Dzidziso yePrime Number
Nhamba dzePrime ndeimwe yezvinhu zviri nyore asi zvisinganzwisisike mumasvomhu. Zviri nyore nekuti tsananguro yadzo yakatwasuka: nhamba yePrime inhamba yakakura kupfuura 1 ine zvikamu zviviri zvakanaka: 1 uye pachayo. Zvinoshamisa nekuti, kunyangwe yakadzidzwa kwezviuru zvemakore, mibvunzo yakawanda inokosha nezve nhamba dzePrime haisati yapindurwa nanhasi. Bazi remasvomhu rinoongorora hunhu, mapatani, uye kugoverwa kwenhamba dzePrime rinowanzo kurukurwa mudzidziso yenhamba, uye nyaya iyi inozivikanwa zvakanyanya sedzidziso yePrime Number.
Tsanangudzo uye Mienzaniso yeNhamba dzeNhamba
Manhamba ePrime anotanga na2, 3, 5, 7, 11, 13, 17, 19, zvichingodaro. Kubva pane runyorwa urwu, tinogona kuona kuti 2 ndiyo yega nhamba yePrime yakafanana. Mamwe manhamba ese eV even anogona kupatsanurwa ne2, saka ane madivisor anopfuura maviri uye haagone kunzi maPrime.
Zvinopesana nenhamba huru inhamba yakasanganiswa, inova nhamba yakakura kupfuura 1 ine zvikamu zvinopfuura zviviri. Semuenzaniso, 4 ine zvikamu 1, 2, uye 4; 12 ine zvikamu 1, 2, 3, 4, 6, uye 12. Nhamba 1 haisi yekutanga kana kuti yakasanganiswa, nekuti ine chikamu chimwe chete, 1.
Kunzwisisa nhamba dzekutanga kwakakosha nekuti dzinowanzonzi "zvivharo zvekuvaka" nhamba dzese. Nhamba dzese huru kupfuura imwe dzinogona kupatsanurwa kuita chibereko chenhamba dzekutanga.
Dzidziso huru dzeArithmetic
Imwe yemhedzisiro yakakosha mudzidziso yenhamba yepamusoro ndiyo Fundamental Theorem yeArithmetic. Iyi dzidziso inotaura kuti nhamba imwe neimwe yakakura kupfuura 1 inogona kunyorwa sechigadzirwa chakasiyana chenhamba dzepamusoro, zvichienderana nekurongeka kwezvinhu zvayo.
Muenzaniso:
– 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
– 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Kusiyanisa uku kweprime factorization ndiko hwaro hwepfungwa dzakawanda dzemasvomhu, kubva pakupatsanura, least common multiple (LCM), greatest common factor (GCF), kusvika kumaalgorithms akasiyana-siyana musainzi yemakombiyuta.
Nzira Yokuziva Nhamba Dzakakosha
Kune nzira dzakasiyana siyana dzekuona kana nhamba iri prime. Nzira iri nyore ndeyekutarisa kana nhamba yacho ichikamurwa neimwe nhamba isiri 1 uye pachayo. Zvisinei, nzira iyi haishande zvakanaka panhamba huru.
Nzira inoshanda zvikuru ndeyekutarisa madivisor kusvika pa square root yenhamba. Kana nhamba n iine zvimwe zvinhu zvisiri 1 na n, saka chimwe chezvinhu zvacho hachipfuure √n. Semuenzaniso, kuti utarise kana 97 iri prime, ingoiedza kuti ionekwe kuti inogovaniswa here ne prime numbers ≤ √97 (inenge 9,8), kureva 2, 3, 5, na 7. Sezvo 97 isingagovaniswe nechero ipi yeaya mana, i prime.
Pamusoro pezvo, kune nzira dzekare dzakadai seSieve of Eratosthenes, dzinoshanda pakutsvaga nhamba dzese dze prime kusvika pamuganho wakati. Nzira iyi inosanganisira kunyora nhamba dzese kubva pa2 kusvika kuN, wobva wamaka nhamba dze multiples dze 2, multiples dze 3, multiples dze 5, zvichingodaro. Nhamba dzisina chiratidzo ndidzo dze prime.
