{"id":3639,"date":"2022-01-29T15:10:12","date_gmt":"2022-01-29T15:10:12","guid":{"rendered":"https:\/\/www.lifescienceart.com\/?p=3639"},"modified":"2022-01-29T15:10:12","modified_gmt":"2022-01-29T15:10:12","slug":"prime-numbers-surprises-and-mysteries","status":"publish","type":"post","link":"https:\/\/www.lifescienceart.com\/cs\/science\/mathematics\/prime-numbers-surprises-and-mysteries\/","title":{"rendered":"Prvo\u010d\u00edsla: P\u0159ekvapen\u00ed a z\u00e1hady pro matematiky"},"content":{"rendered":"<h2 class=\"wp-block-heading\">Prvo\u010d\u00edsla: P\u0159ekvapen\u00ed a z\u00e1hady pro matematiky<\/h2>\n\n<h2 class=\"wp-block-heading\">Co jsou prvo\u010d\u00edsla?<\/h2>\n\n<p>Prvo\u010d\u00edsla jsou cel\u00e1 \u010d\u00edsla v\u011bt\u0161\u00ed ne\u017e 1, kter\u00e1 lze beze zbytku d\u011blit pouze \u010d\u00edslem 1 a sebou sam\u00fdm. Nap\u0159\u00edklad 7 je prvo\u010d\u00edslo, proto\u017ee beze zbytku jej lze d\u011blit pouze \u010d\u00edslem 1 a 7.<\/p>\n\n<h2 class=\"wp-block-heading\">Historie prvo\u010d\u00edsel<\/h2>\n\n<p>Matematikov\u00e9 studuj\u00ed prvo\u010d\u00edsla ji\u017e v\u00edce ne\u017e 2 300 let. Starov\u011bk\u00fd \u0159eck\u00fd matematik Eukleid dok\u00e1zal, \u017ee existuje nekone\u010dn\u011b mnoho prvo\u010d\u00edsel. V 17. stolet\u00ed objevil francouzsk\u00fd matematik Pierre de Fermat zp\u016fsob, jak pomoc\u00ed Eratosthenova s\u00edta nal\u00e9zt prvo\u010d\u00edsla.<\/p>\n\n<h2 class=\"wp-block-heading\">Eratosthenovo s\u00edto<\/h2>\n\n<p>Eratosthenovo s\u00edto je metoda, jak nal\u00e9zt v\u0161echna prvo\u010d\u00edsla a\u017e do ur\u010dit\u00e9ho \u010d\u00edsla. Funguje tak, \u017ee vy\u0161krtneme v\u0161echny n\u00e1sobky ka\u017ed\u00e9ho prvo\u010d\u00edsla. Nap\u0159\u00edklad pokud chceme nal\u00e9zt v\u0161echna prvo\u010d\u00edsla a\u017e do 100, za\u010dneme t\u00edm, \u017ee vy\u0161krtneme v\u0161echny n\u00e1sobky 2. Pot\u00e9 vy\u0161krtneme v\u0161echny n\u00e1sobky 3, krom\u011b samotn\u00e9 3. Pot\u00e9 vy\u0161krtneme v\u0161echny n\u00e1sobky 5, krom\u011b samotn\u00e9 5. A tak d\u00e1le.<\/p>\n\n<h2 class=\"wp-block-heading\">Rozd\u011blen\u00ed prvo\u010d\u00edsel<\/h2>\n\n<p>Jednou z nejzaj\u00edmav\u011bj\u0161\u00edch vlastnost\u00ed prvo\u010d\u00edsel je jejich rozd\u011blen\u00ed. Prvo\u010d\u00edsla nejsou rovnom\u011brn\u011b rozd\u011blena na \u010d\u00edseln\u00e9 ose. M\u00edsto toho se st\u00e1vaj\u00ed m\u00e9n\u011b \u010dast\u00fdmi, s t\u00edm jak rostou. Tomuto jevu se \u0159\u00edk\u00e1 prvo\u010d\u00edseln\u00e1 v\u011bta.<\/p>\n\n<h2 class=\"wp-block-heading\">Riemannova hypot\u00e9za<\/h2>\n\n<p>Riemannova hypot\u00e9za je slavn\u00fd nevy\u0159e\u0161en\u00fd probl\u00e9m v matematice, kter\u00fd se t\u00fdk\u00e1 rozd\u011blen\u00ed prvo\u010d\u00edsel. Tvrd\u00ed, \u017ee Riemannova funkce zeta m\u00e1 sv\u00e9 nuly pouze v z\u00e1porn\u00fdch sud\u00fdch cel\u00fdch \u010d\u00edslech a v komplexn\u00edch \u010d\u00edslech s re\u00e1lnou \u010d\u00e1st\u00ed 1\/2.<\/p>\n\n<h2 class=\"wp-block-heading\">Anal\u00fdza dat ve studiu prvo\u010d\u00edsel<\/h2>\n\n<p>V posledn\u00edch letech za\u010dali matematikov\u00e9 pou\u017e\u00edvat anal\u00fdzu dat ke studiu prvo\u010d\u00edsel. To vedlo k nov\u00fdm poznatk\u016fm o rozd\u011blen\u00ed prvo\u010d\u00edsel. Nap\u0159\u00edklad matematici zjistili, \u017ee posledn\u00ed \u010d\u00edslice prvo\u010d\u00edsel nejsou rovnom\u011brn\u011b rozd\u011bleny.