{"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\/vi\/science\/mathematics\/prime-numbers-surprises-and-mysteries\/","title":{"rendered":"S\u1ed1 nguy\u00ean t\u1ed1: Nh\u1eefng b\u1ea5t ng\u1edd v\u00e0 b\u00ed \u1ea9n to\u00e1n h\u1ecdc"},"content":{"rendered":"

S\u1ed1 nguy\u00ean t\u1ed1: S\u1ef1 ng\u1ea1c nhi\u00ean v\u00e0 b\u00ed \u1ea9n cho c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc<\/h2>\n\n

S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 g\u00ec?<\/h2>\n\n

S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 1, ch\u1ec9 chia h\u1ebft cho 1 v\u00e0 ch\u00ednh n\u00f3. V\u00ed d\u1ee5, 7 l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean t\u1ed1 v\u00ec n\u00f3 ch\u1ec9 chia h\u1ebft cho 1 v\u00e0 7.<\/p>\n\n

L\u1ecbch s\u1eed c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1 trong h\u01a1n 2.300 n\u0103m. Nh\u00e0 to\u00e1n h\u1ecdc Hy L\u1ea1p c\u1ed5 \u0111\u1ea1i Euclid \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng c\u00f3 v\u00f4 s\u1ed1 s\u1ed1 nguy\u00ean t\u1ed1. V\u00e0o th\u1ebf k\u1ef7 17, nh\u00e0 to\u00e1n h\u1ecdc ng\u01b0\u1eddi Ph\u00e1p Pierre de Fermat \u0111\u00e3 kh\u00e1m ph\u00e1 ra m\u1ed9t c\u00e1ch s\u1eed d\u1ee5ng s\u00e0ng Eratosthenes \u0111\u1ec3 t\u00ecm s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n

S\u00e0ng Eratosthenes<\/h2>\n\n

S\u00e0ng Eratosthenes l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p t\u00ecm t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 cho \u0111\u1ebfn m\u1ed9t s\u1ed1 nh\u1ea5t \u0111\u1ecbnh. N\u00f3 ho\u1ea1t \u0111\u1ed9ng b\u1eb1ng c\u00e1ch g\u1ea1ch b\u1ecf t\u1ea5t c\u1ea3 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a m\u1ed7i s\u1ed1 nguy\u00ean t\u1ed1. V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ecm t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 cho \u0111\u1ebfn 100, tr\u01b0\u1edbc ti\u00ean, b\u1ea1n s\u1ebd g\u1ea1ch b\u1ecf t\u1ea5t c\u1ea3 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a 2. Sau \u0111\u00f3, b\u1ea1n s\u1ebd g\u1ea1ch b\u1ecf t\u1ea5t c\u1ea3 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a 3, ngo\u1ea1i tr\u1eeb ch\u00ednh s\u1ed1 3. Sau \u0111\u00f3, b\u1ea1n s\u1ebd g\u1ea1ch b\u1ecf t\u1ea5t c\u1ea3 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a 5, ngo\u1ea1i tr\u1eeb ch\u00ednh s\u1ed1 5. V\u00e0 c\u1ee9 ti\u1ebfp t\u1ee5c nh\u01b0 v\u1eady.<\/p>\n\n

Ph\u00e2n b\u1ed1 s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

M\u1ed9t trong nh\u1eefng \u0111i\u1ec1u th\u00fa v\u1ecb nh\u1ea5t v\u1ec1 s\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a ch\u00fang. S\u1ed1 nguy\u00ean t\u1ed1 kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed1 \u0111\u1ec1u tr\u00ean tr\u1ee5c s\u1ed1. Thay v\u00e0o \u0111\u00f3, ch\u00fang tr\u1edf n\u00ean th\u01b0a th\u1edbt h\u01a1n khi c\u00e1c s\u1ed1 tr\u1edf n\u00ean l\u1edbn h\u01a1n. \u0110i\u1ec1u n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ecbnh l\u00fd s\u1ed1 nguy\u00ean t\u1ed1.<\/p>\n\n

Gi\u1ea3 thuy\u1ebft Riemann<\/h2>\n\n

Gi\u1ea3 thuy\u1ebft Riemann l\u00e0 m\u1ed9t b\u00e0i to\u00e1n ch\u01b0a c\u00f3 l\u1eddi gi\u1ea3i n\u1ed5i ti\u1ebfng trong to\u00e1n h\u1ecdc li\u00ean quan \u0111\u1ebfn s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1. N\u00f3 n\u00f3i r\u1eb1ng h\u00e0m zeta Riemann ch\u1ec9 c\u00f3 c\u00e1c s\u1ed1 kh\u00f4ng t\u1ea1i c\u00e1c s\u1ed1 ch\u1eb5n \u00e2m v\u00e0 c\u00e1c s\u1ed1 ph\u1ee9c c\u00f3 ph\u1ea7n th\u1ef1c b\u1eb1ng 1\/2.<\/p>\n\n

Ph\u00e2n t\u00edch d\u1eef li\u1ec7u trong nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

Trong nh\u1eefng n\u0103m g\u1ea7n \u0111\u00e2y, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 b\u1eaft \u0111\u1ea7u s\u1eed d\u1ee5ng ph\u00e2n t\u00edch d\u1eef li\u1ec7u \u0111\u1ec3 nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1. \u0110i\u1ec1u n\u00e0y \u0111\u00e3 d\u1eabn \u0111\u1ebfn m\u1ed9t s\u1ed1 hi\u1ec3u bi\u1ebft m\u1edbi v\u1ec1 s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1. V\u00ed d\u1ee5, c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 ph\u00e1t hi\u1ec7n ra r\u1eb1ng c\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1 kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e2n b\u1ed1 \u0111\u1ec1u.<\/p>\n\n

