Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,700;1,400&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,300;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --noir: #0f0e0b;\n --creme: #f5f0e8;\n --indigo: #1a1a4e;\n --indigo-clair: #4a4aaa;\n --indigo-pale: #eeeeff;\n --or: #c8a010;\n --or-clair: #f0d060;\n --rouge: #b03a2e;\n --gris: #6b6560;\n --gris-clair: #e8e2d8;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n background-color: var(--creme);\n color: var(--noir);\n font-family: 'Source Serif 4', Georgia, serif;\n font-weight: 300;\n line-height: 1.8;\n }\n\n .hero {\n background: #08081e;\n color: var(--creme);\n padding: 80px 40px 70px;\n position: relative;\n overflow: hidden;\n }\n .hero::before {\n content: \"2 3 5 7 11\";\n position: absolute;\n top: 20px; right: 40px;\n font-size: 4rem;\n opacity: 0.06;\n font-family: 'Playfair Display', serif;\n letter-spacing: 0.3em;\n }\n .hero-inner { max-width: 760px; margin: 0 auto; }\n\n .article-rubrique {\n display: inline-block;\n background: var(--indigo-clair);\n color: white;\n font-size: 0.7rem;\n letter-spacing: 0.18em;\n text-transform: uppercase;\n padding: 4px 12px;\n margin-bottom: 24px;\n font-weight: 600;\n }\n\n .hero h1 {\n font-family: 'Playfair Display', serif;\n font-size: clamp(2rem, 5vw, 3.4rem);\n line-height: 1.2;\n margin-bottom: 24px;\n font-weight: 700;\n }\n .hero h1 em { color: var(--or-clair); font-style: italic; }\n\n .hero-intro {\n font-size: 1.15rem;\n opacity: 0.75;\n max-width: 600px;\n font-style: italic;\n border-left: 3px solid var(--indigo-clair);\n padding-left: 20px;\n margin-bottom: 32px;\n }\n .meta { font-size: 0.8rem; opacity: 0.45; letter-spacing: 0.08em; text-transform: uppercase; }\n\n .article-body { max-width: 760px; margin: 0 auto; padding: 60px 40px 80px; }\n .article-body p { font-size: 1.05rem; margin-bottom: 1.6em; color: #2a2520; }\n\n h2 {\n font-family: 'Playfair Display', serif;\n font-size: 1.6rem;\n margin: 2.5em 0 0.8em;\n color: var(--noir);\n font-weight: 700;\n }\n h2::before { content: \"\u00a7 \"; color: var(--indigo-clair); }\n\n h3 {\n font-family: 'Playfair Display', serif;\n font-size: 1.15rem;\n font-style: italic;\n margin: 2em 0 0.6em;\n color: var(--rouge);\n }\n\n .encadre {\n border: 1.5px solid var(--indigo-clair);\n background: white;\n padding: 24px 28px;\n margin: 2em 0;\n position: relative;\n }\n .encadre-titre {\n position: absolute;\n top: -12px; left: 20px;\n background: white;\n padding: 0 8px;\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--indigo-clair);\n font-weight: 600;\n }\n .encadre p { margin-bottom: 0.8em; font-size: 0.98rem; }\n .encadre p:last-child { margin-bottom: 0; }\n\n .encadre-histoire {\n background: #08081e;\n color: var(--creme);\n border: none;\n padding: 32px 36px;\n margin: 2.5em 0;\n }\n .encadre-histoire .encadre-titre { background: #08081e; color: var(--or-clair); }\n .encadre-histoire p { color: rgba(245,240,232,0.85); }\n\n .definition {\n background: var(--indigo-pale);\n border-left: 4px solid var(--indigo-clair);\n padding: 20px 24px;\n margin: 1.8em 0;\n font-style: italic;\n }\n .definition strong { font-style: normal; color: var(--indigo); font-family: 'Playfair Display', serif; }\n\n \/* GRILLE CRIBLE *\/\n .crible-grid {\n display: grid;\n grid-template-columns: repeat(10, 1fr);\n gap: 4px;\n margin: 1.5em 0;\n max-width: 500px;\n margin-left: auto;\n margin-right: auto;\n }\n .crible-cell {\n aspect-ratio: 1;\n display: flex;\n align-items: center;\n justify-content: center;\n font-size: 0.82rem;\n font-family: 'Playfair Display', serif;\n font-weight: 400;\n border-radius: 2px;\n }\n .premier { background: var(--indigo); color: white; font-weight: 700; }\n .compose { background: var(--gris-clair); color: var(--gris); text-decoration: line-through; }\n .un { background: #f0ebe3; color: #aaa; }\n\n .schema-container {\n background: white;\n border: 1.5px solid var(--indigo-clair);\n padding: 24px;\n margin: 2em 0;\n text-align: center;\n }\n .schema-titre {\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--indigo-clair);\n font-weight: 600;\n margin-bottom: 16px;\n }\n\n .formule {\n text-align: center;\n font-size: 1.3rem;\n font-family: 'Playfair Display', serif;\n margin: 1.5em 0;\n color: var(--noir);\n padding: 16px;\n background: white;\n border-top: 2px solid var(--indigo-clair);\n border-bottom: 2px solid var(--indigo-clair);\n }\n\n .etape {\n background: white;\n border-left: 3px solid var(--indigo-clair);\n padding: 12px 20px;\n margin: 0.6em 0;\n font-size: 0.97rem;\n }\n .etape-numero { font-family: 'Playfair Display', serif; font-weight: 700; color: var(--indigo-clair); margin-right: 8px; }\n\n .code-block {\n background: #08081e;\n color: #d0d0f0;\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.88rem;\n line-height: 1.7;\n overflow-x: auto;\n position: relative;\n }\n .code-label { position: absolute; top: 8px; right: 12px; font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--indigo-clair); font-family: 'Source Serif 4', serif; }\n .code-comment { color: #6a6aaa; }\n .code-keyword { color: #8888dd; }\n .code-string { color: var(--or-clair); }\n .code-number { color: #a0c0f0; }\n .code-function { color: #c0c0ff; }\n\n .table-container { overflow-x: auto; margin: 2em 0; }\n table { width: 100%; border-collapse: collapse; background: white; font-size: 0.95rem; }\n th { background: var(--indigo); color: white; padding: 12px 16px; text-align: center; font-family: 'Playfair Display', serif; font-weight: 400; }\n td { padding: 10px 16px; text-align: center; border-bottom: 1px solid var(--gris-clair); color: #2a2520; }\n tr:last-child td { border-bottom: none; }\n tr:nth-child(even) td { background: #f0f0ff; }\n\n .exercice {\n background: #08081e;\n color: var(--creme);\n padding: 36px 40px;\n margin: 3em 0;\n }\n .exercice h3 { color: var(--or-clair); font-style: normal; margin-top: 0; margin-bottom: 1em; font-size: 1.1rem; }\n .exercice p { color: rgba(245,240,232,0.82); font-size: 0.97rem; margin-bottom: 0.8em; }\n .exercice .correction { border-top: 1px solid rgba(74,74,170,0.4); margin-top: 1.5em; padding-top: 1.2em; }\n .exercice .correction-titre { font-size: 0.7rem; letter-spacing: 0.18em; text-transform: uppercase; color: var(--or-clair); margin-bottom: 0.8em; font-weight: 600; }\n\n blockquote {\n padding: 0 0 0 32px;\n margin: 2em 0;\n position: relative;\n font-style: italic;\n font-size: 1.12rem;\n color: #3a3530;\n }\n blockquote::before {\n content: \"\\201C\";\n position: absolute;\n left: 0; top: -10px;\n font-size: 3.5rem;\n color: var(--indigo-clair);\n font-family: 'Playfair Display', serif;\n line-height: 1;\n }\n blockquote cite { display: block; font-size: 0.82rem; font-style: normal; letter-spacing: 0.1em; text-transform: uppercase; color: var(--gris); margin-top: 8px; }\n\n .conclusion { border-top: 2px solid var(--noir); margin-top: 3em; padding-top: 2em; }\n\n @media (max-width: 600px) {\n .hero { padding: 50px 20px 40px; }\n .article-body { padding: 40px 20px 60px; }\n .exercice { padding: 24px 20px; }\n .code-block { padding: 16px; font-size: 0.78rem; }\n .crible-cell { font-size: 0.68rem; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"hero\">\n <div class=\"hero-inner\">\n <div class=\"article-rubrique\">Arithm\u00e9tique \u00b7 Article #8<\/div>\n <h1>Les nombres premiers :<br><em>le myst\u00e8re infini des maths<\/em><\/h1>\n <p class=\"hero-intro\">Ils sont simples \u00e0 d\u00e9finir, impossibles \u00e0 pr\u00e9voir, infinis en nombre \u2014 et ils prot\u00e8gent chaque transaction bancaire que tu fais sur ton t\u00e9l\u00e9phone. Les nombres premiers sont les atomes des math\u00e9matiques. Et leur myst\u00e8re r\u00e9siste depuis 2 500 ans aux plus grands esprits de l’histoire.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 11 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n <p>\n Quand tu envoies de l’argent via Mobile Money au B\u00e9nin \u2014 MTN ou Moov \u2014 ta transaction est prot\u00e9g\u00e9e par un secret math\u00e9matique. Ce secret repose enti\u00e8rement sur une propri\u00e9t\u00e9 myst\u00e9rieuse de certains nombres entiers, d\u00e9couverte par les Grecs il y a 2 500 ans. Ces nombres, ce sont les <strong>nombres premiers<\/strong>.\n <\/p>\n\n <p>\n Ils sont au c\u0153ur de l’arithm\u00e9tique, de la cryptographie moderne, et de certains des probl\u00e8mes les plus profonds et les plus non r\u00e9solus de toutes les math\u00e9matiques. Commen\u00e7ons par le commencement.