{"id":1456,"date":"2020-07-14T10:24:20","date_gmt":"2020-07-14T10:24:20","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1456"},"modified":"2024-07-14T18:36:53","modified_gmt":"2024-07-14T16:36:53","slug":"sieb-des-eratosthenes","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1456","title":{"rendered":"Sieb des Eratosthenes"},"content":{"rendered":"\n<p><img loading=\"lazy\" decoding=\"async\" width=\"50\" height=\"50\" class=\"wp-image-7501\" style=\"width: 50px;\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png\" alt=\"\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png 100w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-80x80.png 80w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-50x50.png 50w\" sizes=\"auto, (max-width: 50px) 100vw, 50px\" \/><\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Sucht man nach den Primzahlen in einem Zahlenbereich , so streicht man zuerst alle Vielfachen von 2. Danach folgen die Glieder der 3-er Reihe und so weiter. \u00dcbrig bleiben die Zahlen, die nur 1 als Teiler haben und sich selbst, die Primzahlen.<br>Dieses Verfahren geht auf den griechischen Gelehrten <strong><a rel=\"noreferrer noopener\" href=\"https:\/\/de.wikipedia.org\/wiki\/Eratosthenes\" target=\"_blank\">Eratosthenes<\/a> <\/strong>zur\u00fcck.<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f5ffd8\">Hier findest Du das Beispiel f\u00fcr die Zahlen 1 bis 100:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Sieb des Eratosthenes\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/b7qduxne\/width\/1200\/height\/600\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"1200px\" height=\"420px\" style=\"border:0px;\"> <\/iframe>\nAutor:\n<a href=\"https:\/\/www.geogebra.org\/u\/just01120\">just01120<\/a>,&nbsp;<a href=\"https:\/\/www.geogebra.org\/u\/hermann.benetseder\">BeHe<\/a> , geogebra.org<\/pre>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1456\" class=\"pvc_stats all  \" data-element-id=\"1456\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>Sucht man nach den Primzahlen in einem Zahlenbereich , so streicht man zuerst alle Vielfachen von 2. Danach folgen die Glieder der 3-er Reihe und so weiter. \u00dcbrig bleiben die Zahlen, die nur 1 als Teiler haben und sich selbst, die Primzahlen.Dieses Verfahren geht auf den griechischen Gelehrten Eratosthenes zur\u00fcck. Hier findest Du das Beispiel f\u00fcr die Zahlen 1 bis<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1456\" class=\"pvc_stats all  \" data-element-id=\"1456\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,31,28],"tags":[869,870,716,755,763,866,867,868],"class_list":["post-1456","post","type-post","status-publish","format-standard","hentry","category-natuerliche-zahlen","category-gebrochene-zahlen","category-anteile-und-groessen","tag-sieben","tag-ausschliessen","tag-ermitteln","tag-teiler","tag-bestimmen","tag-sieb","tag-eratosthenes","tag-primzahlen"],"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1456","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1456"}],"version-history":[{"count":1,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1456\/revisions"}],"predecessor-version":[{"id":8252,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1456\/revisions\/8252"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}