{"id":5228,"date":"2019-12-09T05:30:05","date_gmt":"2019-12-09T03:30:05","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5228"},"modified":"2019-12-17T08:03:52","modified_gmt":"2019-12-17T06:03:52","slug":"suma-de-primos-menores","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/suma-de-primos-menores\/","title":{"rendered":"Suma de primos menores"},"content":{"rendered":"<p>La suma de los primos menores que 10 es 2 + 3 + 5 + 7 = 17.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumaPrimosMenores :: Integer -> Integer\n<\/pre>\n<p>tal que (sumaPrimosMenores n) es la suma de los primos menores que n. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   sumaPrimosMenores 10        ==  17\n   sumaPrimosMenores (5*10^5)  ==  9914236195\n<\/pre>\n<p><strong>Nota<\/strong>: Este ejercicio est\u00e1 basado en el <a href=\"https:\/\/projecteuler.net\/problem=10\">problema 10<\/a> del <a href=\"https:\/\/projecteuler.net\">Proyecto Euler<\/a><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (primes)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsumaPrimosMenores :: Integer -> Integer\nsumaPrimosMenores n = sum (takeWhile (<n) primos)\n\n-- primos es la lista de los n\u00fameros primos. Por ejemplo,\n--    \u03bb> take 12 primos\n--    [2,3,5,7,11,13,17,19,23,29,31,37]\nprimos :: [Integer]\nprimos = 2 : filter esPrimo [3,5..]\n\nesPrimo :: Integer -> Bool\nesPrimo n = null [x | x <- [2..(ceiling . sqrt . fromIntegral) n]\n                    , n `mod` x == 0]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsumaPrimosMenores2 :: Integer -> Integer\nsumaPrimosMenores2 n = sum (takeWhile (<n) primos2)\n\nprimos2 :: [Integer]\nprimos2 = 2 : filter esPrimo2 [3,5..]\n \nesPrimo2 :: Integer -> Bool\nesPrimo2 x =\n  all ((\/= 0) . mod x)\n  (takeWhile (<= floor (sqrt (fromIntegral x))) primos2)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsumaPrimosMenores3 :: Integer -> Integer\nsumaPrimosMenores3 n = sum (takeWhile (<n) primes)\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> sumaPrimosMenores (2*10^5)\n--    1709600813\n--    (2.56 secs, 1,522,015,240 bytes)\n--    \u03bb> sumaPrimosMenores2 (2*10^5)\n--    1709600813\n--    (0.56 secs, 376,951,456 bytes)\n--    \u03bb> sumaPrimosMenores3 (2*10^5)\n--    1709600813\n--    (0.07 secs, 62,321,888 bytes)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nEl movimiento no es nada esencial. La fuerza puede ser inm\u00f3vil (lo es en su estado de pureza); mas no por ello deja de ser activa.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>La suma de los primos menores que 10 es 2 + 3 + 5 + 7 = 17. Definir la funci\u00f3n sumaPrimosMenores :: Integer -> Integer tal que (sumaPrimosMenores n) es la suma de los primos menores que n. Por ejemplo, sumaPrimosMenores 10 == 17 sumaPrimosMenores (5*10^5) == 9914236195 Nota: Este ejercicio est\u00e1 basado en&#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":[4],"tags":[41,322,8,481,38,183,89,141,11,173,236,40,34],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5228"}],"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=5228"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5228\/revisions"}],"predecessor-version":[{"id":5271,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5228\/revisions\/5271"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}