{"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":"2026-10-07T17:44:10","modified_gmt":"2026-10-07T15:44:10","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=\"\">\r\n          \n\n<p class=\"wp-block-paragraph\">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\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Partimos de una lista de n\u00fameros que van de 2 hasta un determinado n\u00famero.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Eliminamos de la lista los m\u00faltiplos de 2.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">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\n\r\n                       \n\n<p class=\"wp-block-paragraph\">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\n\r\n                        \n\n<p class=\"wp-block-paragraph\">Los n\u00fameros que permanecen en la lista son los primos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/section><br><section id=\"am\" style=\"\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Ejemplo<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><!-- fin div-sombra-tit--><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos a calcular por este algoritmo los n\u00fameros primos menores que 40.<\/p>\n\n\r\n                        \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">1.\r\n                        <\/h2>\n\n Escribimos los n\u00fameros, en nuestro caso ser\u00e1n los comprendidos entre 2 y 40. <\/p>\n\n\r\n                       <table class=\"responsive\" data-min=\"8\" data-max=\"12\">\r\n                              <tr >\r\n                                <td><\/td>\r\n                                <td>2<\/td>\r\n                                <td>3<\/td>\r\n                                <td>4<\/td>\r\n                                <td>5<\/td>\r\n                                <td>6<\/td>\r\n                                <td>7<\/td>\r\n                                <td>8<\/td>\r\n                                <td>9<\/td>\r\n                                <td>10<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>11<\/td>\r\n                                <td>12<\/td>\r\n                                <td>13<\/td>\r\n                                <td>14<\/td>\r\n                                <td>15<\/td>\r\n                                <td>16<\/td>\r\n                                <td>17<\/td>\r\n                                <td>18<\/td>\r\n                                <td>19<\/td>\r\n                                <td>20<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>21<\/td>\r\n                                <td>22<\/td>\r\n                                <td>23<\/td>\r\n                                <td>24<\/td>\r\n                                <td>25<\/td>\r\n                                <td>26<\/td>\r\n                                <td>27<\/td>\r\n                                <td>28<\/td>\r\n                                <td>29<\/td>\r\n                                <td>30<\/td>\r\n                              <\/tr>\r\n                              <tr>\r\n                                <td>31<\/td>\r\n                                <td>32<\/td>\r\n                                <td>33<\/td>\r\n                                <td>34<\/td>\r\n                                <td>35<\/td>\r\n                                <td>36<\/td>\r\n                                <td>37<\/td>\r\n                                <td>38<\/td>\r\n                                <td>39<\/td>\r\n                                <td>40<\/td>\r\n                              <\/tr>\r\n                             \r\n                        <\/table>\r\n                            \r\n                        \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">2. <\/h2>\n\n Eliminamos los m\u00faltiplos de 2.<\/p>\n\n\r\n                        <table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\r\n                          <tr >\r\n                            <td><\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\" >2<\/td>\r\n                            <td>3<\/td>\r\n                            <td>   <\/td>\r\n                            <td>5<\/td>\r\n                            <td> <\/td>\r\n                            <td>7<\/td>\r\n                            <td>   <\/td>\r\n                            <td>9<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>11<\/td>\r\n                            <td>   <\/td>\r\n                            <td>13<\/td>\r\n                            <td>   <\/td>\r\n                            <td>15<\/td>\r\n                            <td>   <\/td>\r\n                            <td>17<\/td>\r\n                            <td>   <\/td>\r\n                            <td>19<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>21<\/td>\r\n                            <td>   <\/td>\r\n                            <td>23<\/td>\r\n                            <td>   <\/td>\r\n                            <td>25<\/td>\r\n                            <td>   <\/td>\r\n                            <td>27<\/td>\r\n                            <td>   <\/td>\r\n                            <td>29<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>31<\/td>\r\n                            <td>   <\/td>\r\n                            <td>33<\/td>\r\n                            <td>   <\/td>\r\n                            <td>35<\/td>\r\n                            <td>   <\/td>\r\n                            <td>37<\/td>\r\n                            <td>   <\/td>\r\n                            <td>39<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                         \r\n                        <\/table>\r\n                        \r\n                        \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">3. <\/h2>\n\n El siguiente n\u00famero es 3, como 3<sup>2<\/sup> < 40 eliminamos los m\u00faltiplos de 3.<\/p>\n\n\r\n                        <table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\r\n                          <tr >\r\n                            <td>    <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">2<\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">3<\/td>\r\n                            <td>   <\/td>\r\n                            <td>5<\/td>\r\n                            <td>   <\/td>\r\n                            <td>7<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>11<\/td>\r\n                            <td>   <\/td>\r\n                            <td>13<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>17<\/td>\r\n                            <td>   <\/td>\r\n                            <td>19<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>23<\/td>\r\n                            <td>   <\/td>\r\n                            <td>25<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>29<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>31<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>35<\/td>\r\n                            <td>   <\/td>\r\n                            <td>37<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                         \r\n                        <\/table>\r\n                        \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">4. <\/h2>\n\n El siguiente n\u00famero es 5, como 5<sup>2<\/sup> < 40 eliminamos los m\u00faltiplos de 5.<\/p>\n\n\r\n                       <table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\r\n                          <tr >\r\n                            <td>    <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">2<\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">3<\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">5<\/td>\r\n                            <td>   <\/td>\r\n                            <td>7<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>11<\/td>\r\n                            <td>   <\/td>\r\n                            <td>13<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>17<\/td>\r\n                            <td>   <\/td>\r\n                            <td>19<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>23<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>29<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>31<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>37<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                         \r\n                        <\/table>\r\n                         \r\n                        \n\n<p class=\"wp-block-paragraph\">\n\n<h2 class=\"wp-block-heading\">5. <\/h2>\n\n El siguiente n\u00famero es 7, como 7<sup>2<\/sup> > 40  el algoritmo termina y los n\u00fameros que nos quedan son <strong>primos<\/strong>.<\/p>\n\n\r\n                        \n\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\r\n                          <tr >\r\n                            <td>    <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">2<\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">3<\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">5<\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">7<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td style=\"color:#900; background-color:#eee;\">11<\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">13<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">17<\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">19<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">23<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">29<\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                          <tr>\r\n                            <td style=\"color:#900; background-color:#eee;\">31<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td style=\"color:#900; background-color:#eee;\">37<\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                            <td>   <\/td>\r\n                          <\/tr>\r\n                         \r\n                        <\/table>\n\n\n\n<\/section>\n\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 7 a\u00f1os hace","modified":"Actualizado 2 semanas hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 7 octubre 2026"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 13 min","modified":"Actualizado el 7 octubre 2026 17 h 44 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":4,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/108981\/revisions"}],"predecessor-version":[{"id":141882,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/108981\/revisions\/141882"}],"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}]}}