\n <\/p>\n\n <h2>Qu’est-ce qu’un nombre premier ?<\/h2>\n\n <div class=\"definition\">\n <strong>Nombre premier :<\/strong> Un entier naturel sup\u00e9rieur \u00e0 1 qui n’est divisible que par 1 et par lui-m\u00eame. Autrement dit, il n’a exactement que deux diviseurs : 1 et lui-m\u00eame.\n <\/div>\n\n <p>\n Les premiers nombres premiers sont : <strong>2, 3, 5, 7, 11, 13, 17, 19, 23, 29…<\/strong>\n <\/p>\n\n <p>\n Pourquoi 4 n’est pas premier ? Parce que 4 = 2 \u00d7 2 \u2014 il est divisible par 2.\n Pourquoi 6 n’est pas premier ? Parce que 6 = 2 \u00d7 3.\n Pourquoi 1 n’est pas premier ? Par convention math\u00e9matique \u2014 et pour des raisons profondes li\u00e9es au th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique.\n <\/p>\n\n <p>\n Et 2 ? C’est le seul nombre premier <em>pair<\/em> \u2014 tous les autres pairs sont divisibles par 2, donc non premiers. Le 2 est vraiment unique.\n <\/p>\n\n <h2>Le th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique<\/h2>\n\n <p>\n Voici pourquoi les nombres premiers sont les <strong>atomes des math\u00e9matiques<\/strong> :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83c\udfdb\ufe0f Th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique<\/span>\n <p>Tout entier naturel sup\u00e9rieur \u00e0 1 peut s’\u00e9crire de fa\u00e7on <strong>unique<\/strong> comme produit de nombres premiers.<\/p>\n <p style=\"text-align:center; font-family:'Playfair Display',serif; font-size:1.1rem; margin: 12px 0;\">\n 12 = 2\u00b2 \u00d7 3 60 = 2\u00b2 \u00d7 3 \u00d7 5 100 = 2\u00b2 \u00d7 5\u00b2\n <\/p>\n <p>Comme les atomes composent toute la mati\u00e8re, les nombres premiers composent tous les entiers. C’est pour \u00e7a qu’on les appelle les \u00ab\u00a0atomes\u00a0\u00bb des math\u00e9matiques.<\/p>\n <\/div>\n\n <p>\n Cette d\u00e9composition en facteurs premiers est unique \u2014 il n’existe qu’une seule fa\u00e7on d’\u00e9crire un entier comme produit de premiers (\u00e0 l’ordre des facteurs pr\u00e8s). C’est une des propri\u00e9t\u00e9s les plus fondamentales de l’arithm\u00e9tique.\n <\/p>\n\n <h2>Le crible d’\u00c9ratosth\u00e8ne : trouver les premiers<\/h2>\n\n <div class=\"encadre-histoire encadre\">\n <span class=\"encadre-titre\">\ud83d\udcdc \u00c9ratosth\u00e8ne d’Alexandrie \u2014 III<sup>e<\/sup> si\u00e8cle av. J.-C.<\/span>\n <p>\n \u00c9ratosth\u00e8ne \u00e9tait un savant grec n\u00e9 \u00e0 Cyr\u00e8ne, dans l’actuelle Libye \u2014 en Afrique ! Il dirigeait la Grande Biblioth\u00e8que d’Alexandrie en \u00c9gypte. Il est c\u00e9l\u00e8bre pour avoir calcul\u00e9 avec une pr\u00e9cision remarquable la circonf\u00e9rence de la Terre, en mesurant les ombres \u00e0 diff\u00e9rents endroits d’Afrique du Nord.\n <\/p>\n <p>\n Il a \u00e9galement invent\u00e9 une m\u00e9thode simple et \u00e9l\u00e9gante pour trouver tous les nombres premiers jusqu’\u00e0 un certain nombre : le <strong>crible d’\u00c9ratosth\u00e8ne<\/strong>. Une invention africaine au c\u0153ur des math\u00e9matiques !\n <\/p>\n <\/div>\n\n <p><strong>Comment fonctionne le crible ?<\/strong> La m\u00e9thode est d’une simplicit\u00e9 d\u00e9sarmante :<\/p>\n\n <div class=\"etape\"><span class=\"etape-numero\">\u2460<\/span> \u00c9cris tous les entiers de 2 \u00e0 N<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2461<\/span> Commence par 2 : barre tous ses multiples (4, 6, 8…)<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2462<\/span> Passe au prochain nombre non barr\u00e9 (3) : barre tous ses multiples<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2463<\/span> Continue jusqu’\u00e0 \u221aN<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2464<\/span> Les nombres restants non barr\u00e9s sont tous premiers \u2705<\/div>\n\n <p>Voici le crible appliqu\u00e9 aux nombres de 1 \u00e0 50 :<\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83d\udd22 Crible d’\u00c9ratosth\u00e8ne \u2014 nombres de 1 \u00e0 50<\/div>\n <div class=\"crible-grid\">\n \n <div class=\"crible-cell un\">1<\/div>\n <div class=\"crible-cell premier\">2<\/div>\n <div class=\"crible-cell premier\">3<\/div>\n <div class=\"crible-cell compose\">4<\/div>\n <div class=\"crible-cell premier\">5<\/div>\n <div class=\"crible-cell compose\">6<\/div>\n <div class=\"crible-cell premier\">7<\/div>\n <div class=\"crible-cell compose\">8<\/div>\n <div class=\"crible-cell compose\">9<\/div>\n <div class=\"crible-cell compose\">10<\/div>\n \n <div class=\"crible-cell premier\">11<\/div>\n <div class=\"crible-cell compose\">12<\/div>\n <div class=\"crible-cell premier\">13<\/div>\n <div class=\"crible-cell compose\">14<\/div>\n <div class=\"crible-cell compose\">15<\/div>\n <div class=\"crible-cell compose\">16<\/div>\n <div class=\"crible-cell premier\">17<\/div>\n <div class=\"crible-cell compose\">18<\/div>\n <div class=\"crible-cell premier\">19<\/div>\n <div class=\"crible-cell compose\">20<\/div>\n \n <div class=\"crible-cell compose\">21<\/div>\n <div class=\"crible-cell compose\">22<\/div>\n <div class=\"crible-cell premier\">23<\/div>\n <div class=\"crible-cell compose\">24<\/div>\n <div class=\"crible-cell compose\">25<\/div>\n <div class=\"crible-cell compose\">26<\/div>\n <div class=\"crible-cell compose\">27<\/div>\n <div class=\"crible-cell compose\">28<\/div>\n <div class=\"crible-cell premier\">29<\/div>\n <div class=\"crible-cell compose\">30<\/div>\n \n <div class=\"crible-cell premier\">31<\/div>\n <div class=\"crible-cell compose\">32<\/div>\n <div class=\"crible-cell compose\">33<\/div>\n <div class=\"crible-cell compose\">34<\/div>\n <div class=\"crible-cell compose\">35<\/div>\n <div class=\"crible-cell compose\">36<\/div>\n <div class=\"crible-cell premier\">37<\/div>\n <div class=\"crible-cell compose\">38<\/div>\n <div class=\"crible-cell compose\">39<\/div>\n <div class=\"crible-cell compose\">40<\/div>\n \n <div class=\"crible-cell premier\">41<\/div>\n <div class=\"crible-cell compose\">42<\/div>\n <div class=\"crible-cell premier\">43<\/div>\n <div class=\"crible-cell compose\">44<\/div>\n <div class=\"crible-cell compose\">45<\/div>\n <div class=\"crible-cell compose\">46<\/div>\n <div class=\"crible-cell premier\">47<\/div>\n <div class=\"crible-cell compose\">48<\/div>\n <div class=\"crible-cell compose\">49<\/div>\n <div class=\"crible-cell compose\">50<\/div>\n <\/div>\n <p style=\"font-size:0.82rem; color:#6b6560; margin-top:12px;\">\n <span style=\"background:#1a1a4e; color:white; padding:2px 6px; margin-right:6px;\">Nombres premiers<\/span>\n <span style=\"background:#e8e2d8; color:#6b6560; padding:2px 6px; text-decoration:line-through;\">Compos\u00e9s (barr\u00e9s)<\/span>\n <\/p>\n <\/div>\n\n <h2>Y en a-t-il une infinit\u00e9 ? La preuve d’Euclide<\/h2>\n\n <p>\n Une question naturelle : est-ce que les nombres premiers continuent ind\u00e9finiment, ou s’arr\u00eatent-ils \u00e0 un moment ? Euclide a r\u00e9pondu \u00e0 cette question il y a 2 300 ans avec une d\u00e9monstration d’une beaut\u00e9 rare \u2014 consid\u00e9r\u00e9e comme l’une des plus \u00e9l\u00e9gantes de toute l’histoire des math\u00e9matiques.\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83c\udfdb\ufe0f Th\u00e9or\u00e8me d’Euclide : il existe une infinit\u00e9 de nombres premiers<\/span>\n <p><strong>Preuve par l’absurde :<\/strong><\/p>\n <p>Supposons qu’il n’existe qu’un nombre <em>fini<\/em> de premiers : p\u2081, p\u2082, p\u2083, …, p\u2099.<\/p>\n <p>Construisons le nombre : <strong>M = (p\u2081 \u00d7 p\u2082 \u00d7 p\u2083 \u00d7 … \u00d7 p\u2099) + 1<\/strong><\/p>\n <p>M n’est divisible par aucun des p\u1d62 (il donne le reste 1 pour chacun).<\/p>\n <p>Donc soit M est premier lui-m\u00eame, soit il a un facteur premier qui n’est pas dans notre liste.<\/p>\n <p>Dans les deux cas \u2192 <strong>contradiction<\/strong> ! Notre liste n’\u00e9tait pas compl\u00e8te.<\/p>\n <p>Conclusion : <strong>il existe une infinit\u00e9 de nombres premiers.<\/strong> \u2713<\/p>\n <\/div>\n\n <p>\n Cette preuve n’utilise aucune formule compliqu\u00e9e \u2014 juste de la logique pure. C’est la marque des grandes d\u00e9monstrations math\u00e9matiques.\n <\/p>\n\n <h2>La distribution des premiers : un myst\u00e8re profond<\/h2>\n\n <p>\n Si les premiers sont infinis, comment sont-ils distribu\u00e9s ? Deviennent-ils de plus en plus rares ? Existe-t-il un motif dans leur apparition ?