{"id":37766,"date":"2026-07-15T04:51:05","date_gmt":"2026-07-15T02:51:05","guid":{"rendered":"https:\/\/xmau.com\/notiziole\/?p=37766"},"modified":"2026-07-12T18:56:02","modified_gmt":"2026-07-12T16:56:02","slug":"la-congettura-di-gilbreath","status":"publish","type":"post","link":"https:\/\/xmau.com\/notiziole\/2026\/07\/15\/la-congettura-di-gilbreath\/","title":{"rendered":"La congettura di Gilbreath"},"content":{"rendered":"<p><a href=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/07\/gilbreath.jpg?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"alignright size-medium wp-image-37767\" src=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/07\/gilbreath.jpg?resize=300%2C175&#038;ssl=1\" alt=\"Schema dell'articolo di Proth (vedi il testo per i particolari)\" width=\"300\" height=\"175\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/07\/gilbreath.jpg?resize=300%2C175&amp;ssl=1 300w, https:\/\/i0.wp.com\/xmau.com\/notiziole\/wp-content\/uploads\/sites\/6\/2026\/07\/gilbreath.jpg?w=548&amp;ssl=1 548w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Scrivete i primi numeri primi:<\/p>\n<p style=\"text-align: center;\">2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, &#8230;<\/p>\n<p>Ora calcolate il valore assoluto della differenza tra due valori consecutivi. Lo so, la successione \u00e8 crescente e non serve calcolare il valore assoluto, ma fidatevi.<\/p>\n<p style=\"text-align: center;\">1, 2, 2, 4, 2, 4, 2, 4, 6, 2, &#8230;<\/p>\n<p>Continuate a fare la stessa cosa: stavolta il valore assoluto serve eccome.<\/p>\n<p style=\"text-align: center;\">1, 0, 2, 2, 2, 2, 2, 2, 4, &#8230;<\/p>\n<p style=\"text-align: center;\">1, 2, 0, 0, 0, 0, 0, 2, &#8230;<\/p>\n<p>Come vedete, il primo numero delle successioni \u00e8 sempre 1. D&#8217;accordo, deve essere dispari, ma in linea di principio potrebbe anche essere 3, 5 o qualcos&#8217;altro, no? Il matematico e prestigiatore Norman Gilbreath, un giorno in cui non aveva nulla da fare, si \u00e8 accorto della cosa e nel 1958 ha presentato quella che \u00e8 nota come\u00a0<a href=\"https:\/\/it.wikipedia.org\/w\/index.php?title=Congettura_di_Gilbreath\">congettura di Gilbreath<\/a>, che afferm appunto che ci sar\u00e0 sempre un 1 come prima cifra.\u00a0Ovviamente vale anche in questo caso la legge di Stigler sull&#8217;eponimia: ottant&#8217;anni prima di Gilbreath, Fran\u00e7ois Proth aveva enunciato il teorema, ma <a href=\"https:\/\/gdz.sub.uni-goettingen.de\/id\/PPN598948236_0004?tify=%7B%22pages%22%3A%5B270%5D%2C%22pan%22%3A%7B%22x%22%3A0.569%2C%22y%22%3A0.581%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.431%7D\">la sua dimostrazione<\/a> era errata&#8230; Ah, notate come nel 1878 si considerava ancora 1 come numero primo.<\/p>\n<p>La congettura \u00e8 una di quelle tipiche in teoria dei numeri: facile da enunciare ma che non si sa come attaccare, tanto che Paul Erd\u0151s disse che probabilmente era vera, ma che ci sarebbero voluti almeno 200 anni per dimostrarlo. Manca ancora tanto tempo, ma forse qualche passetto avanti lo si \u00e8 fatto: John Cook <a href=\"https:\/\/www.johndcook.com\/blog\/2026\/07\/11\/progress-on-gilbreaths-conjecture\/\">segnala<\/a> che Terence Tao ha coautorato un articolo &#8211; ne parla <a href=\"https:\/\/terrytao.wordpress.com\/2026\/07\/11\/gilbreaths-conjecture-a-cramer-random-model-and-a-deterministic-analysis\/\">nel suo blog<\/a> &#8211; che presenta un modello stocastico che generalizza la congettura di Gilbreath e che euristicamente la fa sembrare vera. Peccato che si affretti ad aggiungere che anche se la loro analisi \u00e8 pi\u00f9 trattabile da un punto di vista matematico, non hanno idea di come andare avanti&#8230;<span hidden class=\"__iawmlf-post-loop-links\" data-iawmlf-links=\"[{&quot;id&quot;:227,&quot;href&quot;:&quot;https:\\\/\\\/it.wikipedia.org\\\/w\\\/index.php?title=Congettura_di_Gilbreath&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20260712165123\\\/https:\\\/\\\/it.wikipedia.org\\\/w\\\/index.php?title=Congettura_di_Gilbreath&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2026-07-15 03:07:44&quot;,&quot;http_code&quot;:200}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-07-15 03:07:44&quot;,&quot;http_code&quot;:200},&quot;process&quot;:&quot;done&quot;},{&quot;id&quot;:228,&quot;href&quot;:&quot;https:\\\/\\\/gdz.sub.uni-goettingen.de\\\/id\\\/PPN598948236_0004?tify=%7B%22pages%22%3A%5B270%5D%2C%22pan%22%3A%7B%22x%22%3A0.569%2C%22y%22%3A0.581%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.431%7D&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20260712165129\\\/https:\\\/\\\/gdz.sub.uni-goettingen.de\\\/id\\\/PPN598948236_0004?tify=%7B%22pages%22%3A%5B270%5D%2C%22pan%22%3A%7B%22x%22%3A0.569%2C%22y%22%3A0.581%7D%2C%22view%22%3A%22info%22%2C%22zoom%22%3A0.431%7D&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[],&quot;broken&quot;:false,&quot;last_checked&quot;:null,&quot;process&quot;:&quot;done&quot;},{&quot;id&quot;:236,&quot;href&quot;:&quot;https:\\\/\\\/www.johndcook.com\\\/blog\\\/2026\\\/07\\\/11\\\/progress-on-gilbreaths-conjecture&quot;,&quot;archived_href&quot;:&quot;&quot;,&quot;redirect_href&quot;:&quot;https:\\\/\\\/www.johndcook.com\\\/blog\\\/2026\\\/07\\\/11\\\/progress-on-gilbreaths-conjecture\\\/&quot;,&quot;checks&quot;:[],&quot;broken&quot;:false,&quot;last_checked&quot;:null,&quot;process&quot;:&quot;done&quot;},{&quot;id&quot;:237,&quot;href&quot;:&quot;https:\\\/\\\/terrytao.wordpress.com\\\/2026\\\/07\\\/11\\\/gilbreaths-conjecture-a-cramer-random-model-and-a-deterministic-analysis&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20260712232814\\\/https:\\\/\\\/terrytao.wordpress.com\\\/2026\\\/07\\\/11\\\/gilbreaths-conjecture-a-cramer-random-model-and-a-deterministic-analysis\\\/&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2026-07-15 02:52:09&quot;,&quot;http_code&quot;:200}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-07-15 02:52:09&quot;,&quot;http_code&quot;:200},&quot;process&quot;:&quot;done&quot;}]\"><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Una di quelle propriet\u00e0 facili da enunciare ma che non si sa dimostrare o confutare.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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