{"id":5311,"date":"2019-12-30T05:30:04","date_gmt":"2019-12-30T03:30:04","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5311"},"modified":"2020-01-06T08:36:11","modified_gmt":"2020-01-06T06:36:11","slug":"postulado-de-bertrand","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/postulado-de-bertrand\/","title":{"rendered":"Postulado de Bertrand"},"content":{"rendered":"<p>El <a href=\"http:\/\/bit.ly\/35Se7OO\">postulado de Bertrand<\/a> afirma que para cualquier n\u00famero entero n > 1, existe al menos un n\u00famero primo p con n &lt; p &lt; 2n.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   siguientePrimo :: Integer -> Integer\n<\/pre>\n<p>tal que (siguientePrimo n) es el menor primo mayor que n. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   siguientePrimo 8   ==  11\n   siguientePrimo 11  ==  13\n<\/pre>\n<p>Comprobar con QuickCheck el postulado de Bertrand; es decir, para todo entero n > 1, se verifica que n &lt; p &lt; 2n, donde p es (siguientePrimo n).<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes\nimport Test.QuickCheck\n\nsiguientePrimo :: Integer -> Integer\nsiguientePrimo n = head (dropWhile (<= n) primes)\n\n-- La propiedad es\npostuladoDeBertrand :: Integer -> Property\npostuladoDeBertrand n =\n  n > 1 ==> n < p &#038;&#038; p < 2 * n\n  where p = siguientePrimo n\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck postuladoDeBertrand\n--    +++ OK, passed 100 tests.\n<\/pre>\n<h4>Referencias<\/h4>\n<ul>\n<li><a href=\"http:\/\/bit.ly\/35Se7OO\">Bertrand&#8217;s postulate<\/a> en Wikipedia.<\/li>\n<\/ul>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nPero caer de cabeza,<br \/>\nen esta noche sin luna,<br \/>\nen medio de esta maleza,<br \/>\njunto a la negra laguna.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>El postulado de Bertrand afirma que para cualquier n\u00famero entero n > 1, existe al menos un n\u00famero primo p con n &lt; p &lt; 2n. Definir la funci\u00f3n siguientePrimo :: Integer -> Integer tal que (siguientePrimo n) es el menor primo mayor que n. Por ejemplo, siguientePrimo 8 == 11 siguientePrimo 11 == 13&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[5],"tags":[59,71,415,11,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5311"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=5311"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5311\/revisions"}],"predecessor-version":[{"id":5349,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5311\/revisions\/5349"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}