\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Intervalle<\/th>\n <th>Nombres premiers<\/th>\n <th>Densit\u00e9 approximative<\/th>\n <\/tr>\n <tr><td>1 \u2014 100<\/td><td>25<\/td><td>1 sur 4<\/td><\/tr>\n <tr><td>1 \u2014 1 000<\/td><td>168<\/td><td>1 sur 6<\/td><\/tr>\n <tr><td>1 \u2014 10 000<\/td><td>1 229<\/td><td>1 sur 8<\/td><\/tr>\n <tr><td>1 \u2014 100 000<\/td><td>9 592<\/td><td>1 sur 10<\/td><\/tr>\n <tr><td>1 \u2014 1 000 000<\/td><td>78 498<\/td><td>1 sur 13<\/td><\/tr>\n <\/table>\n <\/div>\n\n <p>\n Les premiers deviennent progressivement plus rares, mais ne disparaissent jamais. Le <strong>th\u00e9or\u00e8me des nombres premiers<\/strong> dit que la densit\u00e9 des premiers pr\u00e8s de N est approximativement <strong>1\/ln(N)<\/strong>. Plus N est grand, plus les premiers sont espac\u00e9s \u2014 mais ils ne s’arr\u00eatent jamais.\n <\/p>\n\n <h2>Les nombres premiers et la cryptographie<\/h2>\n\n <p>\n Voil\u00e0 le lien avec ton Mobile Money. Le syst\u00e8me RSA \u2014 qui prot\u00e8ge la quasi-totalit\u00e9 des communications num\u00e9riques mondiales \u2014 repose sur un fait simple mais puissant :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udd10 Le secret RSA<\/span>\n <p><strong>Multiplier deux grands nombres premiers est facile.<\/strong><\/p>\n <p>Exemple : 104 729 \u00d7 224 737 = 23 537 063 273<\/p>\n <p style=\"margin-top: 8px\"><strong>Faire l’inverse \u2014 trouver les deux premiers \u00e0 partir du produit \u2014 est extr\u00eamement difficile.<\/strong><\/p>\n <p>Si on te donne 23 537 063 273, retrouver 104 729 et 224 737 prend du temps m\u00eame pour un ordinateur.<\/p>\n <p style=\"margin-top: 8px\">Avec des nombres de 300 chiffres, m\u00eame les supercalculateurs actuels ne peuvent pas factoriser en un temps raisonnable. C’est sur cette asym\u00e9trie que repose toute la s\u00e9curit\u00e9 d’Internet.<\/p>\n <\/div>\n\n <p>\n Chaque fois que tu vois le cadenas \ud83d\udd12 dans ton navigateur, ou que tu envoies de l’argent par t\u00e9l\u00e9phone, des nombres premiers de 300 chiffres travaillent en silence pour prot\u00e9ger tes donn\u00e9es.\n <\/p>\n\n <h2>Les myst\u00e8res non r\u00e9solus<\/h2>\n\n <p>\n Ce qui rend les nombres premiers fascinants, c’est que malgr\u00e9 2 500 ans d’\u00e9tudes, ils gardent encore des secrets profonds. Voici les grands probl\u00e8mes ouverts :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\u2753 Probl\u00e8mes non r\u00e9solus \u2014 des millions d’euros en jeu<\/span>\n <p><strong>Conjecture de Goldbach (1742) :<\/strong> Tout entier pair sup\u00e9rieur \u00e0 2 est la somme de deux nombres premiers. Ex : 8 = 3+5, 10 = 3+7. V\u00e9rifi\u00e9 jusqu’\u00e0 4\u00d710\u00b9\u2078 \u2014 jamais prouv\u00e9 en g\u00e9n\u00e9ral.<\/p>\n <p><strong>Conjecture des premiers jumeaux :<\/strong> Il existe une infinit\u00e9 de paires de premiers s\u00e9par\u00e9s de 2 (comme 11 et 13, 17 et 19, 41 et 43). Non prouv\u00e9.<\/p>\n <p><strong>Hypoth\u00e8se de Riemann (1859) :<\/strong> Le probl\u00e8me le plus c\u00e9l\u00e8bre des math\u00e9matiques. Concerne la distribution des nombres premiers. Non r\u00e9solu. L’Institut Clay offre <strong>1 million de dollars<\/strong> \u00e0 qui le r\u00e9soudra.<\/p>\n <\/div>\n\n <h2>Le code Python : crible et applications<\/h2>\n\n <div class=\"code-block\">\n <span class=\"code-label\">Python<\/span>\n<span class=\"code-comment\"># Nombres premiers : crible, v\u00e9rification et applications<\/span>\n<span class=\"code-keyword\">import<\/span> math\n\n<span class=\"code-comment\"># — Crible d’\u00c9ratosth\u00e8ne —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">crible_eratosthene<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbRetourne tous les nombres premiers jusqu’\u00e0 n\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n est_premier = [<span class=\"code-keyword\">True<\/span>] * (n + <span class=\"code-number\">1<\/span>)\n est_premier[<span class=\"code-number\">0<\/span>] = est_premier[<span class=\"code-number\">1<\/span>] = <span class=\"code-keyword\">False<\/span>\n <span class=\"code-keyword\">for<\/span> i <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">2<\/span>, <span class=\"code-function\">int<\/span>(math.<span class=\"code-function\">sqrt<\/span>(n)) + <span class=\"code-number\">1<\/span>):\n <span class=\"code-keyword\">if<\/span> est_premier[i]:\n <span class=\"code-keyword\">for<\/span> j <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(i*i, n+<span class=\"code-number\">1<\/span>, i):\n est_premier[j] = <span class=\"code-keyword\">False<\/span>\n <span class=\"code-keyword\">return<\/span> [i <span class=\"code-keyword\">for<\/span> i <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">2<\/span>, n+<span class=\"code-number\">1<\/span>) <span class=\"code-keyword\">if<\/span> est_premier[i]]\n\n<span class=\"code-comment\"># Trouver tous les premiers jusqu’\u00e0 100<\/span>\npremiers = <span class=\"code-function\">crible_eratosthene<\/span>(<span class=\"code-number\">100<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbPremiers jusqu’\u00e0 100 : {premiers}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbNombre de premiers : {len(premiers)}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># — D\u00e9composition en facteurs premiers —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">facteurs_premiers<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbD\u00e9compose n en facteurs premiers\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n facteurs = {}\n d = <span class=\"code-number\">2<\/span>\n <span class=\"code-keyword\">while<\/span> d * d <= n:\n <span class=\"code-keyword\">while<\/span> n % d == <span class=\"code-number\">0<\/span>:\n facteurs[d] = facteurs.<span class=\"code-function\">get<\/span>(d, <span class=\"code-number\">0<\/span>) + <span class=\"code-number\">1<\/span>\n n \/\/= d\n d += <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">if<\/span> n > <span class=\"code-number\">1<\/span>:\n facteurs[n] = facteurs.<span class=\"code-function\">get<\/span>(n, <span class=\"code-number\">0<\/span>) + <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> facteurs\n\n<span class=\"code-comment\"># Exemples de d\u00e9compositions<\/span>\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">12<\/span>, <span class=\"code-number\">60<\/span>, <span class=\"code-number\">360<\/span>, <span class=\"code-number\">1000<\/span>]:\n f = <span class=\"code-function\">facteurs_premiers<\/span>(n)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb{n} = {‘ \u00d7 ‘.join([f'{p}^{e}’ if e>1 else str(p) for p,e in f.items()])}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># — V\u00e9rification conjecture de Goldbach —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">goldbach<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbTrouve deux premiers dont la somme = n\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n premiers_set = <span class=\"code-function\">set<\/span>(<span class=\"code-function\">crible_eratosthene<\/span>(n))\n <span class=\"code-keyword\">for<\/span> p <span class=\"code-keyword\">in<\/span> premiers_set:\n <span class=\"code-keyword\">if<\/span> (n – p) <span class=\"code-keyword\">in<\/span> premiers_set:\n <span class=\"code-keyword\">return<\/span> (p, n – p)\n <span class=\"code-keyword\">return<\/span> <span class=\"code-keyword\">None<\/span>\n\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">\u00ab\u00a0\\nConjecture de Goldbach :\u00a0\u00bb<\/span>)\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">8<\/span>, <span class=\"code-number\">20<\/span>, <span class=\"code-number\">100<\/span>, <span class=\"code-number\">2026<\/span>]:\n p1, p2 = <span class=\"code-function\">goldbach<\/span>(n)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb{n} = {p1} + {p2}\u00a0\u00bb<\/span>)\n <\/div>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udcbb R\u00e9sultat attendu<\/span>\n <p>Premiers jusqu’\u00e0 100 : [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]<\/p>\n <p>Nombre de premiers : <strong>25<\/strong><\/p>\n <p>12 = 2\u00b2 \u00d7 3 | 60 = 2\u00b2 \u00d7 3 \u00d7 5 | 360 = 2\u00b3 \u00d7 3\u00b2 \u00d7 5<\/p>\n <p>Goldbach : 2026 = 3 + 2023 … ou une autre paire \u2713<\/p>\n <\/div>\n\n <blockquote>\n Les nombres premiers sont comme les \u00e9toiles dans le ciel nocturne de Cotonou \u2014 impr\u00e9visibles dans leur position, infinis dans leur nombre, et pourtant gouvern\u00e9s par des lois profondes que nous commen\u00e7ons \u00e0 peine \u00e0 comprendre.