h\u1ecdc gi\u1ea3<\/a> c\u1ed5 Hy l\u1ea1p Erathos Thenes \u0111\u00e3 \u0111\u01b0a ra m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p.<\/p>\n\n\n\n\u00d4ng vi\u1ebft d\u00e3y c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u00ean m\u1ed9t trang gi\u1ea5y r\u1ed3i d\u00e1n l\u00ean m\u1ed9t c\u00e1i khung, sau \u0111\u00f3 l\u1ea7n l\u01b0\u1ee3t kho\u00e9t h\u1ebft c\u00e1c h\u1ee3p s\u1ed1 trong \u0111\u00f3 v\u00e0 thu \u0111\u01b0\u1ee3c m\u1ed9t v\u1eadt gi\u1ed1ng nh\u01b0 c\u00e1i r\u00e2y, c\u00e1c l\u1ed7 r\u00e2y ch\u00ednh l\u00e0 ch\u1ed7 c\u00e1c h\u1ee3p s\u1ed1 \u0111\u00e3 b\u1ecf \u0111i. Ng\u01b0\u1eddi ta g\u1ecdi trang gi\u1ea5y n\u00e0y l\u00e0 chi\u1ebfc \u201cs\u00e0ng Eratosthenes\u201d n\u1ed5i ti\u1ebfng.<\/p>\n\n\n\n
B\u1eb1ng c\u00e1ch n\u00e0y, Eratosthenes \u0111\u00e3 thu \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 trong d\u00e3y s\u1ed1 50 s\u1ed1 nguy\u00ean \u0111\u1ea7u ti\u00ean. \u00d4ng vi\u1ebft c\u00e1c s\u1ed1 t\u1eeb 1 \u0111\u1ebfn 50, tr\u01b0\u1edbc h\u1ebft \u0111\u1ee5c b\u1ecf s\u1ed1 1, gi\u1eef l\u1ea1i s\u1ed1 2. Sau \u0111\u00f3 \u0111\u1ee5c b\u1ecf c\u00e1c s\u1ed1 l\u00e0 b\u1ed9i s\u1ed1 c\u1ee7a 2, \u0111\u1ec3 l\u1ea1i s\u1ed1<\/p>\n\n\n\n
Sau \u0111\u00f3 \u0111\u1ee5c b\u1ecf s\u1ed1 l\u00e0 b\u1ed9i s\u1ed1 c\u1ee7a 3, \u0111\u1ec3 l\u1ea1i s\u1ed1 5. Sau \u0111\u00f3 lo\u1ea1i b\u1ecf c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a 5\u2026Nh\u1edd c\u00e1ch n\u00e0y ng\u01b0\u1eddi ta thu nh\u1eadn \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 trong 50 s\u1ed1 nguy\u00ean \u0111\u1ea7u ti\u00ean. \u0110\u00e2y ch\u00ednh l\u00e0 \u201cph\u01b0\u01a1ng ph\u00e1p r\u00e2y\u201d n\u1ed5i ti\u1ebfng.<\/p>\n\n\n\n
Theo ph\u01b0\u01a1ng ph\u00e1p n\u00e0y, ta vi\u1ebft c\u00e1c con s\u1ed1 t\u1eeb 1 – 100 r\u1ed3i s\u00e0ng ra c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 trong c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 1 – 100.<\/p>\n\n\n\n
Nh\u01b0ng theo c\u00e1ch c\u1ee7a Eratosthenes, li\u1ec7u c\u00f3 t\u00ecm \u0111\u01b0\u1ee3c s\u1ed1 nguy\u00ean t\u1ed1 cu\u1ed1i c\u00f9ng hay kh\u00f4ng? V\u00e0 li\u1ec7u c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 ph\u1ea3i l\u00e0 h\u1eefu h\u1ea1n hay kh\u00f4ng? V\u00e0o n\u0103m 275 n\u0103m tr\u01b0\u1edbc C\u00f4ng nguy\u00ean, nh\u00e0 to\u00e1n h\u1ecdc Hy L\u1ea1p ki\u1ec7t xu\u1ea5t \u01a0clit (Euclide) \u0111\u00e3 d\u00f9ng m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p k\u00ec di\u1ec7u \u0111\u1ec3 ch\u1ee9ng minh c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 v\u00f4 h\u1ea1n.<\/p>\n\n\n\n
