=\"center\">W<\/td><td class=\"has-text-align-center\" data-align=\"center\">X<\/td><td class=\"has-text-align-center\" data-align=\"center\">Y<\/td><td class=\"has-text-align-center\" data-align=\"center\">Z<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pour votre plus grand plaisir, je vous propose une fonction Python pour v\u00e9rifier si un IBAN est correct:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">def cle(iban):\n    L = {}\n    alphabet = 'ABCDEFGHIJKLMNOPQR'\n    alphabet2 = 'STUVWXYZ'\n    n = 1\n    for lettre in alphabet:\n        L[lettre] = str(n)\n        n = (n + 1) % 10\n        if n == 0:\n            n += 1\n        \n    n = 2\n    for lettre in alphabet2:\n        L[lettre] = str(n)\n        n = n+1\n        \n    iban = iban.replace(' ','')\n    for c in iban:\n        if c in L:\n            iban = iban.replace(c,L[c])\n            \n    K = int( iban[-2:] )\n    iban = iban[4:-2]\n    R = ( 89 * int( iban[0:5] ) + 15*int( iban[5:10] ) + 3*int( iban[10:] ) ) % 97\n    N = 97 - R\n    return N == K<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Ce script est bas\u00e9 sur les op\u00e9ration pr\u00e9c\u00e9dentes.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>>>> cle('FR7613335003010412345678981')\nTrue\n>>> cle('FR7613335003010412345678957')\nFalse<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Pourquoi_ces_calculs\"><\/span>Pourquoi ces calculs ?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">En fait, la cl\u00e9 de contr\u00f4le d&rsquo;un num\u00e9ro de compte en France est le nombre K de deux chiffres tel que le nombre \\(R\\) d\u00e9fini par:$$R=A\\times10^{18}+B\\times10^{13}+C\\times10^{2} + K$$ est tel que \\(R \\equiv 0 \\mod 97\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remarquez  que les exposants ne sont pas choisis au hasard et sont en fonction du nombre de chiffres qu&rsquo;il y a dans le num\u00e9ro de compte. C&rsquo;est pour cela que ces calculs ne fonctionnent pas sur un compte \u00e9tranger par exemple.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il faut donc l&rsquo;adapter aux diff\u00e9rentes normes&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Comment calculer la cl\u00e9 du num\u00e9ro qui compose votre compte bancaire ou votre num\u00e9ro de s\u00e9curit\u00e9 sociale ? Vous allez voir que la notion de nombres premiers n&rsquo;est pas \u00e9trang\u00e8re \u00e0 cette question&#8230;<\/p>\n","protected":false},"author":1,"featured_media":7659,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[349,348,124,101],"class_list":["post-7652","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","tag-comptes","tag-division-euclidienne","tag-nombres-premiers","tag-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculer la cl\u00e9 du num\u00e9ro (compte bancaire ou s\u00e9curit\u00e9 sociale)<\/title>\n<meta name=\"description\" content=\"Comment calculer la cl\u00e9 du num\u00e9ro qui compose votre compte bancaire ou votre num\u00e9ro de s\u00e9curit\u00e9 sociale ?\" \/>\n<meta name=\"robots\" content=\"index, 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