{"id":5282,"date":"2019-12-24T05:30:18","date_gmt":"2019-12-24T03:30:18","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5282"},"modified":"2019-12-31T08:42:13","modified_gmt":"2019-12-31T06:42:13","slug":"infinitud-de-primos-gemelos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/infinitud-de-primos-gemelos\/","title":{"rendered":"Infinitud de primos gemelos"},"content":{"rendered":"<p>Un par de n\u00fameros primos (p,q) es un par de <a href=\"http:\/\/bit.ly\/1RAo6KU\">n\u00fameros primos gemelos<\/a> si su distancia de 2; es decir, si q = p+2. Por ejemplo, (17,19) es una par de n\u00fameros primos gemelos.<\/p>\n<p>La <a href=\"http:\/\/bit.ly\/36ZbB9C\">conjetura de los primos gemelos<\/a> postula la existencia de infinitos pares de primos gemelos.<\/p>\n<p>Definir la constante<\/p>\n<pre lang=\"text\">\n   primosGemelos :: [(Integer,Integer)]\n<\/pre>\n<p>tal que sus elementos son los pares de primos gemelos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> take 7 primosGemelos\n   [(3,5),(5,7),(11,13),(17,19),(29,31),(41,43),(59,61)]\n   \u03bb> primosGemelos !! (4*10^4)\n   (6381911,6381913)\n<\/pre>\n<p>Comprobar con QuickCheck la conjetura de los primos gemelos.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Numbers.Primes (primes, isPrime)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\nprimosGemelos :: [(Integer,Integer)]\nprimosGemelos = [(x,x+2) | x <- primes, isPrime (x+2)]\n\n-- 2\u00aa soluci\u00f3n\nprimosGemelos2 :: [(Integer,Integer)]\nprimosGemelos2 = [(x,y) | (x,y) <- zip primes (tail primes)\n                        , y - x == 2]\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> primosGemelos !! (2*10^4)\n--    (2840447,2840449)\n--    (3.93 secs, 12,230,474,952 bytes)\n--    \u03bb> primosGemelos2 !! (2*10^4)\n--    (2840447,2840449)\n--    (0.77 secs, 2,202,822,456 bytes)\n\n-- Propiedad\n-- =========\n\n-- La propiedad es\nprop_primosGemelos :: Integer -> Property\nprop_primosGemelos n =\n  n >= 0 ==> not (null [(x,y) | (x,y) <- primosGemelos2, x > n])\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_primosGemelos\n--    +++ OK, passed 100 tests.\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nEl sentimiento ha de tener tanto de individual como de gen\u00e9rico; debe orientarse hacia valores universales, o que pretenden serlo.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Un par de n\u00fameros primos (p,q) es un par de n\u00fameros primos gemelos si su distancia de 2; es decir, si q = p+2. Por ejemplo, (17,19) es una par de n\u00fameros primos gemelos. La conjetura de los primos gemelos postula la existencia de infinitos pares de primos gemelos. Definir la constante primosGemelos :: [(Integer,Integer)]&#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":[8,174,415,181,141,173,45,146,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5282"}],"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=5282"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5282\/revisions"}],"predecessor-version":[{"id":5326,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5282\/revisions\/5326"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}