Ingabe kuqhathaniswa eyinhloko. isisekelo

Mathematics izincwadi ngezinye izikhathi okunzima ukuyiqonda. ulimi esomile ecacile ababhali akuzona njalo kulula ukuyiqonda. Futhi kukhona njalo ezihlobene izihloko, vzaimovytekayuschie. Ngokuba ukuthuthukiswa ingqikithi kubalulekile ukukhulisa eziningi odlule futhi ngezinye izikhathi flip lonke ebhukwinitifundvo. Iyinkimbinkimbi? Yebo. Ake alinge aphazamisa lezi ubunzima futhi bazame ukuthola isihloko akayena ngempela indlela ejwayelekile. Senza uhlobo uhambo ku izinombolo ezweni. Incazelo Nokho, thina namanje akukashintshi, ngoba imithetho wezibalo asikwazi ukuhlehliswa. izinombolo Ngakho, uma kuqhathaniswa prime - isibalo zemvelo, nge isihlukanisi ezivamile lingana kuze fike. Ingabe ukuthi waqonda? Kuyinto.

Ukuze uthole isibonelo ingcaca ngaphezulu, ake uthathe inani 6 futhi 13. Futhi-ke, nokuningi - kukhona sihlukaniswe ngu eyodwa (kuqhathaniswa prime). Kodwa izinombolo 12 no-14 - njengoba enjalo ngeke, ngoba ukuwa akuyona 1 kuphela, kodwa futhi kwi 2 izinombolo ezilandelayo - 21 47 futhi zehlukile isigaba "kuqhathaniswa eyinhloko": bona ingahlukaniswa hhayi 1 kuphela, kodwa futhi 7.

Lumelela izinombolo kuqhathaniswa prime njengoba (a, y) = 1.

Singasho nakakhulu nje: isihlukanisi ezivamile (eliphakeme) ilingana komunye.
Kungani senza ingaba nalo ulwazi olunjalo? Izizathu ngokwanele.

Okusizayo izinombolo eziyinhloko kufakwe abanye uhlelo ukubethela. Labo asebenza ne-Hill cipher noma zikaKhesari izinhlelo ubhalwe kabusha, uqonde ukuthi ngaphandle lolu lwazi - kuphi. Uma uke wezwa okungahleliwe inombolo generator, akunakwenzeka ukuba alinge ukuphika: izinombolo kuqhathaniswa prime asetshenziswa futhi kukhona.

Manje ake sixoxe ngendlela ukuthola lezi izinombolo. Inombolo elula, njengoba wazi, kungase kudingeke divisors ezimbili kuphela: behlukanisa bebodwa ngomunye. Ithi, 11, 7, 5, 3 - isibalo esilula, kodwa 9 - akukho, kungcono kakade inombolo uyahlukaniswa futhi 9, no-3, futhi 1.

Futhi uma - a inombolo esiyinhloko, kuyilapho - isethi {1, 2, ... futhi - 1} ke okuqinisekisiwe (a, y) = 1, noma izinombolo Okusizayo prime - a kanye y.

Kuyinto, kunalokho, ngisho incazelo nemphindza noma kufinyeta obekushiwo.

Ukuthola primes mhlawumbe ngesihlungo Eratosthenes, kodwa izinombolo umxhwele (izigidigidi, isibonelo), le ndlela lide kakhulu, kodwa, ngokungafani super-ifomula, ngezinye izikhathi benza amaphutha, ithembeke.

Ungasebenza ngokukhetha> a. Ukuze wenze lokhu, it is ekhethiwe ukuze isibalo ku hhayi ihlukaniswe. Ngenxa yale njongo, inombolo prime iyanda yi inombolo yemvelo futhi wanezela (noma, kungenjalo, sisuswe) Inani (isibonelo, p), okuyinto kancane kahle:

y = p + k futhi

Uma, ukwenza isibonelo, i = 71, p = 3, q = 10 Khona-ke, ngokufanelekile, kuyoba ulingana 713. Omunye Ukukhetha kungenzeka, ne degree.

izinombolo Compound njengoba kuqhathaniswa kuqhathaniswa prime, kanye yabelana, futhi 1, nezinye izinombolo (futhi ngaphandle umsalela).

Ngamanye amazwi, lo izinombolo yemvelo (ngaphandle koyedwa) zihlukaniswe ingxenye futhi elula.

izinombolo Prime - isibalo zemvelo, non-eziwubala (sihluke izinombolo namayunithi) abahlukanisi. kubalulekile ikakhulukazi indima yabo yesimanje, indlela yokubhala efihla incazelo lanamuhla omatasatasa, sibonga ngalo imfundiso yokuziphendukela izinombolo, kwakucatshangwa isiyalo abstract kakhulu, isibe ngakho ziphoqa: yokuvikela idatha algorithm ethu njalo ngcono.

Inani elikhulu prime wathola udokotela-ophthalmologist Martin Novak, owaba nengxenye iphrojekthi GIMPS (Computing wokusakaza) kanye nezinye abathanda Abangaba ngu ayizinkulungwane 15. Ngo izibalo wathatha iminyaka eyisithupha eside. ama-computers amabili kanye nedlanzana isigamu emtholampilo iso Novak ababehilelekile. Waba yini umphumela wesibindi titanic umsebenzi nokubekezela kwaba nenani 225964951-1, ubhala kwi aya 7,816,230-e. By the way, umlando inani elikhulu wakhululwa izinyanga eziyisithupha ngaphambi wokuvula. Kwakukhona nezibonakaliso Ingxenye engezansi.

Thina ubuhlakani ofuna Ukushayela inombolo, lapho isikhathi se-idesimali "gxuma" uphawu eziyishumi-sesigidi, kukhona ithuba uthole hhayi kuphela udumo emhlabeni wonke kuphela kodwa $ 100 000. By the way, izinombolo wakunqoba milestone sesigidi kumaka Nayan Hayratval litholé inani aphansi (50 000 dollars).