<\/p>\n\n<h2 class=\"wp-block-heading\">Budoucnost studia prvo\u010d\u00edsel<\/h2>\n\n<p>Studium prvo\u010d\u00edsel je st\u00e1le velmi aktivn\u00ed oblast\u00ed v\u00fdzkumu. Matematikov\u00e9 pou\u017e\u00edvaj\u00ed celou \u0159adu r\u016fzn\u00fdch technik, v\u010detn\u011b anal\u00fdzy dat, aby se pokusili vy\u0159e\u0161it Riemannovu hypot\u00e9zu a dal\u0161\u00ed nevy\u0159e\u0161en\u00e9 probl\u00e9my.<\/p>\n\n<h2 class=\"wp-block-heading\">Vzorce v prvo\u010d\u00edslech<\/h2>\n\n<h2 class=\"wp-block-heading\">Posledn\u00ed \u010d\u00edslice prvo\u010d\u00edsel<\/h2>\n\n<p>Krom\u011b 2 a 5 kon\u010d\u00ed v\u0161echna prvo\u010d\u00edsla \u010d\u00edslic\u00ed 1, 3, 7 nebo 9. V 19. stolet\u00ed bylo dok\u00e1z\u00e1no, \u017ee tyto mo\u017en\u00e9 posledn\u00ed \u010d\u00edslice jsou stejn\u011b \u010dast\u00e9.<\/p>\n\n<h2 class=\"wp-block-heading\">Frekvence p\u00e1r\u016f posledn\u00edch \u010d\u00edslic<\/h2>\n\n<p>P\u0159ed n\u011bkolika lety objevili teoretici \u010d\u00edsel Lemke Oliver a Kannan Soundararajan ze Stanfordu p\u0159ekvapiv\u00fd vzorec v posledn\u00edch \u010d\u00edslic\u00edch prvo\u010d\u00edsel. Zjistili, \u017ee n\u011bkter\u00e9 p\u00e1ry posledn\u00edch \u010d\u00edslic jsou b\u011b\u017en\u011bj\u0161\u00ed ne\u017e jin\u00e9. Nap\u0159\u00edklad p\u00e1r 3-9 je b\u011b\u017en\u011bj\u0161\u00ed ne\u017e p\u00e1r 3-7, i kdy\u017e oba p\u00e1ry poch\u00e1zej\u00ed ze stejn\u00e9ho rozmez\u00ed \u0161esti.<\/p>\n\n<h2 class=\"wp-block-heading\">V\u00fdzvy ve studiu prvo\u010d\u00edsel<\/h2>\n\n<h2 class=\"wp-block-heading\">Obt\u00ed\u017enost dokazov\u00e1n\u00ed v\u00fdsledk\u016f<\/h2>\n\n<p>Jednou z nejv\u011bt\u0161\u00edch v\u00fdzev ve studiu prvo\u010d\u00edsel je obt\u00ed\u017enost dokazov\u00e1n\u00ed v\u00fdsledk\u016f. Mnoho z domn\u011bnek, kter\u00e9 maj\u00ed matematici o prvo\u010d\u00edslech, je velmi obt\u00ed\u017en\u00e9 dok\u00e1zat. Nap\u0159\u00edklad Riemannova hypot\u00e9za je nevy\u0159e\u0161ena ji\u017e v\u00edce ne\u017e 150 let.<\/p>\n\n<h2 class=\"wp-block-heading\">Z\u00e1v\u011br<\/h2>\n\n<p>Prvo\u010d\u00edsla jsou fascinuj\u00edc\u00edm a z\u00e1hadn\u00fdm t\u00e9matem. Matematikov\u00e9 je studuj\u00ed ji\u017e po stalet\u00ed a st\u00e1le existuje mnoho v\u011bc\u00ed, kter\u00e9 nev\u00edme. Pou\u017e\u00edv\u00e1n\u00ed anal\u00fdzy dat a dal\u0161\u00edch nov\u00fdch technik v\u0161ak pom\u00e1h\u00e1 matematik\u016fm \u010dinit pokroky v porozum\u011bn\u00ed rozd\u011blen\u00ed prvo\u010d\u00edsel.<\/p>","protected":false},"excerpt":{"rendered":"<p>Prvo\u010d\u00edsla: P\u0159ekvapen\u00ed a z\u00e1hady pro matematiky Co jsou prvo\u010d\u00edsla? Prvo\u010d\u00edsla jsou cel\u00e1 \u010d\u00edsla v\u011bt\u0161\u00ed ne\u017e 1, kter\u00e1 lze beze zbytku d\u011blit pouze \u010d\u00edslem 1 a sebou sam\u00fdm. Nap\u0159\u00edklad 7 je&hellip;<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[220],"tags":[6881,214,6880,97,342],"class_list":["post-3639","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-math-mysteries","tag-mathematics","tag-prime-numbers","tag-science","tag-life-science"],"_links":{"self":[{"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/posts\/3639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/comments?post=3639"}],"version-history":[{"count":1,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/posts\/3639\/revisions"}],"predecessor-version":[{"id":3640,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/posts\/3639\/revisions\/3640"}],"wp:attachment":[{"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/media?parent=3639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/categories?post=3639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/cs\/wp-json\/wp\/v2\/tags?post=3639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}