\n <cite>\u2014 Inspiration math\u00e9matique<\/cite>\n <\/blockquote>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9<\/h3>\n <p>\n Un \u00e9l\u00e8ve de 5\u00e8me \u00e0 Abomey-Calavi travaille sur les nombres premiers.\n <\/p>\n <p><strong>a)<\/strong> Donne la liste de tous les nombres premiers compris entre 50 et 80.<\/p>\n <p><strong>b)<\/strong> D\u00e9compose 360 en produit de facteurs premiers.<\/p>\n <p><strong>c)<\/strong> V\u00e9rifie la conjecture de Goldbach pour n = 28 et n = 50.<\/p>\n <p><strong>d)<\/strong> Parmi ces nombres : 91, 97, 101, 111 \u2014 lesquels sont premiers ? Justifie.<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n <p><strong>a)<\/strong> On teste la divisibilit\u00e9 par les premiers \u2264 \u221a80 \u2248 9 (donc 2, 3, 5, 7) :<\/p>\n <p>53 \u2713, 59 \u2713, 61 \u2713, 67 \u2713, 71 \u2713, 73 \u2713, 79 \u2713<\/p>\n <p>R\u00e9ponse : <strong>53, 59, 61, 67, 71, 73, 79<\/strong><\/p>\n <p><strong>b)<\/strong> 360 = 2 \u00d7 180 = 2 \u00d7 2 \u00d7 90 = 2 \u00d7 2 \u00d7 2 \u00d7 45 = 2 \u00d7 2 \u00d7 2 \u00d7 9 \u00d7 5 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 5<\/p>\n <p>\u2192 <strong>360 = 2\u00b3 \u00d7 3\u00b2 \u00d7 5<\/strong><\/p>\n <p><strong>c)<\/strong> 28 = 5 + 23 \u2713 (5 et 23 premiers) | 50 = 3 + 47 \u2713 (3 et 47 premiers)<\/p>\n <p><strong>d)<\/strong> 91 = 7 \u00d7 13 \u2192 <strong>non premier<\/strong><\/p>\n <p>97 : non divisible par 2, 3, 5, 7 (\u221a97 \u2248 9,8) \u2192 <strong>premier \u2713<\/strong><\/p>\n <p>101 : non divisible par 2, 3, 5, 7 (\u221a101 \u2248 10) \u2192 <strong>premier \u2713<\/strong><\/p>\n <p>111 = 3 \u00d7 37 \u2192 <strong>non premier<\/strong><\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n <p>\n Les nombres premiers sont \u00e0 la fois les objets math\u00e9matiques les plus simples \u00e0 d\u00e9finir et les plus difficiles \u00e0 comprendre en profondeur. Ils sont les fondations invisibles sur lesquelles repose toute l’arithm\u00e9tique \u2014 et, par extension, toute la s\u00e9curit\u00e9 num\u00e9rique moderne.\n <\/p>\n <p>\n La prochaine fois que tu envoies de l’argent par Mobile Money, souviens-toi : quelque part dans les circuits de ton t\u00e9l\u00e9phone, deux nombres premiers g\u00e9ants se multiplient en silence pour garder ton argent en s\u00e9curit\u00e9. Les maths de \u00c9ratosth\u00e8ne \u2014 n\u00e9 en Afrique \u2014 prot\u00e8gent ton portefeuille aujourd’hui.\n <\/p>\n <p>\n Dans le prochain article, nous plongerons dans la <strong>loi normale et la courbe en cloche<\/strong> \u2014 cette forme myst\u00e9rieuse qui appara\u00eet partout : dans les notes des \u00e9l\u00e8ves, la taille des adultes, les erreurs de mesure, et m\u00eame les fluctuations des prix au march\u00e9 de Dantokpa.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-89","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Nombres premiers - AfrikIntelligent<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vmi3217629.contaboserver.net\/?p=89\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nombres premiers - AfrikIntelligent\" \/>\n<meta property=\"og:description\" content=\"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vmi3217629.contaboserver.net\/?p=89\" \/>\n<meta property=\"og:site_name\" content=\"AfrikIntelligent\" \/>\n<meta property=\"article:published_time\" content=\"2026-04-19T22:37:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-19T22:37:36+00:00\" \/>\n<meta name=\"author\" content=\"Odilon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Odilon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"},\"author\":{\"name\":\"Odilon\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"headline\":\"Nombres premiers\",\"datePublished\":\"2026-04-19T22:37:34+00:00\",\"dateModified\":\"2026-04-19T22:37:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"},\"wordCount\":1611,\"commentCount\":0,\"articleSection\":[\"Fondements\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\",\"name\":\"Nombres premiers - AfrikIntelligent\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\"},\"datePublished\":\"2026-04-19T22:37:34+00:00\",\"dateModified\":\"2026-04-19T22:37:36+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Nombres premiers\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\",\"name\":\"AfrikIntelligent\",\"description\":\"Append autrement\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\",\"name\":\"Odilon\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"caption\":\"Odilon\"},\"sameAs\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\"],\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?author=1\"}]}<\/script>\n","yoast_head_json":{"title":"Nombres premiers - AfrikIntelligent","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/vmi3217629.contaboserver.net\/?p=89","og_locale":"fr_FR","og_type":"article","og_title":"Nombres premiers - AfrikIntelligent","og_description":"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]","og_url":"https:\/\/vmi3217629.contaboserver.net\/?p=89","og_site_name":"AfrikIntelligent","article_published_time":"2026-04-19T22:37:34+00:00","article_modified_time":"2026-04-19T22:37:36+00:00","author":"Odilon","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Odilon","Dur\u00e9e de lecture estim\u00e9e":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#article","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89"},"author":{"name":"Odilon","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"headline":"Nombres premiers","datePublished":"2026-04-19T22:37:34+00:00","dateModified":"2026-04-19T22:37:36+00:00","mainEntityOfPage":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89"},"wordCount":1611,"commentCount":0,"articleSection":["Fondements"],"inLanguage":"fr-FR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/vmi3217629.contaboserver.net\/?p=89#respond"]}]},{"@type":"WebPage","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89","url":"https:\/\/vmi3217629.contaboserver.net\/?p=89","name":"Nombres premiers - AfrikIntelligent","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#website"},"datePublished":"2026-04-19T22:37:34+00:00","dateModified":"2026-04-19T22:37:36+00:00","author":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"breadcrumb":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/vmi3217629.contaboserver.net\/?p=89"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/vmi3217629.contaboserver.net\/"},{"@type":"ListItem","position":2,"name":"Nombres premiers"}]},{"@type":"WebSite","@id":"https:\/\/vmi3217629.contaboserver.net\/#website","url":"https:\/\/vmi3217629.contaboserver.net\/","name":"AfrikIntelligent","description":"Append autrement","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vmi3217629.contaboserver.net\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923","name":"Odilon","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","caption":"Odilon"},"sameAs":["https:\/\/vmi3217629.contaboserver.net"],"url":"https:\/\/vmi3217629.contaboserver.net\/?author=1"}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"Odilon","author_link":"https:\/\/vmi3217629.contaboserver.net\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]","_links":{"self":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=89"}],"version-history":[{"count":1,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":90,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89\/revisions\/90"}],"wp:attachment":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":89,"date":"2026-04-19T23:37:34","date_gmt":"2026-04-19T22:37:34","guid":{"rendered":"https:\/\/vmi3217629.contaboserver.net\/?p=89"},"modified":"2026-04-19T23:37:36","modified_gmt":"2026-04-19T22:37:36","slug":"nombres-premiers","status":"publish","type":"post","link":"https:\/\/vmi3217629.contaboserver.net\/?p=89","title":{"rendered":"Nombres premiers"},"content":{"rendered":"\n\n\n\n\n\nLes nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,700;1,400&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,300;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n :root {\n --noir: #0f0e0b;\n --creme: #f5f0e8;\n --indigo: #1a1a4e;\n --indigo-clair: #4a4aaa;\n --indigo-pale: #eeeeff;\n --or: #c8a010;\n --or-clair: #f0d060;\n --rouge: #b03a2e;\n --gris: #6b6560;\n --gris-clair: #e8e2d8;\n }\n\n * { margin: 0; padding: 0; box-sizing: border-box; }\n\n body {\n background-color: var(--creme);\n color: