Farawa lambobi. Tushen

Litattafai na ilimin lissafi suna da wuya a fahimta wasu lokuta. Harshen bushe da bayyane na marubuta ba koyaushe ne don ganewa ba. Kuma batutuwa da ke tattare da juna a kowane lokaci suna gudana. Don samun jagora daya kalma, wajibi ne mutum ya ɗaga da dama daga baya, sa'annan wani lokaci har ya rubuta ta cikin littafi. Yana da wuya? Ee. Kuma bari mu yi ƙoƙari mu kewaye waɗannan matsalolin kuma muyi kokarin gano wannan batu ba daidai ba ce. Bari mu sanya digression zuwa cikin ƙasa lambobi. Ma'anar, duk da haka, har yanzu muna barin wannan, domin ba a iya soke dokoki na lissafi ba. Saboda haka, lambobin mahimmanci suna lambobi ne na halitta, tare da rabaccen raba daidai da ɗaya. Shin wannan ya bayyana? Gaba ɗaya.

Don ƙarin misali, bari mu ɗauki lambobin 6 da 13. Dukansu suna rarraba daya (mai sauki). Amma lambobi 12 da 14 - ba za su iya kasancewa ba, domin suna rabuwa ba kawai a cikin 1 ba, amma har zuwa 2. Lambobin da suka biyo baya - 21 da 47 kuma basu shiga cikin jinsin "lambobin jinsi": zasu iya rarraba ba kawai ta 1 ba, amma Har ila yau a ranar 7.

Nuna a fakaice gwada da Firayim lambobi kamar (a, y) = 1.

Za a iya cewa a sauƙaƙe: mai rarraba na kowa (mafi girma) a nan yana daidai da ɗaya.
Me yasa muke bukatan irin wannan ilimin? Akwai dalilai masu yawa.

Yardatayya da Firayim lambobin kunshe a wasu boye-boye tsarin. Wadanda suke yin aiki tare da magoya bayan Hill ko tare da tsarin tsarin Kaisar, sun fahimci: ba tare da wannan ilimin ba - ko'ina. Idan kun ji game da masu samar da na'ura na lambobi marasa amfani, ba za ku iya yin ƙaryatãwa ba game da cewa ana amfani da lambobin da suka fi dacewa a can.

Yanzu bari mu magana game da yadda za a sami wadannan lambobin. Yawan sauki, kamar yadda ka sani, na iya samun kawai biyu divisors: suka raba da kansu da kuma ta daya. Ka ce 11, 7, 5, 3 lambobi ne masu sauƙi, amma 9 ba, saboda wannan lambar an riga an rarraba ta 9, da 3, da kuma 1.

Kuma idan wata - Firayim lambar, yayin da - a cikin sa {1, 2, ... kuma - 1}, sa'an nan tabbace (a, y) = 1, ko da jũna Firayim lambobin - a kuma y.

Wannan shine, maimakon haka, ba ma bayani ba, amma maimaitawa ko taƙaita abubuwan da aka fada kawai.

Samun primes yiwu sieve na Eratosthenes, amma ga m lambobin (biliyoyin, misali), wannan hanya ne tsayi da yawa, amma, sabanin da super-dabara, wanda wani lokacin yin kuskure, mafi m.

Za ka iya aiki da zabi daga> wata. Don yin wannan, shi ne zaba don haka da cewa yawan on da kuma kada ku rarraba. A saboda wannan dalili, wani Firayim lambar da aka yawaita da wata halitta da lambar kuma aka kara (ko, a madadin, mu cire) darajar (misali, p), wanda shi ne kasa da:

y = p + k da

Idan, misali, wata = 71, p = 3, q = 10, sa'an nan, daidai da, za a daidaita 713. Wani yiwu selection, tare da digiri.

Lambobin lambobi, ba kamar waɗanda suke da sauki ba, suna rarraba a kansu, da kuma 1, da zuwa wasu lambobi (har ma ba tare da saura) ba.

A wasu kalmomin, da na halitta lambobi (sai dai daya) ya kasu kashi bangaren kuma sauki.

Firayim mintun lambobi ne waɗanda ba su da rabawa masu rarrabe (bambanta daga lambar da ɗaya). Musamman muhimmanci shi ne rawar da suka taka a yau zamani, dafa-paced cryptography, godiya ga wanda ka'idar lambobi, baya tunani sosai m horo, ya zama haka a bukatar: data kariya Algorithms aka kullum ana inganta.

Mafi mahimmanci lambar da aka samu daga masanin ilimin lissafi Dokta Martin Novak, wanda ya halarci aikin GIMPS (ƙayyadaddun lissafin), tare da sauran masu goyon baya, wanda ya ƙidaya kusan 15,000. Lissafin ya ɗauki shekaru shida. Ya ƙunshi kwakwalwa biyu da rabi na kwakwalwa a cikin asibiti na Nowak. Sakamakon aikin titaniki da juriya shine lamba 225964951-1, tare da rubutun a cikin 7816230-wurare maras kyau. A hanyar, an saka rikodin yawan mafi yawan adadin rabin shekara kafin wannan budewa. Kuma alamu akwai rabin miliyan m.

Wani mashahurin wanda yake so ya yi suna a cikin adadin yawan adadin ladabi na "tsalle" alamar lambar yabo ta 10 shi ne damar samun karfin duniya ba kawai, amma har da dala 100,000. A hanyar, Nyan Hiratwal ya karbi adadin kuɗi ($ 50,000) don lambar da ta ci nasara da layin miliyon daya.