Ngaba oyinhloko kakhulu. isisekelo

Iincwadi zezifundo zeMathematika ngamanye amaxesha kunzima ukuyiqonda. ulwimi eyomileyo ecacileyo Abalobi akusoloko kulula ukuyiqonda. Kwaye kukho basoloko zihlobene izihloko, vzaimovytekayuschie. Kuba uphuhliso ngomxholo kuyimfuneko ukuba ukuphakamisa inani yangaphambili yaye maxa wambi flip kuyo yonke incwadi. Nzima? Ewe. Makhe nesibindi ukuze kuthintelwe ezi ubunzima futhi bazame ukufumana isihloko ayikho ncam indlela eqhelekileyo. Senza uhlobo excursion kungena amanani lizwe. Inkcazelo, Noko ke, kusekho kuhlala injalo, ngokuba imithetho imathematika awunakungenziwa. amanani Ngoko ke, inkulumbuso kakhulu - inani zendalo, kunye, umahluli eqhelekileyo elingana omnye. Ingaba elakuqondayo? Kuyinto.

Kuba Umzekelo graphic ngakumbi, makhe uthabathe inani 6 13 Ke ngoko, nangaphezulu - iyakwazi ukuhluleka ngo omnye (prime kakhulu). amanani 12 no-14 Ke - njengokuba ayide ikwazi kuba, ngenxa yokuba ukuwa ayikho-1 kuphela, kodwa ngomhla we-2 amanani alandelayo - 21 no 47 nayo ezingangeniyo phants 'yinkulumbuso kakhulu ": zibe kwahlulelana kungekhona-1 kuphela, kodwa kwakhona 7.

Libhekisela amanani prime noko njengoko (a, y) = 1.

Sinako bathi nje ngakumbi: linokwahlulwa eqhelekileyo (ephezulu) ilingana omnye.
Kutheni sinalo ulwazi olunjalo? Izizathu ngokwaneleyo.

Bentsebenziswano amanani prime zifakiwe kwezinye kwinkqubo encryption. Abo basebenza kunye cipher Hill okanye iinkqubo Yeremiya uKesare, baqonde ukuba ngaphandle olu lwazi - naphi na. Ukuba bakuva random number generator, akuthandeki ukuba nabuganga ukukhanyela: amanani prime noko zisetyenziswa yaye apho.

Ngoku makhe sithethe malunga nendlela yokufumana ezi manani. Inani ezilula, njengokuba usazi, ukuze angawona ezimbini kuphela, njengokuvuyelela kwabo ekwabeni kwabo ngabanye. Yithi, 11, 7, 5, 3 - inani alula, kodwa 9 - hayi, ukuba sele inani liyohluleka no-9, no-3, no-1.

Ke ukuba - inani obalaseleyo, lo gama - kwiseti {1, 2, ... kwaye - 1}, ngoko eqinisekiswe (a, y) = 1, okanye amanani ngokufanayo yinkulumbuso - a no y.

Ngoko ke, kunoko, nkqu inkcazo kunye phindo okanye ukushwankathela oko utshilo.

Ukufumana etsala mhlawumbi ngentluzo Eratosthenes, kodwa amanani umxhelo (amawaka ezigidi, umzekelo), le ndlela inde kakhulu, kodwa ke, ngokungafaniyo super-ifomula, nto leyo maxa wambi ukwenza iimpazamo, zithembeke ngakumbi.

Uyakwazi ukusebenza ngokukhetha> a. Ukwenza oku, kuye unyule ukwenzela ukuba inani labantu kwaye zahlukene. Ukulungiselela le njongo, kukho inani esiyintloko yande linani yendalo ize idityaniswe (okanye, kungenjalo, sisuswe) Ixabiso (umzekelo, p), nesingaphantsi kakuhle:

y = p + k kunye

Ukuba, umzekelo, kukho = 71, p = 3, q = 10, ngoko, oko, akukho iya kulingana 713. Enye ukhetho kunokwenzeka, kunye izidanga.

amanani ambaxa njengoko kuchasiwe yinkulumbuso kakhulu, kwaye share, no-1, kunye nezinye amanani (kwakhona ngaphandle nentsalela).

Ngamanye amazwi, le amanani zendalo (ngaphandle enye) zahlulwe zibe licandelo ilula.

amanani Prime - inani zendalo, non-ezingenamsebenzi (ahlukeneyo ukusuka amanani kunye neeyunithi) Izahluli. Ingakumbi ebalulekileyo indima yabo mihla, zokufihlakeleyoComment ngokukhawuleza ngokukhawuleza banamhlanje, sibonga ngalo kwithiyori amanani, ngaphambili ekwakucingwa ingqeqesho abstract kakhulu, iye njalo kwemfuneko: algorithms yokhuseleko data isoloko ngcono.

Inani elikhulu kakhulu wafumana ugqirha-wezifo Martin Novak, inxaxheba kwiprojekthi GIMPS (computing nosasazwayo) kunye nabanye abathanda, Abangaba ngu-15 amawaka. Kule izibalo wathabatha iminyaka emithandathu elide. computers ezimbini ezinesiqingatha abalishumi kwiklinikhi iliso Novak inxaxheba. Isiphumo yomsebenzi Titanic nokuzingisa yaba inani 225964951-1, ubhala kwi 7,816,230-in needesimali. Hi ndlela leyi, ingxelo elona nani likhulu wazala iinyanga ezintandathu phambi kokuba kuvulwe. Kwaye kukho imiqondiso apha ezantsi.

Thina genius ofuna ukubiza inani, apho ixesha kwesishumi "jump" uphawu ezilishumi ezizigidi ezingama-, kukho ithuba ukufumana udumo ngamazwe nje kuphela kodwa $ 100 000. Hi ndlela leyi, amanani woyisa imbali ezizigidi uphawula nayan Hayratval wafumana imali ephantsi (50 000 zeerandi).