var(--noir);\n font-family: 'Source Serif 4', Georgia, serif;\n font-weight: 300;\n line-height: 1.8;\n }\n\n .hero {\n background: #08081e;\n color: var(--creme);\n padding: 80px 40px 70px;\n position: relative;\n overflow: hidden;\n }\n .hero::before {\n content: \"2 3 5 7 11\";\n position: absolute;\n top: 20px; right: 40px;\n font-size: 4rem;\n opacity: 0.06;\n font-family: 'Playfair Display', serif;\n letter-spacing: 0.3em;\n }\n .hero-inner { max-width: 760px; margin: 0 auto; }\n\n .article-rubrique {\n display: inline-block;\n background: var(--indigo-clair);\n color: white;\n font-size: 0.7rem;\n letter-spacing: 0.18em;\n text-transform: uppercase;\n padding: 4px 12px;\n margin-bottom: 24px;\n font-weight: 600;\n }\n\n .hero h1 {\n font-family: 'Playfair Display', serif;\n font-size: clamp(2rem, 5vw, 3.4rem);\n line-height: 1.2;\n margin-bottom: 24px;\n font-weight: 700;\n }\n .hero h1 em { color: var(--or-clair); font-style: italic; }\n\n .hero-intro {\n font-size: 1.15rem;\n opacity: 0.75;\n max-width: 600px;\n font-style: italic;\n border-left: 3px solid var(--indigo-clair);\n padding-left: 20px;\n margin-bottom: 32px;\n }\n .meta { font-size: 0.8rem; opacity: 0.45; letter-spacing: 0.08em; text-transform: uppercase; }\n\n .article-body { max-width: 760px; margin: 0 auto; padding: 60px 40px 80px; }\n .article-body p { font-size: 1.05rem; margin-bottom: 1.6em; color: #2a2520; }\n\n h2 {\n font-family: 'Playfair Display', serif;\n font-size: 1.6rem;\n margin: 2.5em 0 0.8em;\n color: var(--noir);\n font-weight: 700;\n }\n h2::before { content: \"\u00a7 \"; color: var(--indigo-clair); }\n\n h3 {\n font-family: 'Playfair Display', serif;\n font-size: 1.15rem;\n font-style: italic;\n margin: 2em 0 0.6em;\n color: var(--rouge);\n }\n\n .encadre {\n border: 1.5px solid var(--indigo-clair);\n background: white;\n padding: 24px 28px;\n margin: 2em 0;\n position: relative;\n }\n .encadre-titre {\n position: absolute;\n top: -12px; left: 20px;\n background: white;\n padding: 0 8px;\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--indigo-clair);\n font-weight: 600;\n }\n .encadre p { margin-bottom: 0.8em; font-size: 0.98rem; }\n .encadre p:last-child { margin-bottom: 0; }\n\n .encadre-histoire {\n background: #08081e;\n color: var(--creme);\n border: none;\n padding: 32px 36px;\n margin: 2.5em 0;\n }\n .encadre-histoire .encadre-titre { background: #08081e; color: var(--or-clair); }\n .encadre-histoire p { color: rgba(245,240,232,0.85); }\n\n .definition {\n background: var(--indigo-pale);\n border-left: 4px solid var(--indigo-clair);\n padding: 20px 24px;\n margin: 1.8em 0;\n font-style: italic;\n }\n .definition strong { font-style: normal; color: var(--indigo); font-family: 'Playfair Display', serif; }\n\n \/* GRILLE CRIBLE *\/\n .crible-grid {\n display: grid;\n grid-template-columns: repeat(10, 1fr);\n gap: 4px;\n margin: 1.5em 0;\n max-width: 500px;\n margin-left: auto;\n margin-right: auto;\n }\n .crible-cell {\n aspect-ratio: 1;\n display: flex;\n align-items: center;\n justify-content: center;\n font-size: 0.82rem;\n font-family: 'Playfair Display', serif;\n font-weight: 400;\n border-radius: 2px;\n }\n .premier { background: var(--indigo); color: white; font-weight: 700; }\n .compose { background: var(--gris-clair); color: var(--gris); text-decoration: line-through; }\n .un { background: #f0ebe3; color: #aaa; }\n\n .schema-container {\n background: white;\n border: 1.5px solid var(--indigo-clair);\n padding: 24px;\n margin: 2em 0;\n text-align: center;\n }\n .schema-titre {\n font-size: 0.72rem;\n letter-spacing: 0.15em;\n text-transform: uppercase;\n color: var(--indigo-clair);\n font-weight: 600;\n margin-bottom: 16px;\n }\n\n .formule {\n text-align: center;\n font-size: 1.3rem;\n font-family: 'Playfair Display', serif;\n margin: 1.5em 0;\n color: var(--noir);\n padding: 16px;\n background: white;\n border-top: 2px solid var(--indigo-clair);\n border-bottom: 2px solid var(--indigo-clair);\n }\n\n .etape {\n background: white;\n border-left: 3px solid var(--indigo-clair);\n padding: 12px 20px;\n margin: 0.6em 0;\n font-size: 0.97rem;\n }\n .etape-numero { font-family: 'Playfair Display', serif; font-weight: 700; color: var(--indigo-clair); margin-right: 8px; }\n\n .code-block {\n background: #08081e;\n color: #d0d0f0;\n padding: 24px 28px;\n margin: 2em 0;\n font-family: 'Courier New', monospace;\n font-size: 0.88rem;\n line-height: 1.7;\n overflow-x: auto;\n position: relative;\n }\n .code-label { position: absolute; top: 8px; right: 12px; font-size: 0.65rem; letter-spacing: 0.15em; text-transform: uppercase; color: var(--indigo-clair); font-family: 'Source Serif 4', serif; }\n .code-comment { color: #6a6aaa; }\n .code-keyword { color: #8888dd; }\n .code-string { color: var(--or-clair); }\n .code-number { color: #a0c0f0; }\n .code-function { color: #c0c0ff; }\n\n .table-container { overflow-x: auto; margin: 2em 0; }\n table { width: 100%; border-collapse: collapse; background: white; font-size: 0.95rem; }\n th { background: var(--indigo); color: white; padding: 12px 16px; text-align: center; font-family: 'Playfair Display', serif; font-weight: 400; }\n td { padding: 10px 16px; text-align: center; border-bottom: 1px solid var(--gris-clair); color: #2a2520; }\n tr:last-child td { border-bottom: none; }\n tr:nth-child(even) td { background: #f0f0ff; }\n\n .exercice {\n background: #08081e;\n color: var(--creme);\n padding: 36px 40px;\n margin: 3em 0;\n }\n .exercice h3 { color: var(--or-clair); font-style: normal; margin-top: 0; margin-bottom: 1em; font-size: 1.1rem; }\n .exercice p { color: rgba(245,240,232,0.82); font-size: 0.97rem; margin-bottom: 0.8em; }\n .exercice .correction { border-top: 1px solid rgba(74,74,170,0.4); margin-top: 1.5em; padding-top: 1.2em; }\n .exercice .correction-titre { font-size: 0.7rem; letter-spacing: 0.18em; text-transform: uppercase; color: var(--or-clair); margin-bottom: 0.8em; font-weight: 600; }\n\n blockquote {\n padding: 0 0 0 32px;\n margin: 2em 0;\n position: relative;\n font-style: italic;\n font-size: 1.12rem;\n color: #3a3530;\n }\n blockquote::before {\n content: \"\\201C\";\n position: absolute;\n left: 0; top: -10px;\n font-size: 3.5rem;\n color: var(--indigo-clair);\n font-family: 'Playfair Display', serif;\n line-height: 1;\n }\n blockquote cite { display: block; font-size: 0.82rem; font-style: normal; letter-spacing: 0.1em; text-transform: uppercase; color: var(--gris); margin-top: 8px; }\n\n .conclusion { border-top: 2px solid var(--noir); margin-top: 3em; padding-top: 2em; }\n\n @media (max-width: 600px) {\n .hero { padding: 50px 20px 40px; }\n .article-body { padding: 40px 20px 60px; }\n .exercice { padding: 24px 20px; }\n .code-block { padding: 16px; font-size: 0.78rem; }\n .crible-cell { font-size: 0.68rem; }\n }\n<\/style>\n<\/head>\n<body>\n\n<div class=\"hero\">\n <div class=\"hero-inner\">\n <div class=\"article-rubrique\">Arithm\u00e9tique \u00b7 Article #8<\/div>\n <h1>Les nombres premiers :<br><em>le myst\u00e8re infini des maths<\/em><\/h1>\n <p class=\"hero-intro\">Ils sont simples \u00e0 d\u00e9finir, impossibles \u00e0 pr\u00e9voir, infinis en nombre \u2014 et ils prot\u00e8gent chaque transaction bancaire que tu fais sur ton t\u00e9l\u00e9phone. Les nombres premiers sont les atomes des math\u00e9matiques. Et leur myst\u00e8re r\u00e9siste depuis 2 500 ans aux plus grands esprits de l’histoire.<\/p>\n <div class=\"meta\">Par Odilon AKOWANOU \u00b7 MathsVivantes \u00b7 Lecture : 11 min<\/div>\n <\/div>\n<\/div>\n\n<article class=\"article-body\">\n\n <p>\n Quand tu envoies de l’argent via Mobile Money au B\u00e9nin \u2014 MTN ou Moov \u2014 ta transaction est prot\u00e9g\u00e9e par un secret math\u00e9matique. Ce secret repose enti\u00e8rement sur une propri\u00e9t\u00e9 myst\u00e9rieuse de certains nombres entiers, d\u00e9couverte par les Grecs il y a 2 500 ans. Ces nombres, ce sont les <strong>nombres premiers<\/strong>.\n <\/p>\n\n <p>\n Ils sont au c\u0153ur de l’arithm\u00e9tique, de la cryptographie moderne, et de certains des probl\u00e8mes les plus profonds et les plus non r\u00e9solus de toutes les math\u00e9matiques. Commen\u00e7ons par le commencement.\n <\/p>\n\n <h2>Qu’est-ce qu’un nombre premier ?<\/h2>\n\n <div class=\"definition\">\n <strong>Nombre premier :<\/strong> Un entier naturel sup\u00e9rieur \u00e0 1 qui n’est divisible que par 1 et par lui-m\u00eame. Autrement dit, il n’a exactement que deux diviseurs : 1 et lui-m\u00eame.