Masvomhu aripo kubva pakutanga. Kana kuwanikwa kwepfupa reIshango (makore anopfuura 20.000 XNUMX apfuura) kuchidavirwa, inogona kunge yakave chiratidzo chekutanga cheruzivo rwenhamba dzekutanga uye kuwanda, asi nyaya yacho inoramba iine nharo. Nepo masvomhu achiramba ari chakavanzika kune vazhinji vedu, anoonekwa nevamwe senzira huru yekunzwisisa nekuongorora nyika. Mumasvomhu variko nhamba dzakakwanaChinhu chisingazivikanwi nevanhu vakawanda.
Muchikamu chino tichakuudza zvese zvaunoda kuziva nezve nhamba dzakakwana uye maitiro avo.
ndedzipi nhamba dzakakwana
Nhamba dzakakwana ndezvekutsvaga Mersenne primes. Zvakadaro, Proposition 36 yeBhuku IX reEuclid's Elements inoti kana Mersenne nhamba 2n – 1 iri huru, zvino 2n-1 (2n – 1) inhamba yakakwana.
René Descartes akasimbisa mutsamba kuna Mason kuti chero nhamba yaive Euclid, asi haana kuratidza dzidziso yake. Pane kudaro, nyanzvi yemasvomhu yekuSwitzerland Leonhard Euler Akanga ari wekutanga kuratidza kucherechedzwa kweCartesian. Iko kusanganiswa kwemhedzisiro yeEuclid naEuler inobvumira kuwana hunhu hwakakwana hwehuwandu hwakakwana.
Nhamba ina dzekutanga dzakakwana dzave dzichizivikanwa kubva kare. Ivo vanoonekwa mumabasa aNico Marcos de Graça naTheon de Smyrna. Nhamba yechishanu yakakwana inotaurwa muLatin Code ye1456. Nhamba yechitanhatu neyechinomwe yakakwana yakawanikwa neCataldi muzana remakore rechiXNUMX. uye wechisere naEuler muna 1772.
Saka mukutanga kwema1950 takaziva nhamba gumi nembiri dzakakwana, asi zvino nekuda kweGIMPS (Great Internet Mersenne Prime Search), kutsvaga kwakakurumidza nekuwedzera kwehunyanzvi hwekuita uye kushandiswa kwemakombuta muma12.
Ndezvipi izvi
Kana nyanzvi zhinji dzemasvomhu dzichiona nhamba dzekutanga sehwaro hwemasvomhu, saka nhamba dzakakwana hadzina chadzinoshandisa, sezvo ivo vasina kushandiswa kugadzirisa equations, chinhu kana kupinda munzvimbo yecryptography.
Munguva dzekare, vainzi vakakwirira, uye mumwe munhu akaona mariri basa risinganzwisisike: "Nhamba yetanhatu pachayo inhamba yakakwana, kwete nokuti Mwari akasika zvinhu zvose mumazuva matanhatu, asi nokuti Mwari akasika zvinhu zvose mumazuva matanhatu nokuti nhamba yakakwana" - Mutsvene Augustine muGuta raMwari (420 AD)
Ndiyo imwe yezvakavanzika zvemasvomhu, uye kutsvaga kwenhamba itsva dzakakwana kunoramba kuchifadza nyanzvi dzemasvomhu dzakawanda.
Pane zvakawanda zvekufungidzira nezve nhamba dzakakwana. Kufungidzira mutemo usina kumbobvira waonekwa. Hezvino zvitatu:
- Nhamba dzakakwana dzaEuclid ese ari manhamba nekuti chimwe chezvikonzero isimba re2. Asi hapana humbowo hunoratidza kuti hakuna zvisinganzwisisiki nhamba dzakakwana;
- Nhamba dzese dzinozivikanwa dzakakwana dzinopera muna 6 kana 28, asi izvi hazvisi nguva dzose;
- Uyewo hazvina kuratidzwa kuti zvechokwadi kune nhamba dzisingaperi dzakawanda dzakakwana.
ndedzipi nhamba dzakakwana
Nhamba dzakakwana hadzisi nyore. Nepo vese masvomhu vachibvumirana kuti kune nhamba isingaperi yavo (haina kumboratidzwa), nhasi tinongoziva makumi mashanu uye hatitombove nechokwadi chekuti hapana nhamba yakakwana isina kuwanikwa kubva makumi mana nemanomwe.
