izinombolo eziphelele

izinombolo eziphelele ezibalweni

Izibalo bezikhona kusukela ekuqaleni. Uma ukutholakala kwethambo le-Ishango (eminyakeni engaphezu kuka-20.000 edlule) kuzokholakala, kungase kube ubufakazi bokuqala bolwazi lwezinombolo eziyinhloko kanye nokuphindaphinda, kodwa isihloko sihlala siphikisana. Nakuba izibalo ziseyimpicabadala kwabaningi bethu, zibonwa ngabanye njengendlela enhle yokuqonda nokuhlaziya umhlaba. Ezibalweni zikhona izinombolo ezipheleleInto abantu abaningi abangayazi.

Kulesi sihloko sizokutshela konke okudingeka ukwazi mayelana nezinombolo eziphelele nezici zazo.

yiziphi izinombolo eziphelele

eziyisithupha inombolo

Izinombolo eziphelele zimayelana nokuthola ama-primes e-Mersenne. Eqinisweni, iSiphakamiso 36 seNcwadi IX ye-Euclid's Elements sithi uma inombolo ye-Mersenne 2n – 1 iyinhloko, kusho ukuthi u-2n-1 (2n – 1) uyinombolo ephelele.

URené Descartes ukuqinisekisile encwadini ayibhalela uMason ukuthi noma iyiphi inombolo kwakungu-Euclid, kodwa akazange afakazele umbono wakhe. Kunalokho, isazi sezibalo saseSwitzerland uLeonhard Euler Ube ngowokuqala ukukhombisa ukubonwa kweCartesian. Inhlanganisela yemiphumela ye-Euclid ne-Euler ivumela ukuthola ukucaciswa okuphelele kwezinombolo eziphelele.

Izinombolo ezine zokuqala eziphelele zaziwa kusukela ezikhathini zasendulo. Bavela emisebenzini kaNico Marcos de Graça kanye noTheon de Smyrna. Inombolo yesihlanu ephelele ishiwo ku-Latin Code of 1456. Izinombolo zesithupha nezesikhombisa eziphelele zatholwa yiCataldi ngekhulu le-XNUMX. futhi eyesishiyagalombili ngu-Euler ngo-1772.

Ngakho-ke ekuqaleni kwawo-1950 sasazi izinombolo eziphelele ezingu-12, kodwa-ke ngenxa ye-GIMPS (Usesho Olukhulu Lwe-Internet Mersenne), ukusesha kwashesha ngobuchwepheshe oba buyinkimbinkimbi kanye nokusetshenziswa kwamakhompyutha ngawo-1990.

Zenzeleni

izinombolo eziphelele

Uma izazi zezibalo eziningi zibheka izinombolo eziyinhloko njengesisekelo se-arithmetic, khona-ke izinombolo eziphelele azisebenzisi okuthile, njengoba zingasetshenziselwa ukuxazulula izibalo, isici noma ukungena endaweni ye-cryptography.

Ezikhathini zasendulo, babebhekwa njengabaphakeme, futhi othile wabona kuyo indima engaqondakali: “Isithupha ngokwaso siyinani eliphelele, hhayi ngoba uNkulunkulu wadala zonke izinto ngezinsuku eziyisithupha, kodwa ngenxa yokuthi uNkulunkulu wadala zonke izinto ngezinsuku eziyisithupha ngoba inani liphelele”— I-Saint Augustine in The City of God (420 AD)

Zingenye yezimfihlakalo zezibalo, futhi ukufuna izinombolo ezintsha eziphelele kuyaqhubeka kuthakazelisa izazi zezibalo eziningi.

Kuningi ukuqagela mayelana nezinombolo eziphelele. Umcabango uwumthetho ongakaze ufakazelwe. Nazi ezintathu:

  • Izinombolo eziphelele zika-Euclid zonke ziyizinombolo ngoba enye yezinto ingamandla ka-2. Kodwa abukho ubufakazi bokufakazela ukuthi azikho izinombolo eziphelele eziyinqaba;
  • Zonke izinombolo ezaziwayo eziphelele zigcina ngo-6 noma 28, kodwa lokhu akunjalo ngaso sonke isikhathi;
  • Futhi akufakazelwanga ukuthi zikhona ngempela izinombolo eziphelele ezingenasiphelo.

yiziphi izinombolo eziphelele

uhlu izinombolo

Izinombolo eziphelele azivamile. Ngenkathi zonke izazi zezibalo zivuma ukuthi kunenombolo engapheli yazo (engakaze ifakazelwe), namuhla sazi kuphela ama-50 futhi asikwazi ngisho nokuqiniseka ukuthi alikho inani eliphelele elingakatholwa kusukela ku-47.

Inombolo yokugcina ephelele yatholwa ngo-January 2018. Ukutholwa kwe-prime entsha enkulu kakhulu kusho ukutholwa kwenombolo entsha ephelele, okuwukutholwa kwenombolo 2⁷⁷²³²⁹¹⁷-1.