\n <\/div>\n\n <p>\n Les premiers nombres premiers sont : <strong>2, 3, 5, 7, 11, 13, 17, 19, 23, 29…<\/strong>\n <\/p>\n\n <p>\n Pourquoi 4 n’est pas premier ? Parce que 4 = 2 \u00d7 2 \u2014 il est divisible par 2.\n Pourquoi 6 n’est pas premier ? Parce que 6 = 2 \u00d7 3.\n Pourquoi 1 n’est pas premier ? Par convention math\u00e9matique \u2014 et pour des raisons profondes li\u00e9es au th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique.\n <\/p>\n\n <p>\n Et 2 ? C’est le seul nombre premier <em>pair<\/em> \u2014 tous les autres pairs sont divisibles par 2, donc non premiers. Le 2 est vraiment unique.\n <\/p>\n\n <h2>Le th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique<\/h2>\n\n <p>\n Voici pourquoi les nombres premiers sont les <strong>atomes des math\u00e9matiques<\/strong> :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83c\udfdb\ufe0f Th\u00e9or\u00e8me fondamental de l’arithm\u00e9tique<\/span>\n <p>Tout entier naturel sup\u00e9rieur \u00e0 1 peut s’\u00e9crire de fa\u00e7on <strong>unique<\/strong> comme produit de nombres premiers.<\/p>\n <p style=\"text-align:center; font-family:'Playfair Display',serif; font-size:1.1rem; margin: 12px 0;\">\n 12 = 2\u00b2 \u00d7 3 60 = 2\u00b2 \u00d7 3 \u00d7 5 100 = 2\u00b2 \u00d7 5\u00b2\n <\/p>\n <p>Comme les atomes composent toute la mati\u00e8re, les nombres premiers composent tous les entiers. C’est pour \u00e7a qu’on les appelle les \u00ab\u00a0atomes\u00a0\u00bb des math\u00e9matiques.<\/p>\n <\/div>\n\n <p>\n Cette d\u00e9composition en facteurs premiers est unique \u2014 il n’existe qu’une seule fa\u00e7on d’\u00e9crire un entier comme produit de premiers (\u00e0 l’ordre des facteurs pr\u00e8s). C’est une des propri\u00e9t\u00e9s les plus fondamentales de l’arithm\u00e9tique.\n <\/p>\n\n <h2>Le crible d’\u00c9ratosth\u00e8ne : trouver les premiers<\/h2>\n\n <div class=\"encadre-histoire encadre\">\n <span class=\"encadre-titre\">\ud83d\udcdc \u00c9ratosth\u00e8ne d’Alexandrie \u2014 III<sup>e<\/sup> si\u00e8cle av. J.-C.<\/span>\n <p>\n \u00c9ratosth\u00e8ne \u00e9tait un savant grec n\u00e9 \u00e0 Cyr\u00e8ne, dans l’actuelle Libye \u2014 en Afrique ! Il dirigeait la Grande Biblioth\u00e8que d’Alexandrie en \u00c9gypte. Il est c\u00e9l\u00e8bre pour avoir calcul\u00e9 avec une pr\u00e9cision remarquable la circonf\u00e9rence de la Terre, en mesurant les ombres \u00e0 diff\u00e9rents endroits d’Afrique du Nord.\n <\/p>\n <p>\n Il a \u00e9galement invent\u00e9 une m\u00e9thode simple et \u00e9l\u00e9gante pour trouver tous les nombres premiers jusqu’\u00e0 un certain nombre : le <strong>crible d’\u00c9ratosth\u00e8ne<\/strong>. Une invention africaine au c\u0153ur des math\u00e9matiques !\n <\/p>\n <\/div>\n\n <p><strong>Comment fonctionne le crible ?<\/strong> La m\u00e9thode est d’une simplicit\u00e9 d\u00e9sarmante :<\/p>\n\n <div class=\"etape\"><span class=\"etape-numero\">\u2460<\/span> \u00c9cris tous les entiers de 2 \u00e0 N<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2461<\/span> Commence par 2 : barre tous ses multiples (4, 6, 8…)<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2462<\/span> Passe au prochain nombre non barr\u00e9 (3) : barre tous ses multiples<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2463<\/span> Continue jusqu’\u00e0 \u221aN<\/div>\n <div class=\"etape\"><span class=\"etape-numero\">\u2464<\/span> Les nombres restants non barr\u00e9s sont tous premiers \u2705<\/div>\n\n <p>Voici le crible appliqu\u00e9 aux nombres de 1 \u00e0 50 :<\/p>\n\n <div class=\"schema-container\">\n <div class=\"schema-titre\">\ud83d\udd22 Crible d’\u00c9ratosth\u00e8ne \u2014 nombres de 1 \u00e0 50<\/div>\n <div class=\"crible-grid\">\n \n <div class=\"crible-cell un\">1<\/div>\n <div class=\"crible-cell premier\">2<\/div>\n <div class=\"crible-cell premier\">3<\/div>\n <div class=\"crible-cell compose\">4<\/div>\n <div class=\"crible-cell premier\">5<\/div>\n <div class=\"crible-cell compose\">6<\/div>\n <div class=\"crible-cell premier\">7<\/div>\n <div class=\"crible-cell compose\">8<\/div>\n <div class=\"crible-cell compose\">9<\/div>\n <div class=\"crible-cell compose\">10<\/div>\n \n <div class=\"crible-cell premier\">11<\/div>\n <div class=\"crible-cell compose\">12<\/div>\n <div class=\"crible-cell premier\">13<\/div>\n <div class=\"crible-cell compose\">14<\/div>\n <div class=\"crible-cell compose\">15<\/div>\n <div class=\"crible-cell compose\">16<\/div>\n <div class=\"crible-cell premier\">17<\/div>\n <div class=\"crible-cell compose\">18<\/div>\n <div class=\"crible-cell premier\">19<\/div>\n <div class=\"crible-cell compose\">20<\/div>\n \n <div class=\"crible-cell compose\">21<\/div>\n <div class=\"crible-cell compose\">22<\/div>\n <div class=\"crible-cell premier\">23<\/div>\n <div class=\"crible-cell compose\">24<\/div>\n <div class=\"crible-cell compose\">25<\/div>\n <div class=\"crible-cell compose\">26<\/div>\n <div class=\"crible-cell compose\">27<\/div>\n <div class=\"crible-cell compose\">28<\/div>\n <div class=\"crible-cell premier\">29<\/div>\n <div class=\"crible-cell compose\">30<\/div>\n \n <div class=\"crible-cell premier\">31<\/div>\n <div class=\"crible-cell compose\">32<\/div>\n <div class=\"crible-cell compose\">33<\/div>\n <div class=\"crible-cell compose\">34<\/div>\n <div class=\"crible-cell compose\">35<\/div>\n <div class=\"crible-cell compose\">36<\/div>\n <div class=\"crible-cell premier\">37<\/div>\n <div class=\"crible-cell compose\">38<\/div>\n <div class=\"crible-cell compose\">39<\/div>\n <div class=\"crible-cell compose\">40<\/div>\n \n <div class=\"crible-cell premier\">41<\/div>\n <div class=\"crible-cell compose\">42<\/div>\n <div class=\"crible-cell premier\">43<\/div>\n <div class=\"crible-cell compose\">44<\/div>\n <div class=\"crible-cell compose\">45<\/div>\n <div class=\"crible-cell compose\">46<\/div>\n <div class=\"crible-cell premier\">47<\/div>\n <div class=\"crible-cell compose\">48<\/div>\n <div class=\"crible-cell compose\">49<\/div>\n <div class=\"crible-cell compose\">50<\/div>\n <\/div>\n <p style=\"font-size:0.82rem; color:#6b6560; margin-top:12px;\">\n <span style=\"background:#1a1a4e; color:white; padding:2px 6px; margin-right:6px;\">Nombres premiers<\/span>\n <span style=\"background:#e8e2d8; color:#6b6560; padding:2px 6px; text-decoration:line-through;\">Compos\u00e9s (barr\u00e9s)<\/span>\n <\/p>\n <\/div>\n\n <h2>Y en a-t-il une infinit\u00e9 ? La preuve d’Euclide<\/h2>\n\n <p>\n Une question naturelle : est-ce que les nombres premiers continuent ind\u00e9finiment, ou s’arr\u00eatent-ils \u00e0 un moment ? Euclide a r\u00e9pondu \u00e0 cette question il y a 2 300 ans avec une d\u00e9monstration d’une beaut\u00e9 rare \u2014 consid\u00e9r\u00e9e comme l’une des plus \u00e9l\u00e9gantes de toute l’histoire des math\u00e9matiques.\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83c\udfdb\ufe0f Th\u00e9or\u00e8me d’Euclide : il existe une infinit\u00e9 de nombres premiers<\/span>\n <p><strong>Preuve par l’absurde :<\/strong><\/p>\n <p>Supposons qu’il n’existe qu’un nombre <em>fini<\/em> de premiers : p\u2081, p\u2082, p\u2083, …, p\u2099.<\/p>\n <p>Construisons le nombre : <strong>M = (p\u2081 \u00d7 p\u2082 \u00d7 p\u2083 \u00d7 … \u00d7 p\u2099) + 1<\/strong><\/p>\n <p>M n’est divisible par aucun des p\u1d62 (il donne le reste 1 pour chacun).<\/p>\n <p>Donc soit M est premier lui-m\u00eame, soit il a un facteur premier qui n’est pas dans notre liste.<\/p>\n <p>Dans les deux cas \u2192 <strong>contradiction<\/strong> ! Notre liste n’\u00e9tait pas compl\u00e8te.<\/p>\n <p>Conclusion : <strong>il existe une infinit\u00e9 de nombres premiers.<\/strong> \u2713<\/p>\n <\/div>\n\n <p>\n Cette preuve n’utilise aucune formule compliqu\u00e9e \u2014 juste de la logique pure. C’est la marque des grandes d\u00e9monstrations math\u00e9matiques.\n <\/p>\n\n <h2>La distribution des premiers : un myst\u00e8re profond<\/h2>\n\n <p>\n Si les premiers sont infinis, comment sont-ils distribu\u00e9s ? Deviennent-ils de plus en plus rares ? Existe-t-il un motif dans leur apparition ?