{"id":109020,"date":"2020-01-29T18:13:19","date_gmt":"2020-01-29T17:13:19","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/aritmetica\/numeros-primos.html"},"modified":"2024-05-27T17:51:43","modified_gmt":"2024-05-27T15:51:43","slug":"numeros-primos","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/aritmetica\/numeros-primos.html","title":{"rendered":"N\u00fameros primos"},"content":{"rendered":"<section style=\"\">\n<p class=\"\">Un n\u00famero <span><strong>primo<\/strong><\/span> s\u00f3lo tiene <strong>dos divisores<\/strong>: <strong>\u00e9l mismo y la unidad<\/strong>.<\/p>\n<p class=\"actividades_2_g\">5, 13, 59. <\/p>\n<p class=\"\" style=\"\">El n\u00famero 1 s\u00f3lo tiene un divisor, por eso no lo consideramos primo. <\/p>\n<p class=\"\">Para averiguar si un <strong>n\u00famero es primo<\/strong>, <strong>se divide<\/strong> ordenadamente <strong>por<\/strong> todos los<strong> n\u00fameros primos menores que \u00e9l<\/strong>. Cuando, sin resultar divisiones exactas, <strong>llega<\/strong> a obtenerse <strong>un cociente menor o igual al divisor<\/strong>, se dice que el n\u00famero es primo. <\/p>\n<p class=\"actividades_2_g\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/n\u00fameros-primos-1.gif\" alt=\"Explicaciones y ejemplos de n\u00fameros primos\"  ><\/p>\n<p class=\"actividades_2_v\">Por tanto 179 es <strong>primo<\/strong>.<\/p>\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<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 t_izq\" 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<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<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<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<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<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<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<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<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<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<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<h3 class=\"r\" style=\"margin-top:30px;\">Tabla de  n\u00fameros primos<\/h3>\n<table class=\"responsive t_izq\" data-min=\"8\" data-max=\"12\">\n<tr >\n<td>    <\/td>\n<td>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>   <\/td>\n<td>   <\/td>\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<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<tr>\n<td>41<\/td>\n<td>   <\/td>\n<td>43<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>47<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>53<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>59<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>61<\/td>\n<td>   <\/td>\n<td> <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>67<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>71<\/td>\n<td>   <\/td>\n<td>73<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>79<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>83<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>89<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>97<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>101<\/td>\n<td>   <\/td>\n<td>103<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>107<\/td>\n<td>   <\/td>\n<td>109<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>113<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>127<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>131<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>137<\/td>\n<td>   <\/td>\n<td>139<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>149<\/td>\n<td>   <\/td>\n<td>151<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>157<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>   <\/td>\n<td>163<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>167<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>173<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>179<\/td>\n<td>   <\/td>\n<\/tr>\n<tr>\n<td>181<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>191<\/td>\n<td>   <\/td>\n<td>193<\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>   <\/td>\n<td>197<\/td>\n<td>   <\/td>\n<td>199<\/td>\n<td>   <\/td>\n<\/tr>\n<\/table>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero primo s\u00f3lo tiene dos divisores: \u00e9l mismo y la unidad. 5, 13, 59. El n\u00famero 1 s\u00f3lo tiene un divisor, por eso no lo consideramos primo. Para averiguar si un n\u00famero es primo, se divide ordenadamente por todos los n\u00fameros primos menores que \u00e9l. Cuando, sin resultar divisiones exactas, llega a obtenerse un [&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":[362],"class_list":["post-109020","post","type-post","status-publish","format-standard","hentry","category-aritmetica","tag-n"],"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\">n<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">n<\/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\/109020","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=109020"}],"version-history":[{"count":1,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/109020\/revisions"}],"predecessor-version":[{"id":136201,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/109020\/revisions\/136201"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=109020"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=109020"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=109020"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}