T\u01b0\u01a1ng lai c\u1ee7a nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

Nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1 v\u1eabn l\u00e0 m\u1ed9t l\u0129nh v\u1ef1c nghi\u00ean c\u1ee9u r\u1ea5t s\u00f4i \u0111\u1ed9ng. C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111ang s\u1eed d\u1ee5ng nhi\u1ec1u k\u1ef9 thu\u1eadt kh\u00e1c nhau, bao g\u1ed3m c\u1ea3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u, \u0111\u1ec3 c\u1ed1 g\u1eafng gi\u1ea3i quy\u1ebft gi\u1ea3 thuy\u1ebft Riemann v\u00e0 c\u00e1c b\u00e0i to\u00e1n ch\u01b0a c\u00f3 l\u1eddi gi\u1ea3i kh\u00e1c.<\/p>\n\n

C\u00e1c m\u1eabu trong s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

C\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

Ngo\u1ea1i tr\u1eeb 2 v\u00e0 5, t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 \u0111\u1ec1u c\u00f3 ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng l\u00e0 1, 3, 7 ho\u1eb7c 9. V\u00e0o th\u1ebf k\u1ef7 19, ng\u01b0\u1eddi ta \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng nh\u1eefng ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u00f3 th\u1ec3 c\u00f3 n\u00e0y xu\u1ea5t hi\u1ec7n v\u1edbi t\u1ea7n su\u1ea5t b\u1eb1ng nhau.<\/p>\n\n

T\u1ea7n su\u1ea5t c\u1ee7a c\u00e1c c\u1eb7p ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng<\/h2>\n\n

V\u00e0i n\u0103m tr\u01b0\u1edbc, c\u00e1c nh\u00e0 l\u00fd thuy\u1ebft s\u1ed1 c\u1ee7a \u0110\u1ea1i h\u1ecdc Stanford, Lemke Oliver v\u00e0 Kannan Soundararajan, \u0111\u00e3 ph\u00e1t hi\u1ec7n ra m\u1ed9t m\u1eabu b\u1ea5t ng\u1edd trong c\u00e1c ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1. H\u1ecd ph\u00e1t hi\u1ec7n ra r\u1eb1ng m\u1ed9t s\u1ed1 c\u1eb7p ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng xu\u1ea5t hi\u1ec7n th\u01b0\u1eddng xuy\u00ean h\u01a1n nh\u1eefng c\u1eb7p kh\u00e1c. V\u00ed d\u1ee5, c\u1eb7p 3-9 xu\u1ea5t hi\u1ec7n th\u01b0\u1eddng xuy\u00ean h\u01a1n c\u1eb7p 3-7, m\u1eb7c d\u00f9 c\u1ea3 hai c\u1eb7p \u0111\u1ec1u c\u00e1ch nhau s\u00e1u \u0111\u01a1n v\u1ecb.<\/p>\n\n

Nh\u1eefng th\u00e1ch th\u1ee9c trong nghi\u00ean c\u1ee9u s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n\n

Kh\u00f3 kh\u0103n trong vi\u1ec7c ch\u1ee9ng minh k\u1ebft qu\u1ea3<\/h2>\n\n

M\u1ed9t trong nh\u1eefng th\u00e1ch th\u1ee9c l\u1edbn nh\u1ea5t trong nghi\u00ean c\u1ee9u v\u1ec1 s\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 kh\u00f3 kh\u0103n trong vi\u1ec7c ch\u1ee9ng minh k\u1ebft qu\u1ea3. Nhi\u1ec1u ph\u1ecfng \u0111o\u00e1n m\u00e0 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u01b0a ra v\u1ec1 s\u1ed1 nguy\u00ean t\u1ed1 r\u1ea5t kh\u00f3 ch\u1ee9ng minh. V\u00ed d\u1ee5, gi\u1ea3 thuy\u1ebft Riemann v\u1eabn ch\u01b0a \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft trong h\u01a1n 150 n\u0103m.<\/p>\n\n

K\u1ebft lu\u1eadn<\/h2>\n\n

S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 m\u1ed9t ch\u1ee7 \u0111\u1ec1 h\u1ea5p d\u1eabn v\u00e0 b\u00ed \u1ea9n. C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 nghi\u00ean c\u1ee9u ch\u00fang trong nhi\u1ec1u th\u1ebf k\u1ef7 v\u00e0 v\u1eabn c\u00f2n nhi\u1ec1u \u0111i\u1ec1u m\u00e0 ch\u00fang ta ch\u01b0a bi\u1ebft. Tuy nhi\u00ean, vi\u1ec7c s\u1eed d\u1ee5ng ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 c\u00e1c k\u1ef9 thu\u1eadt m\u1edbi kh\u00e1c \u0111ang gi\u00fap c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u1ea1t \u0111\u01b0\u1ee3c ti\u1ebfn b\u1ed9 trong vi\u1ec7c hi\u1ec3u s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a s\u1ed1 nguy\u00ean t\u1ed1.<\/p>","protected":false},"excerpt":{"rendered":"

S\u1ed1 nguy\u00ean t\u1ed1: S\u1ef1 ng\u1ea1c nhi\u00ean v\u00e0 b\u00ed \u1ea9n cho c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 g\u00ec? S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 1,…<\/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":[6881,97,342,6880,214],"class_list":["post-3639","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-math-mysteries","tag-science","tag-life-science","tag-prime-numbers","tag-mathematics"],"_links":{"self":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/3639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/comments?post=3639"}],"version-history":[{"count":1,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/3639\/revisions"}],"predecessor-version":[{"id":3640,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/posts\/3639\/revisions\/3640"}],"wp:attachment":[{"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/media?parent=3639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/categories?post=3639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lifescienceart.com\/vi\/wp-json\/wp\/v2\/tags?post=3639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}