\u01a0clit \u0111\u00e3 d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p ph\u1ea3n ch\u1ee9ng \u0111\u1ec3 ch\u1ee9ng minh lu\u1eadn \u0111\u1ec1 v\u1eeba n\u00eau. Tr\u01b0\u1edbc h\u1ebft \u00f4ng gi\u1ea3 thi\u1ebft s\u1ed1 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 h\u1eefu h\u1ea1n th\u00ec to\u00e0n b\u1ed9 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 s\u1ebd l\u00e0 2, 3, 5, 7\u2026p, trong \u0111\u00f3 p l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 l\u1edbn nh\u1ea5t. Sau \u0111\u00f3 ta l\u1eadp s\u1ed1 A = 2. 3. 5. 7\u2026p + 1.<\/p>\n\n\n\n
V\u1eady ch\u1ec9 c\u00f3 th\u1ec3 ho\u1eb7c A chia h\u1ebft cho c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 ho\u1eb7c b\u1ea3n th\u00e2n n\u00f3 l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1. V\u00ec theo c\u00e1ch th\u00e0nh l\u1eadp th\u00ec A kh\u00f4ng chia h\u1ebft cho b\u1ea5t k\u00ec s\u1ed1 nguy\u00ean t\u1ed1 n\u00e0o t\u1eeb 2, 3,\u2026p v\u00ec s\u1ed1 A chia cho c\u00e1c s\u1ed1 b\u1ea5t k\u00ec 2, 3, 5 \u2026p th\u00ec \u0111\u1ec1u c\u00f3 s\u1ed1 d\u01b0 l\u00e0 1 t\u1ee9c l\u00e0 A kh\u00f4ng chia h\u1ebft cho b\u1ea5t k\u00ec s\u1ed1 n\u00e0o trong c\u00e1c s\u1ed1 2,3, 5\u2026p, \u0111i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 n\u00f3 s\u1ebd chia h\u1ebft cho m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1 kh\u00e1c l\u1edbn h\u01a1n p v\u00e0 tr\u00e1i v\u1edbi gi\u1ea3 thi\u1ebft \u0111\u1eb7t ra. V\u1eady s\u1ed1 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 v\u00f4 h\u1ea1n.<\/p>\n\n\n\n
\u0110\u00e2y l\u00e0 m\u1ed9t \u0111\u1ecbnh l\u00ed quan tr\u1ecdng trong l\u00ed thuy\u1ebft s\u1ed1. L\u00ed thuy\u1ebft s\u1ed1 hay c\u00f2n g\u1ecdi l\u00e0 s\u1ed1 lu\u1eadn l\u00e0 ng\u00e0nh to\u00e1n h\u1ecdc quan tr\u1ecdng, ch\u1ee7 y\u1ebfu nghi\u00ean c\u1ee9u c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a s\u1ed1, trong \u0111\u00f3 c\u00f3 nhi\u1ec1u d\u1ef1 \u0111o\u00e1n, nhi\u1ec1u v\u1ea5n \u0111\u1ec1 h\u1ebft s\u1ee9c l\u00ed th\u00fa, c\u00f3 nhi\u1ec1u v\u1ea5n \u0111\u1ec1 cho \u0111\u1ebfn nay v\u1eabn c\u00f2n ch\u01b0a \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft. Gi\u1ea3 thuy\u1ebft Goldbach l\u00e0 m\u1ed9t trong c\u00e1c s\u1ed1 \u0111\u00f3.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: S\u1ed1 nguy\u00ean t\u1ed1; S\u1ed1 lu\u1eadn \u01a0clit v\u00e0 Eratosthenes.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Trong c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean th\u00ec 2, 3, 5, 7\u2026ch\u1ec9 c\u00f3 th\u1ec3 chia h\u1ebft cho s\u1ed1 1 v\u00e0 b\u1ea3n th\u00e2n s\u1ed1 \u0111\u00f3, \u0111\u00f3 l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1. C\u00e1c s\u1ed1 4, 6, 8, 9\u2026 th\u00ec ngo\u00e0i s\u1ed1 1, c\u00e1c s\u1ed1 n\u00e0y c\u00f2n c\u00f3 th\u1ec3 chia h\u1ebft cho nhi\u1ec1u s\u1ed1 kh\u00e1c, c\u00e1c s\u1ed1 n\u00e0y thu\u1ed9c lo\u1ea1i […]<\/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-7507","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\/7507","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=7507"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7507\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}