{"id":4936,"date":"2022-09-08T10:46:32","date_gmt":"2022-09-08T08:46:32","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=4936"},"modified":"2022-09-08T10:47:47","modified_gmt":"2022-09-08T08:47:47","slug":"numeros-primos-de-mersenne","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/numeros-primos-de-mersenne\/","title":{"rendered":"N\u00fameros primos de Mersenne"},"content":{"rendered":"

Marin Mersenne<\/strong> (1588-1648) fue un sacerdote, matem\u00e1tico y fil\u00f3sofo franc\u00e9s.<\/span><\/p>\n

Un n\u00famero de Mersenne <\/strong>es un n\u00famero de la forma Mp<\/sub>= 2<\/span>p<\/sup>\u20131, siendo p un n\u00famero primo.<\/span><\/span><\/p>\n

Un n\u00famero primo de Mersenne <\/strong>es un n\u00famero primo de la forma Mp<\/sub>= 2<\/span>p<\/sup>\u20131, siendo p un n\u00famero primo.<\/span><\/span><\/p>\n

Los primeros n\u00fameros de Mersenne, son:<\/span><\/p>\n

n = 2   \u2192  <\/span>M<\/span>2<\/sub> = <\/span><\/span><\/span>2<\/span>2<\/sup>\u2013<\/span>1 = 3   primo<\/span><\/span><\/p>\n

n = 3   \u2192  M3<\/sub> = <\/span><\/span>23<\/sup>\u20131<\/span> = 7   primo<\/span><\/p>\n

n = 5   \u2192  M5<\/sub> = <\/span><\/span>25<\/sup>\u20131<\/span> = 31   primo<\/span><\/p>\n

n = 7   \u2192  M7<\/sub> =  <\/span><\/span>27<\/sup>\u20131<\/span> = 127   primo<\/span><\/p>\n

n = 11   \u2192  M11<\/sub> = <\/span><\/span>211<\/sup>\u20131<\/span> = 2047 = 23 \u00b7 89   compuest<\/span>o<\/span><\/p>\n

n = 13   \u2192  M13<\/sub> = <\/span><\/span>213<\/sup>\u20131<\/span> = 8191   primo<\/span><\/p>\n

n = 17   \u2192  M17<\/sub> = <\/span><\/span>217<\/sup>\u20131<\/span> = 131071   primo<\/span><\/p>\n

n = 19   \u2192  M19<\/sub> =  <\/span><\/span>219<\/sup>\u20131<\/span> = 524287   primo<\/span><\/p>\n

n = 23   \u2192  M23<\/sub> = <\/span><\/span>223<\/sup>\u20131<\/span> = 8388607 = 47 \u00b7 178481   compuest<\/span>o<\/span><\/p>\n

n = 29   \u2192  M29<\/sub> = <\/span><\/span>229<\/sup>\u20131<\/span> = 536870911 = 233 \u00b7 1103 \u00b7 2089   compuest<\/span>o<\/span><\/p>\n

.  .  .<\/p>\n

Actualmente se conocen 51 n\u00fameros primos de Mersenne. El \u00faltimo se obtiene con p=82589933 y tiene 24862048 cifras.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Marin Mersenne (1588-1648) fue un sacerdote, matem\u00e1tico y fil\u00f3sofo franc\u00e9s. Un n\u00famero de Mersenne es un n\u00famero de la forma Mp= 2p\u20131, siendo p un n\u00famero primo. Un n\u00famero primo de Mersenne es un...<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075204],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/4936"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=4936"}],"version-history":[{"count":11,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/4936\/revisions"}],"predecessor-version":[{"id":4947,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/4936\/revisions\/4947"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=4936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=4936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=4936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}