\n <\/p>\n\n <div class=\"table-container\">\n <table>\n <tr>\n <th>Intervalle<\/th>\n <th>Nombres premiers<\/th>\n <th>Densit\u00e9 approximative<\/th>\n <\/tr>\n <tr><td>1 \u2014 100<\/td><td>25<\/td><td>1 sur 4<\/td><\/tr>\n <tr><td>1 \u2014 1 000<\/td><td>168<\/td><td>1 sur 6<\/td><\/tr>\n <tr><td>1 \u2014 10 000<\/td><td>1 229<\/td><td>1 sur 8<\/td><\/tr>\n <tr><td>1 \u2014 100 000<\/td><td>9 592<\/td><td>1 sur 10<\/td><\/tr>\n <tr><td>1 \u2014 1 000 000<\/td><td>78 498<\/td><td>1 sur 13<\/td><\/tr>\n <\/table>\n <\/div>\n\n <p>\n Les premiers deviennent progressivement plus rares, mais ne disparaissent jamais. Le <strong>th\u00e9or\u00e8me des nombres premiers<\/strong> dit que la densit\u00e9 des premiers pr\u00e8s de N est approximativement <strong>1\/ln(N)<\/strong>. Plus N est grand, plus les premiers sont espac\u00e9s \u2014 mais ils ne s’arr\u00eatent jamais.\n <\/p>\n\n <h2>Les nombres premiers et la cryptographie<\/h2>\n\n <p>\n Voil\u00e0 le lien avec ton Mobile Money. Le syst\u00e8me RSA \u2014 qui prot\u00e8ge la quasi-totalit\u00e9 des communications num\u00e9riques mondiales \u2014 repose sur un fait simple mais puissant :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udd10 Le secret RSA<\/span>\n <p><strong>Multiplier deux grands nombres premiers est facile.<\/strong><\/p>\n <p>Exemple : 104 729 \u00d7 224 737 = 23 537 063 273<\/p>\n <p style=\"margin-top: 8px\"><strong>Faire l’inverse \u2014 trouver les deux premiers \u00e0 partir du produit \u2014 est extr\u00eamement difficile.<\/strong><\/p>\n <p>Si on te donne 23 537 063 273, retrouver 104 729 et 224 737 prend du temps m\u00eame pour un ordinateur.<\/p>\n <p style=\"margin-top: 8px\">Avec des nombres de 300 chiffres, m\u00eame les supercalculateurs actuels ne peuvent pas factoriser en un temps raisonnable. C’est sur cette asym\u00e9trie que repose toute la s\u00e9curit\u00e9 d’Internet.<\/p>\n <\/div>\n\n <p>\n Chaque fois que tu vois le cadenas \ud83d\udd12 dans ton navigateur, ou que tu envoies de l’argent par t\u00e9l\u00e9phone, des nombres premiers de 300 chiffres travaillent en silence pour prot\u00e9ger tes donn\u00e9es.\n <\/p>\n\n <h2>Les myst\u00e8res non r\u00e9solus<\/h2>\n\n <p>\n Ce qui rend les nombres premiers fascinants, c’est que malgr\u00e9 2 500 ans d’\u00e9tudes, ils gardent encore des secrets profonds. Voici les grands probl\u00e8mes ouverts :\n <\/p>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\u2753 Probl\u00e8mes non r\u00e9solus \u2014 des millions d’euros en jeu<\/span>\n <p><strong>Conjecture de Goldbach (1742) :<\/strong> Tout entier pair sup\u00e9rieur \u00e0 2 est la somme de deux nombres premiers. Ex : 8 = 3+5, 10 = 3+7. V\u00e9rifi\u00e9 jusqu’\u00e0 4\u00d710\u00b9\u2078 \u2014 jamais prouv\u00e9 en g\u00e9n\u00e9ral.<\/p>\n <p><strong>Conjecture des premiers jumeaux :<\/strong> Il existe une infinit\u00e9 de paires de premiers s\u00e9par\u00e9s de 2 (comme 11 et 13, 17 et 19, 41 et 43). Non prouv\u00e9.<\/p>\n <p><strong>Hypoth\u00e8se de Riemann (1859) :<\/strong> Le probl\u00e8me le plus c\u00e9l\u00e8bre des math\u00e9matiques. Concerne la distribution des nombres premiers. Non r\u00e9solu. L’Institut Clay offre <strong>1 million de dollars<\/strong> \u00e0 qui le r\u00e9soudra.<\/p>\n <\/div>\n\n <h2>Le code Python : crible et applications<\/h2>\n\n <div class=\"code-block\">\n <span class=\"code-label\">Python<\/span>\n<span class=\"code-comment\"># Nombres premiers : crible, v\u00e9rification et applications<\/span>\n<span class=\"code-keyword\">import<\/span> math\n\n<span class=\"code-comment\"># — Crible d’\u00c9ratosth\u00e8ne —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">crible_eratosthene<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbRetourne tous les nombres premiers jusqu’\u00e0 n\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n est_premier = [<span class=\"code-keyword\">True<\/span>] * (n + <span class=\"code-number\">1<\/span>)\n est_premier[<span class=\"code-number\">0<\/span>] = est_premier[<span class=\"code-number\">1<\/span>] = <span class=\"code-keyword\">False<\/span>\n <span class=\"code-keyword\">for<\/span> i <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">2<\/span>, <span class=\"code-function\">int<\/span>(math.<span class=\"code-function\">sqrt<\/span>(n)) + <span class=\"code-number\">1<\/span>):\n <span class=\"code-keyword\">if<\/span> est_premier[i]:\n <span class=\"code-keyword\">for<\/span> j <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(i*i, n+<span class=\"code-number\">1<\/span>, i):\n est_premier[j] = <span class=\"code-keyword\">False<\/span>\n <span class=\"code-keyword\">return<\/span> [i <span class=\"code-keyword\">for<\/span> i <span class=\"code-keyword\">in<\/span> <span class=\"code-function\">range<\/span>(<span class=\"code-number\">2<\/span>, n+<span class=\"code-number\">1<\/span>) <span class=\"code-keyword\">if<\/span> est_premier[i]]\n\n<span class=\"code-comment\"># Trouver tous les premiers jusqu’\u00e0 100<\/span>\npremiers = <span class=\"code-function\">crible_eratosthene<\/span>(<span class=\"code-number\">100<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbPremiers jusqu’\u00e0 100 : {premiers}\u00a0\u00bb<\/span>)\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bbNombre de premiers : {len(premiers)}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># — D\u00e9composition en facteurs premiers —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">facteurs_premiers<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbD\u00e9compose n en facteurs premiers\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n facteurs = {}\n d = <span class=\"code-number\">2<\/span>\n <span class=\"code-keyword\">while<\/span> d * d <= n:\n <span class=\"code-keyword\">while<\/span> n % d == <span class=\"code-number\">0<\/span>:\n facteurs[d] = facteurs.<span class=\"code-function\">get<\/span>(d, <span class=\"code-number\">0<\/span>) + <span class=\"code-number\">1<\/span>\n n \/\/= d\n d += <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">if<\/span> n > <span class=\"code-number\">1<\/span>:\n facteurs[n] = facteurs.<span class=\"code-function\">get<\/span>(n, <span class=\"code-number\">0<\/span>) + <span class=\"code-number\">1<\/span>\n <span class=\"code-keyword\">return<\/span> facteurs\n\n<span class=\"code-comment\"># Exemples de d\u00e9compositions<\/span>\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">12<\/span>, <span class=\"code-number\">60<\/span>, <span class=\"code-number\">360<\/span>, <span class=\"code-number\">1000<\/span>]:\n f = <span class=\"code-function\">facteurs_premiers<\/span>(n)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb{n} = {‘ \u00d7 ‘.join([f'{p}^{e}’ if e>1 else str(p) for p,e in f.items()])}\u00a0\u00bb<\/span>)\n\n<span class=\"code-comment\"># — V\u00e9rification conjecture de Goldbach —<\/span>\n<span class=\"code-keyword\">def<\/span> <span class=\"code-function\">goldbach<\/span>(n):\n <span class=\"code-string\">\u00ab\u00a0\u00a0\u00bb\u00a0\u00bbTrouve deux premiers dont la somme = n\u00a0\u00bb\u00a0\u00bb\u00a0\u00bb<\/span>\n premiers_set = <span class=\"code-function\">set<\/span>(<span class=\"code-function\">crible_eratosthene<\/span>(n))\n <span class=\"code-keyword\">for<\/span> p <span class=\"code-keyword\">in<\/span> premiers_set:\n <span class=\"code-keyword\">if<\/span> (n – p) <span class=\"code-keyword\">in<\/span> premiers_set:\n <span class=\"code-keyword\">return<\/span> (p, n – p)\n <span class=\"code-keyword\">return<\/span> <span class=\"code-keyword\">None<\/span>\n\n<span class=\"code-function\">print<\/span>(<span class=\"code-string\">\u00ab\u00a0\\nConjecture de Goldbach :\u00a0\u00bb<\/span>)\n<span class=\"code-keyword\">for<\/span> n <span class=\"code-keyword\">in<\/span> [<span class=\"code-number\">8<\/span>, <span class=\"code-number\">20<\/span>, <span class=\"code-number\">100<\/span>, <span class=\"code-number\">2026<\/span>]:\n p1, p2 = <span class=\"code-function\">goldbach<\/span>(n)\n <span class=\"code-function\">print<\/span>(<span class=\"code-string\">f\u00a0\u00bb{n} = {p1} + {p2}\u00a0\u00bb<\/span>)\n <\/div>\n\n <div class=\"encadre\">\n <span class=\"encadre-titre\">\ud83d\udcbb R\u00e9sultat attendu<\/span>\n <p>Premiers jusqu’\u00e0 100 : [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]<\/p>\n <p>Nombre de premiers : <strong>25<\/strong><\/p>\n <p>12 = 2\u00b2 \u00d7 3 | 60 = 2\u00b2 \u00d7 3 \u00d7 5 | 360 = 2\u00b3 \u00d7 3\u00b2 \u00d7 5<\/p>\n <p>Goldbach : 2026 = 3 + 2023 … ou une autre paire \u2713<\/p>\n <\/div>\n\n <blockquote>\n Les nombres premiers sont comme les \u00e9toiles dans le ciel nocturne de Cotonou \u2014 impr\u00e9visibles dans leur position, infinis dans leur nombre, et pourtant gouvern\u00e9s par des lois profondes que nous commen\u00e7ons \u00e0 peine \u00e0 comprendre.