Kunezinombolo ezintathu kuphela eziphelele ngaphansi kuka-1000: 6, 28 kanye no-496. Ngokusobala nezinombolo eziphelele zigcina ngo-6 noma 8, nakuba lokhu kungakaze kufakazelwe, akunjalo ngaso sonke isikhathi.

Izinombolo eziphelele eziphelele kufomula ethi 2n-1 (2n – 1) ziyizinombolo ezingunxantathu (noma ngisho nezinezinhlangothi ezine). Ngakolunye uhlangothi, zonke izinombolo ezilinganayo ngaphandle kwenombolo elinganayo yokuqala ziyisamba samakhyubhu angu-2(n-1)/2 wezinombolo ezingavamile. Ngokwesibonelo:

  • = 28 13+ 33,
  • = 496 133 +3 5 +3 + 73,
  • = 8128 133 +3 5 +3 7 +3 9 +3 11 +3 13 +3 15 +3.

Izinombolo zokuqala eziyisishiyagalombili eziphelele yilezi:

  • 6
  • 28
  • 496
  • 8128
  • 336
  • 869.056
  • 691.328
  • 2 305 843 008 139 952 128.

Umlando othile

USanta Augustine, owaziwa nangokuthi u-Augustine waseHippo (354-430), fWayeyisazi sefilosofi, umlobi, isazi sezibalo nompristi ongumRoma. Uma usifundile isihloko sefilosofi, igama uzolazi, ngoba ungomunye wezazi zefilosofi ezivame ukufunda lesi sihloko. Njengabanye ongqondongqondo abaningi besikhathi sakhe, u-Saint Augustine wayengomunye walabo abathuthukisa futhi bajulisa ulwazi emikhakheni esukela kufilosofi kuya kwizibalo, nokuningi esingakubona kunalokho esikucabanga namuhla.

Nokho, u-Augustine waseHippo wathi izinombolo eziphelele zinesizathu sokuba khona. Encwadini yakhe ethi The City of God, wachaza ukuthi u-6 uphelele ngoba uNkulunkulu wadala umhlaba ngezinsuku eziyisithupha. Inombolo elandelayo, 28, ihambisana nenani lezinsuku ezithathayo ukuze iNyanga izungeza Umhlaba kanye. Lesi sitatimende asinakho ingxabano, ukuqondana noma cha?

Ayikho incazelo enikezwa izinombolo ezimbili ezilandelayo. Bangu-496 no-8128. Izinombolo ezine zokuqala zatholwa ekuqaleni kwekhulu lokuqala AD nguNicomachus waseGerasa, isazi sefilosofi nezibalo owayehlala edolobheni lasendulo laseDekapholi, manje iJordani, elalingaphansi koMbuso WaseRoma.

Ukuze sithole inombolo yesihlanu ephelele kwadingeka sithathe igxathu elikhulu emlandweni size sifinyelele ekhulwini leshumi nanhlanu, njengoba inombolo yesihlanu ephelele 33 550 336 yavela emibhalweni yesandla kusukela kuleli khulu leminyaka. Eyesithupha neyesikhombisa, ezingu-8.589.869.056 137.438.691.328 1588 XNUMX nezingu-XNUMX XNUMX XNUMX XNUMX  zatholwa ngemva kwekhulu leminyaka, ngo-XNUMX, isazi sezibalo sase-Italy uPietro Cataldi.

Njengezinombolo eziphelele, inombolo elinganiselwe kuphela yezinombolo ze-Mersenne ezaziwa. Izinombolo ziqanjwe ngoMarin Mason, indoda eyadalula uchungechunge lwemibono mayelana nabo. UMason wayeyisazi sefilosofi saseFrance, isazi sezibalo, nompristi (1588-1648).

Kwakungu-Euler owathola lezi zinombolo ezikhethekile, ngenxa yesisekelo esabekwa uMason. ULeonhard Paul Euler (1707-1783) wayenguchwepheshe wezibalo waseSwitzerland kanye nesazi sefiziksi. Yiqiniso, igama lakhe lizobe selijwayele wena, ngoba ukuthola inombolo yesishiyagalombili ephelele kwakungeyona impumelelo yakhe kuphela. Iphinde yathola igama layo enombolweni ka-Euler (e), esetshenziswa kumafomula amaningi angokwenyama kanye nezibalo.

Ngithemba ukuthi ngalolu lwazi ungafunda kabanzi mayelana nalezi zinombolo nezici zazo.


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  1. Ubhekele imininingwane: Miguel Ángel Gatón
  2. Inhloso yedatha: Lawula Ugaxekile, ukuphathwa kwamazwana.
  3. Ukusemthethweni: Imvume yakho
  4. Ukuxhumana kwemininingwane: Imininingwane ngeke idluliselwe kubantu besithathu ngaphandle kwesibopho esisemthethweni.
  5. Isitoreji sedatha: Idatabase ebanjwe yi-Occentus Networks (EU)
  6. Amalungelo: Nganoma yisiphi isikhathi ungakhawulela, uthole futhi ususe imininingwane yakho.