Ta \u0111\u00e3 bi\u1ebft s\u1ed1 nguy\u00ean t\u1ed1 ch\u1ec9 c\u00f3 th\u1ec3 chia h\u1ebft cho s\u1ed1 1 v\u00e0 ch\u00ednh s\u1ed1 \u0111\u00f3.<\/p>\n\n\n\n
Ch\u00fang ta c\u00f2n bi\u1ebft l\u00e0 c\u00f3 th\u1ec3 nh\u1eadn bi\u1ebft s\u1ed1 nguy\u00ean t\u1ed1 qua \u201cs\u00e0ng Eratosthenes\u201d. Th\u1ebf li\u1ec7u c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n s\u1ed1 nguy\u00ean t\u1ed1 b\u1eb1ng m\u1ed9t bi\u1ec3u th\u1ee9c n\u00e0o \u0111\u00f3 kh\u00f4ng ho\u1eb7c li\u1ec7u c\u00f3 c\u00f4ng th\u1ee9c tuy kh\u00f4ng bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c h\u1ebft c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1, nh\u01b0ng c\u00e1c s\u1ed1 t\u00ednh theo c\u00f4ng th\u1ee9c \u0111\u00f3 \u0111\u1ec1u l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1?<\/p>\n\n\n\n
Nh\u00e0 to\u00e1n h\u1ecdc Ph\u00e1p n\u1ed5i ti\u1ebfng Fecma \u0111\u00e3 \u0111\u01b0a ra c\u00f4ng th\u1ee9c d\u1ef1 \u0111o\u00e1n c\u00e1ch t\u00ednh m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1. \u00d4ng \u0111\u00e3 t\u00ecm th\u1ea5y s\u1ed1:<\/p>\n\n\n\n
F(n) =22n + 1 trong \u0111\u00f3 khi n = 0, 1, 2, 3, 4 th\u00ec F(n) t\u00ednh \u0111\u01b0\u1ee3c l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n\n\n
Nh\u01b0ng v\u1ec1 sau, nh\u00e0 to\u00e1n h\u1ecdc Thu\u1ef5 s\u0129 \u01a0le \u0111\u00e3 ch\u1ec9 ra r\u1eb1ng v\u1edbi n = 5 th\u00ec s\u1ed1 F(5) =225 + 1 = 4294967297 = 641 x 6700417 l\u00e0 m\u1ed9t h\u1ee3p s\u1ed1 v\u00ec v\u1eady d\u1ef1 \u0111o\u00e1n Fecma b\u1ecb b\u00e1c b\u1ecf. T\u1eeb \u0111\u00f3 l\u1ea1i c\u00f3 nhi\u1ec1u ng\u01b0\u1eddi ti\u1ebfp t\u1ee5c \u0111\u01b0a ra nhi\u1ec1u c\u00f4ng th\u1ee9c qua \u0111\u00f3 c\u00f3 th\u1ec3 t\u00ednh ra c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 m\u1ed9t c\u00e1ch t\u1ed5ng qu\u00e1t.<\/p>\n\n\n\n
Trong l\u1ecbch s\u1eed to\u00e1n h\u1ecdc, \u0111\u00e3 t\u1eebng c\u00f3 nhi\u1ec1u c\u00f4ng th\u1ee9c \u0111\u1ec1 ngh\u1ecb t\u00ednh s\u1ed1 nguy\u00ean t\u1ed1 nh\u01b0: f(n) = n2 + n + 17 f(n) = n2 – n + 41 f(n) = n2 – n + 72491 f(n) = n2 – 79n + 1601<\/p>\n\n\n\n
Nh\u01b0ng \u0111\u00e1ng ti\u1ebfc l\u00e0 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u01b0a ra d\u1ea7n d\u1ea7n \u0111\u1ec1u b\u1ecb b\u00e1c b\u1ecf.<\/p>\n\n\n\n
N\u0103m 1983 m\u1ed9t ng\u01b0\u1eddi Trung Qu\u1ed1c \u0111\u01b0a ra m\u1ed9t d\u1ef1 \u0111o\u00e1n kh\u00e1c. N\u1ebfu cho p l\u00e0 m\u1ed9t s\u1ed1 l\u1ebb th\u00ec c\u00f3 th\u1ec3 t\u00ednh s\u1ed1 nguy\u00ean t\u1ed1 theo p b\u1eb1ng c\u00f4ng th\u1ee9c: f(p) =1\/3 (2p + 1)<\/p>\n\n\n\n
Nh\u01b0ng ng\u01b0\u1eddi ta \u0111\u00e3 t\u00ecm th\u1ea5y v\u1edbi p = 29 th\u00ec d\u1ef1 \u0111o\u00e1n b\u1ecb b\u00e1c b\u1ecf.<\/p>\n\n\n\n
Trong th\u1eddi gian \u0111\u00f3 \u1edf c\u00e1c n\u01b0\u1edbc kh\u00e1c c\u0169ng c\u00f3 ng\u01b0\u1eddi \u0111\u01b0a ra c\u00f4ng th\u1ee9c t\u00ednh s\u1ed1 nguy\u00ean t\u1ed1 ph\u1ee5 thu\u1ed9c hai tham s\u1ed1 m v\u00e0 n: f(m,n) = n-1\/2{[m(n+1) – (n! + 1)]2 – [m(n+1)-(n!+1)]2 + 1}+2.<\/p>\n\n\n\n
Trong \u0111\u00f3 m, n l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean n! = 1.2.3\u2026n \u0111\u1ecdc l\u00e0 n giai th\u1eeba.<\/p>\n\n\n\n
Ng\u01b0\u1eddi ta \u0111\u00e3 ki\u1ec3m ch\u1ee9ng \u0111\u01b0\u1ee3c f(1,2) = 3 f(3,4) = 2 f(5,4) = 5 f(103,6) = 7 l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n\n\n
C\u00f4ng th\u1ee9c \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh b\u1eb1ng l\u00ed thuy\u1ebft nh\u1edd \u0111\u00f3 c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 b\u1eb1ng c\u00f4ng th\u1ee9c nh\u01b0ng c\u00f4ng th\u1ee9c qu\u00e1 ph\u1ee9c t\u1ea1p v\u00e0 \u00edt c\u00f3 gi\u00e1 tr\u1ecb th\u1ef1c ti\u1ec5n.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: C\u00f4ng th\u1ee9c t\u00ednh s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ta \u0111\u00e3 bi\u1ebft s\u1ed1 nguy\u00ean t\u1ed1 ch\u1ec9 c\u00f3 th\u1ec3 chia h\u1ebft cho s\u1ed1 1 v\u00e0 ch\u00ednh s\u1ed1 \u0111\u00f3. Ch\u00fang ta c\u00f2n bi\u1ebft l\u00e0 c\u00f3 th\u1ec3 nh\u1eadn bi\u1ebft s\u1ed1 nguy\u00ean t\u1ed1 qua \u201cs\u00e0ng Eratosthenes\u201d. Th\u1ebf li\u1ec7u c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n s\u1ed1 nguy\u00ean t\u1ed1 b\u1eb1ng m\u1ed9t bi\u1ec3u th\u1ee9c n\u00e0o \u0111\u00f3 kh\u00f4ng ho\u1eb7c li\u1ec7u c\u00f3 c\u00f4ng th\u1ee9c tuy […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7509","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7509","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7509"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7509\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}