{"id":4333,"date":"2018-11-26T06:00:10","date_gmt":"2018-11-26T04:00:10","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4333"},"modified":"2019-01-19T12:19:21","modified_gmt":"2019-01-19T10:19:21","slug":"numeros-primos-sumas-de-dos-primos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-primos-sumas-de-dos-primos\/","title":{"rendered":"N\u00fameros primos sumas de dos primos"},"content":{"rendered":"<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   esPrimoSumaDeDosPrimos :: Integer -> Bool\n<\/pre>\n<p>primosSumaDeDosPrimos :: [Integer]<br \/>\ntales que<\/p>\n<ul>\n<li>(esPrimoSumaDeDosPrimos x) se verifica si x es un n\u00famero primo que se puede escribir como la suma de dos n\u00fameros primos. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     esPrimoSumaDeDosPrimos 19        ==  True\n     esPrimoSumaDeDosPrimos 20        ==  False\n     esPrimoSumaDeDosPrimos 23        ==  False\n     esPrimoSumaDeDosPrimos 18409541  ==  False\n<\/pre>\n<ul>\n<li>primosSumaDeDosPrimos es la lista de los n\u00fameros primos que se pueden escribir como la suma de dos n\u00fameros primos. Por ejemplo,        <\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> take 17 primosSumaDeDosPrimos\n     [5,7,13,19,31,43,61,73,103,109,139,151,181,193,199,229,241]\n     \u03bb> primosSumaDeDosPrimos !! (10^5)\n     18409543\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (isPrime, primes)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nesPrimoSumaDeDosPrimos :: Integer -> Bool\nesPrimoSumaDeDosPrimos x =\n  isPrime x && isPrime (x - 2)\n\nprimosSumaDeDosPrimos :: [Integer]\nprimosSumaDeDosPrimos =\n  [x | x <- primes\n     , isPrime (x - 2)]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nprimosSumaDeDosPrimos2 :: [Integer]\nprimosSumaDeDosPrimos2 =\n  [y | (x,y) <- zip primes (tail primes)\n     , y == x + 2]\n\nesPrimoSumaDeDosPrimos2 :: Integer -> Bool\nesPrimoSumaDeDosPrimos2 x = \n  x == head (dropWhile (<x) primosSumaDeDosPrimos2)\n\n-- Equivalencias\n-- =============\n\n-- Equivalencia de esPrimoSumaDeDosPrimos\nprop_esPrimoSumaDeDosPrimos_equiv :: Integer -> Property\nprop_esPrimoSumaDeDosPrimos_equiv x =\n  x > 0 ==>\n  esPrimoSumaDeDosPrimos x == esPrimoSumaDeDosPrimos2 x\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_esPrimoSumaDeDosPrimos_equiv\n--    +++ OK, passed 100 tests.\n\n-- Equivalencia de primosSumaDeDosPrimos\nprop_primosSumaDeDosPrimos_equiv :: Int -> Property\nprop_primosSumaDeDosPrimos_equiv n =\n  n >= 0 ==>\n  primosSumaDeDosPrimos !! n == primosSumaDeDosPrimos2 !! n\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_primosSumaDeDosPrimos_equiv\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> primosSumaDeDosPrimos !! (10^4)\n--    1261081\n--    (2.07 secs, 4,540,085,256 bytes)\n--\n-- Se recarga para evitar memorizaci\u00f3n    \n--    \u03bb> primosSumaDeDosPrimos2 !! (10^4)\n--    1261081\n--    (0.49 secs, 910,718,408 bytes)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nSed incompresivos; yo os aconsejo la incomprensi\u00f3n, aunque s\u00f3lo sea para destripar los chistes de los tontos.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Definir las funciones esPrimoSumaDeDosPrimos :: Integer -> Bool primosSumaDeDosPrimos :: [Integer] tales que (esPrimoSumaDeDosPrimos x) se verifica si x es un n\u00famero primo que se puede escribir como la suma de dos n\u00fameros primos. Por ejemplo, esPrimoSumaDeDosPrimos 19 == True esPrimoSumaDeDosPrimos 20 == False esPrimoSumaDeDosPrimos 23 == False esPrimoSumaDeDosPrimos 18409541 == False primosSumaDeDosPrimos es la&#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":[8,59,71,174,11,173,45,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4333"}],"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=4333"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4333\/revisions"}],"predecessor-version":[{"id":4593,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4333\/revisions\/4593"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}