\n <cite>\u2014 Inspiration math\u00e9matique<\/cite>\n <\/blockquote>\n\n \n <div class=\"exercice\">\n <h3>\u270f\ufe0f Exercice corrig\u00e9<\/h3>\n <p>\n Un \u00e9l\u00e8ve de 5\u00e8me \u00e0 Abomey-Calavi travaille sur les nombres premiers.\n <\/p>\n <p><strong>a)<\/strong> Donne la liste de tous les nombres premiers compris entre 50 et 80.<\/p>\n <p><strong>b)<\/strong> D\u00e9compose 360 en produit de facteurs premiers.<\/p>\n <p><strong>c)<\/strong> V\u00e9rifie la conjecture de Goldbach pour n = 28 et n = 50.<\/p>\n <p><strong>d)<\/strong> Parmi ces nombres : 91, 97, 101, 111 \u2014 lesquels sont premiers ? Justifie.<\/p>\n\n <div class=\"correction\">\n <div class=\"correction-titre\">\u25b8 Correction<\/div>\n <p><strong>a)<\/strong> On teste la divisibilit\u00e9 par les premiers \u2264 \u221a80 \u2248 9 (donc 2, 3, 5, 7) :<\/p>\n <p>53 \u2713, 59 \u2713, 61 \u2713, 67 \u2713, 71 \u2713, 73 \u2713, 79 \u2713<\/p>\n <p>R\u00e9ponse : <strong>53, 59, 61, 67, 71, 73, 79<\/strong><\/p>\n <p><strong>b)<\/strong> 360 = 2 \u00d7 180 = 2 \u00d7 2 \u00d7 90 = 2 \u00d7 2 \u00d7 2 \u00d7 45 = 2 \u00d7 2 \u00d7 2 \u00d7 9 \u00d7 5 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 5<\/p>\n <p>\u2192 <strong>360 = 2\u00b3 \u00d7 3\u00b2 \u00d7 5<\/strong><\/p>\n <p><strong>c)<\/strong> 28 = 5 + 23 \u2713 (5 et 23 premiers) | 50 = 3 + 47 \u2713 (3 et 47 premiers)<\/p>\n <p><strong>d)<\/strong> 91 = 7 \u00d7 13 \u2192 <strong>non premier<\/strong><\/p>\n <p>97 : non divisible par 2, 3, 5, 7 (\u221a97 \u2248 9,8) \u2192 <strong>premier \u2713<\/strong><\/p>\n <p>101 : non divisible par 2, 3, 5, 7 (\u221a101 \u2248 10) \u2192 <strong>premier \u2713<\/strong><\/p>\n <p>111 = 3 \u00d7 37 \u2192 <strong>non premier<\/strong><\/p>\n <\/div>\n <\/div>\n\n <div class=\"conclusion\">\n <h2>Ce qu’on retient<\/h2>\n <p>\n Les nombres premiers sont \u00e0 la fois les objets math\u00e9matiques les plus simples \u00e0 d\u00e9finir et les plus difficiles \u00e0 comprendre en profondeur. Ils sont les fondations invisibles sur lesquelles repose toute l’arithm\u00e9tique \u2014 et, par extension, toute la s\u00e9curit\u00e9 num\u00e9rique moderne.\n <\/p>\n <p>\n La prochaine fois que tu envoies de l’argent par Mobile Money, souviens-toi : quelque part dans les circuits de ton t\u00e9l\u00e9phone, deux nombres premiers g\u00e9ants se multiplient en silence pour garder ton argent en s\u00e9curit\u00e9. Les maths de \u00c9ratosth\u00e8ne \u2014 n\u00e9 en Afrique \u2014 prot\u00e8gent ton portefeuille aujourd’hui.\n <\/p>\n <p>\n Dans le prochain article, nous plongerons dans la <strong>loi normale et la courbe en cloche<\/strong> \u2014 cette forme myst\u00e9rieuse qui appara\u00eet partout : dans les notes des \u00e9l\u00e8ves, la taille des adultes, les erreurs de mesure, et m\u00eame les fluctuations des prix au march\u00e9 de Dantokpa.\n <\/p>\n <\/div>\n\n<\/article>\n\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8],"tags":[],"class_list":["post-89","post","type-post","status-publish","format-standard","hentry","category-fondements"],"yoast_head":"\n<title>Nombres premiers - AfrikIntelligent<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vmi3217629.contaboserver.net\/?p=89\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nombres premiers - AfrikIntelligent\" \/>\n<meta property=\"og:description\" content=\"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/vmi3217629.contaboserver.net\/?p=89\" \/>\n<meta property=\"og:site_name\" content=\"AfrikIntelligent\" \/>\n<meta property=\"article:published_time\" content=\"2026-04-19T22:37:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-04-19T22:37:36+00:00\" \/>\n<meta name=\"author\" content=\"Odilon\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Odilon\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"},\"author\":{\"name\":\"Odilon\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"headline\":\"Nombres premiers\",\"datePublished\":\"2026-04-19T22:37:34+00:00\",\"dateModified\":\"2026-04-19T22:37:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"},\"wordCount\":1611,\"commentCount\":0,\"articleSection\":[\"Fondements\"],\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\",\"name\":\"Nombres premiers - AfrikIntelligent\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\"},\"datePublished\":\"2026-04-19T22:37:34+00:00\",\"dateModified\":\"2026-04-19T22:37:36+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?p=89#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Nombres premiers\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#website\",\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/\",\"name\":\"AfrikIntelligent\",\"description\":\"Append autrement\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/#\\\/schema\\\/person\\\/a3da39574d729b6b3ff7514ccc055923\",\"name\":\"Odilon\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g\",\"caption\":\"Odilon\"},\"sameAs\":[\"https:\\\/\\\/vmi3217629.contaboserver.net\"],\"url\":\"https:\\\/\\\/vmi3217629.contaboserver.net\\\/?author=1\"}]}<\/script>\n","yoast_head_json":{"title":"Nombres premiers - AfrikIntelligent","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/vmi3217629.contaboserver.net\/?p=89","og_locale":"fr_FR","og_type":"article","og_title":"Nombres premiers - AfrikIntelligent","og_description":"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]","og_url":"https:\/\/vmi3217629.contaboserver.net\/?p=89","og_site_name":"AfrikIntelligent","article_published_time":"2026-04-19T22:37:34+00:00","article_modified_time":"2026-04-19T22:37:36+00:00","author":"Odilon","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Odilon","Dur\u00e9e de lecture estim\u00e9e":"10 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#article","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89"},"author":{"name":"Odilon","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"headline":"Nombres premiers","datePublished":"2026-04-19T22:37:34+00:00","dateModified":"2026-04-19T22:37:36+00:00","mainEntityOfPage":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89"},"wordCount":1611,"commentCount":0,"articleSection":["Fondements"],"inLanguage":"fr-FR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/vmi3217629.contaboserver.net\/?p=89#respond"]}]},{"@type":"WebPage","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89","url":"https:\/\/vmi3217629.contaboserver.net\/?p=89","name":"Nombres premiers - AfrikIntelligent","isPartOf":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#website"},"datePublished":"2026-04-19T22:37:34+00:00","dateModified":"2026-04-19T22:37:36+00:00","author":{"@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923"},"breadcrumb":{"@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/vmi3217629.contaboserver.net\/?p=89"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/vmi3217629.contaboserver.net\/?p=89#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/vmi3217629.contaboserver.net\/"},{"@type":"ListItem","position":2,"name":"Nombres premiers"}]},{"@type":"WebSite","@id":"https:\/\/vmi3217629.contaboserver.net\/#website","url":"https:\/\/vmi3217629.contaboserver.net\/","name":"AfrikIntelligent","description":"Append autrement","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vmi3217629.contaboserver.net\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/vmi3217629.contaboserver.net\/#\/schema\/person\/a3da39574d729b6b3ff7514ccc055923","name":"Odilon","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/57bcd6a76fa395ae5e994943b66ccd3dd7e71cd0b1b77b351986e88c27801523?s=96&d=mm&r=g","caption":"Odilon"},"sameAs":["https:\/\/vmi3217629.contaboserver.net"],"url":"https:\/\/vmi3217629.contaboserver.net\/?author=1"}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"Odilon","author_link":"https:\/\/vmi3217629.contaboserver.net\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"Les nombres premiers : le myst\u00e8re infini des maths \u2014 MathsVivantes Arithm\u00e9tique \u00b7 Article #8 Les nombres premiers :le myst\u00e8re […]","_links":{"self":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=89"}],"version-history":[{"count":1,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":90,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=\/wp\/v2\/posts\/89\/revisions\/90"}],"wp:attachment":[{"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vmi3217629.contaboserver.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}