{"id":108981,"date":"2020-01-29T18:13:15","date_gmt":"2020-01-29T17:13:15","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/aritmetica\/criba-eratostenes.html"},"modified":"2024-05-27T17:51:48","modified_gmt":"2024-05-27T15:51:48","slug":"criba-eratostenes","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\/criba-eratostenes.html","title":{"rendered":"Criba de erat\u00f3stenes"},"content":{"rendered":"<section style=\"\">\n<p class=\"\">La <strong>criba de Erat\u00f3stenes<\/strong> es un <strong>algoritmo<\/strong> que permite hallar todos los <strong>n\u00fameros primos<\/strong> menores que un n\u00famero natural dado.<\/p>\n<p class=\"\">Partimos de una lista de n\u00fameros que van de 2 hasta un determinado n\u00famero.<\/p>\n<p class=\"\">Eliminamos de la lista los m\u00faltiplos de 2.<\/p>\n<p class=\"\">Luego tomamos el primer n\u00famero despu\u00e9s del 2 que no fue eliminado (el 3) y eliminamos de la lista sus m\u00faltiplos, y as\u00ed sucesivamente.<\/p>\n<p class=\"\">El proceso termina cuando el cuadrado del mayor n\u00famero confirmado como primo es menor que el n\u00famero  final de la lista.<\/p>\n<p class=\"\">Los n\u00fameros que permanecen en la lista son los primos.<\/p>\n<\/section>\n<p><\/p>\n<section id=\"am\" style=\"\">\n<h2>Ejemplo<\/h2>\n<p>    <!-- fin div-sombra-tit--><\/p>\n<p class=\"\" style=\"\">Vamos a calcular por este algoritmo los n\u00fameros primos menores que 40.<\/p>\n<p class=\"\">\n<h2>1.<br \/>\n                        <\/h2>\n<p> Escribimos los n\u00fameros, en nuestro caso ser\u00e1n los comprendidos entre 2 y 40. <\/p>\n<table class=\"responsive\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td><\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>10<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>12<\/td>\n<td>13<\/td>\n<td>14<\/td>\n<td>15<\/td>\n<td>16<\/td>\n<td>17<\/td>\n<td>18<\/td>\n<td>19<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>21<\/td>\n<td>22<\/td>\n<td>23<\/td>\n<td>24<\/td>\n<td>25<\/td>\n<td>26<\/td>\n<td>27<\/td>\n<td>28<\/td>\n<td>29<\/td>\n<td>30<\/td>\n<\/tr>\n<tr>\n<td>31<\/td>\n<td>32<\/td>\n<td>33<\/td>\n<td>34<\/td>\n<td>35<\/td>\n<td>36<\/td>\n<td>37<\/td>\n<td>38<\/td>\n<td>39<\/td>\n<td>40<\/td>\n<\/tr>\n<\/table>\n<p class=\"\">\n<h2>2. <\/h2>\n<p> Eliminamos los m\u00faltiplos de 2.<\/p>\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td><\/td>\n<td style=\"color:#900; background-color:#eee;\" >2<\/td>\n<td>3<\/td>\n<td>   <\/td>\n<td>5<\/td>\n<td> <\/td>\n<td>7<\/td>\n<td>   <\/td>\n<td>9<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>   <\/td>\n<td>13<\/td>\n<td>   <\/td>\n<td>15<\/td>\n<td>   <\/td>\n<td>17<\/td>\n<td>   <\/td>\n<td>19<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>21<\/td>\n<td>   <\/td>\n<td>23<\/td>\n<td>   <\/td>\n<td>25<\/td>\n<td>   <\/td>\n<td>27<\/td>\n<td>   <\/td>\n<td>29<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>31<\/td>\n<td>   <\/td>\n<td>33<\/td>\n<td>   <\/td>\n<td>35<\/td>\n<td>   <\/td>\n<td>37<\/td>\n<td>   <\/td>\n<td>39<\/td>\n<td>   <\/td>\n<\/tr>\n<\/table>\n<p class=\"\">\n<h2>3. <\/h2>\n<p> El siguiente n\u00famero es 3, como 3<sup>2<\/sup> &lt; 40 eliminamos los m\u00faltiplos de 3.<\/p>\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td>    <\/td>\n<td style=\"color:#900; background-color:#eee;\">2<\/td>\n<td style=\"color:#900; background-color:#eee;\">3<\/td>\n<td>   <\/td>\n<td>5<\/td>\n<td>   <\/td>\n<td>7<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>   <\/td>\n<td>13<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>17<\/td>\n<td>   <\/td>\n<td>19<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>23<\/td>\n<td>   <\/td>\n<td>25<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>29<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>31<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>35<\/td>\n<td>   <\/td>\n<td>37<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<\/table>\n<p class=\"\">\n<h2>4. <\/h2>\n<p> El siguiente n\u00famero es 5, como 5<sup>2<\/sup> &lt; 40 eliminamos los m\u00faltiplos de 5.<\/p>\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td>    <\/td>\n<td style=\"color:#900; background-color:#eee;\">2<\/td>\n<td style=\"color:#900; background-color:#eee;\">3<\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">5<\/td>\n<td>   <\/td>\n<td>7<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>   <\/td>\n<td>13<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>17<\/td>\n<td>   <\/td>\n<td>19<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>23<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>29<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>31<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>37<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<\/table>\n<p class=\"\">\n<h2>5. <\/h2>\n<p> El siguiente n\u00famero es 7, como 7<sup>2<\/sup> &gt; 40  el algoritmo termina y los n\u00fameros que nos quedan son <strong>primos<\/strong>.<\/p>\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td>    <\/td>\n<td style=\"color:#900; background-color:#eee;\">2<\/td>\n<td style=\"color:#900; background-color:#eee;\">3<\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">5<\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">7<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td style=\"color:#900; background-color:#eee;\">11<\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">13<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">17<\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">19<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">23<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">29<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td style=\"color:#900; background-color:#eee;\">31<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td style=\"color:#900; background-color:#eee;\">37<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<\/table>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>La criba de Erat\u00f3stenes es un algoritmo que permite hallar todos los n\u00fameros primos menores que un n\u00famero natural dado. Partimos de una lista de n\u00fameros que van de 2 hasta un determinado n\u00famero. Eliminamos de la lista los m\u00faltiplos de 2. Luego tomamos el primer n\u00famero despu\u00e9s del 2 que no fue eliminado (el [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[377],"tags":[360],"class_list":["post-108981","post","type-post","status-publish","format-standard","hentry","category-aritmetica","tag-c"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">Aritm\u00e9tica<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\" class=\"advgb-post-tax-term\">c<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">c<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 2 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 27 mayo 2024"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 13 min","modified":"Actualizado el 27 mayo 2024 17 h 51 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/108981","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=108981"}],"version-history":[{"count":1,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/108981\/revisions"}],"predecessor-version":[{"id":136204,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/108981\/revisions\/136204"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=108981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=108981"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=108981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}