Nhamba yekupedzisira yakakwana yakawanikwa muna Ndira 2018. Kuwanikwa kwekutanga kukuru kunoreva kuwanikwa kwenhamba nyowani, inova kuwanikwa kwenhamba 2⁷⁷²³²⁹¹⁷-1.
Kune nhamba nhatu chete dzakakwana dzisingasviki 1000: 6, 28 uye 496. Sezviri pachena kunyange nhamba dzakakwana dzinopera mu 6 kana 8, kunyange izvi zvisati zvamboratidzwa, hazvisi nguva dzose.
Idzo nhamba dzakakwana mufomula 2n-1 (2n - 1) inhamba dzine mativi matatu (kana nyangwe ane hexagonal). Nekune rimwe divi, nhamba dzese dzakatowanda kunze kweyekutanga dzakakwana nyangwe nhamba ihomwe ye2(n-1)/2 cubes yenhamba dzekutanga dzisingaite. Semuyenzaniso:
- 28 = 13+ 33,
- 496 = 13+ 33 + 53 + 73,
- 8128 = 13+ 33 + 53 + 73 + 93 + 113 + 133 + 153.
Nhamba sere dzekutanga dzakakwana ndidzo:
- 6
- 28
- 496
- 8128
- 336
- 869.056
- 691.328
- 2 305 843 008 139 952 128.
Dzimwe nhoroondo
Mutsvene Augustine, anozivikanwawo saAugustine weHippo (354-430), fAiva muzivi weRoma, munyori, nyanzvi yemasvomhu, uye mupristi. Kana iwe wakadzidza nyaya yehuzivi, zita rinozoriziva kwauri, sezvo ari mumwe wevazivi anowanzo dzidza nyaya yacho. Sevamwe vachenjeri vazhinji venguva yake, Musande Augustine aive mumwe weavo vakakudziridza nekudzamisa ruzivo mundima kubva kuhuzivi kusvika kusvomhu, nezvakawanda zvekuona kupfuura zvatingafungidzira nhasi.
Eya, Augustine weHippo akataura kuti nhamba dzakakwana dzine chikonzero chokuvapo. Mubhuku rake rinonzi Guta raMwari, akatsanangura kuti 6 yakakwana nokuti Mwari akasika nyika mumazuva matanhatu. Nhamba inotevera, 28, inoenderana nehuwandu hwemazuva anotora Mwedzi kuti utenderere Nyika kamwe chete. Chirevo ichi hachisi pasina kukakavara, kusangana kana kwete?
Hapana tsananguro inopiwa yenhamba mbiri dzinotevera. Ivo 496 uye 8128. Nhamba ina dzekutanga dzakawanikwa kare muzana ramakore rekutanga AD naNicomachus wekuGerasa, muzivi uye nyanzvi yemasvomhu aigara muguta rekare reDhekaporisi, zvino Jorodhani, iro raive rehushe hweRoma.
Kuti tiwane nhamba yechishanu yakakwana taifanira kusvetuka zvikuru munhoroondo kusvikira tasvika muzana remakore rechigumi neshanu, sezvo nhamba yechishanu yakakwana 33 550 336 yakabuda muzvinyorwa zvezana rino remakore. Yechitanhatu neyechinomwe, 8.589.869.056 uye 137.438.691.328, yakawanikwa zana remakore gare gare, muna 1588, nenyanzvi yemasvomhu yokuItaly Pietro Cataldi.
Kufanana nenhamba dzakakwana, nhamba inogumira chete yenhamba dzeMersenne dzinozivikanwa. Nhamba idzi dzakatumidzwa zita raMarin Mason, murume akafumura nhevedzano yefungidziro pamusoro pavo. Mason aive muzivi wechiFrench, nyanzvi yemasvomhu, uye mupristi (1588-1648).
Aive Euler akawana idzi nhamba dzakakosha, nekuda kwenheyo yakaiswa naMason. Leonhard Paul Euler (1707-1783) aiva nyanzvi yemasvomhu uye fizikisi yekuSwitzerland. Hongu, zita rake rinenge rave kutoriziva kwauri, nekuti kuwana nhamba yechisere yakakwana kwaisava budiriro yake chete. Yakawanawo zita rayo kubva kunhamba yaEuler (e), iyo inoshandiswa mune zvakawanda zvemuviri uye computational formula.
Ndinovimba kuti neruzivo urwu unogona kudzidza zvakawanda nezve nhamba idzi uye maitiro avo.