Maitiro uye Kugoverwa kwePrime Numbers
Chimwe chezvinhu zvinoita kuti nhamba dzema prime dzive dzinonakidza ndiko kugoverwa kwadzo kunoratidzika kunge kwakarongeka. Hapana patani iri nyore inoita kuti ma prime ese aite pakarepo. Dzimwe nguva ma prime anoonekwa ari pedyo, senge 11 na13, kana 17 na19, asi ipapo daro riri pakati pawo rinogona kukura.
Mubvunzo unokosha mudzidziso yenhamba yepamusoro ndewekuti: "Manhamba epamusoro anowanikwa kangani?" Kuti vapindure izvi, nyanzvi dzemasvomhu dzakagadzira dzidziso yePrime Number. Iyi dzidziso inotaura kuti huwandu hwemaprimi ari pasi kana akaenzana na n, akanyorwa se π(n), anenge akaenzana na n / ln(n). Izvi zvinoreva kuti sezvo n ichiwedzera, maprimi anova mashoma, asi anoramba achiitika nekusingaperi.
Semuenzaniso, kune n yakakura kwazvo, mukana wekuti nhamba isina kurongeka yakatenderedza n ive prime ingangoita 1/ln(n). Izvi zvinopa tsananguro yehuwandu hwenhamba dzeprime.
Manhamba Matatu Makuru uye Mafungiro Akakurumbira
Mapatya mapini mapini enhamba dzepamusoro ane musiyano uri 2, zvakaita se (3, 5), (11, 13), (17, 19), zvichingodaro. Mubvunzo mukuru uchiripo nhasi ndewekuti Twin Prime Conjecture: “Kune mapatya akawanda kwazvo emapatya mapini here?” Pasinei neuchapupu hwakawanda hunotsigira uye kufambira mberi kwakakura mumakumi emakore achangopfuura, fungidziro iyi haisati yanyatsoratidzwa.
Pamusoro pezvo, kune Goldbach Conjecture, iyo inoti nhamba imwe neimwe yakakura kupfuura 2 inogona kunyorwa sehuwandu hwenhamba mbiri dzeprime. Semuenzaniso:
– 10 = 3 + 7
– 28 = 11 + 17
– 100 = 47 + 53
Fungidziro iyi yakaedzwa kuti ionekwe nevanhu vakawanda uye inogara iri yechokwadi pasi pemiedzo iyi, asi hapasati pave nehumbowo hwakazara.
Basa rePrime Numbers muCryptography yemazuva ano
Kupfuura masvomhu chaiwo, ma prime numbers ane basa guru muhupenyu hwemazuva ano, kunyanya mukuchengetedzwa kwemashoko. RSA cryptosystem, imwe yenzira dzinozivikanwa dze encryption, inoenderana nekuoma kwekubatanidza ma prime factors makuru. MuRSA, kiyi yeruzhinji inogona kugadzirwa kubva mukugadzirwa kwe ma prime numbers maviri makuru. Kuderedza chigadzirwa ichi kuita ma prime maviri ekutanga idambudziko rakaoma zvikuru kana ma prime acho akakura zvakakwana, nokudaro zvichipa hwaro hwekuchengetedzwa.
Nemamwe mashoko, runako rwenhamba dzepamusoro harungori rwedzidziso chete asiwo runoshanda, sezvo ruchibatsira kuchengetedza kuchengetedzeka kwekutengeserana kwedhijitari, kutaurirana kwakavharidzirwa, uye kuchinjana ruzivo rwakavanzika paindaneti.
Penutup
Dzidziso yePrime number ndeimwe yenzvimbo dzakapfuma mu masvomhu. Kubva patsanangudzo iri nyore yeprime number, tinosvika papfungwa dzakadzama dzakadai se unique factorization, prime distribution theorem, uye kunyange fungidziro dzisina kugadziriswa. Prime numbers dzinoramba dzichitishamisa nekuti dzinopinda mumuganhu uri pakati pekurongeka nekusarongeka: dzinoita sedzisina mapatani, asi dzichiteerera mitemo yemasvomhu yakadzama.
Kudzidza nhamba dzeprime hakusi kungoziva kuti ndedzipi nhamba dziri prime nedzisiri, asiwo kunzwisisa kuti "dzinogoverwa" sei pakati penhamba dzese, kuti nei dzichiita basa guru kudaro, uye kuti dzinopesvedzera sei tekinoroji yemazuva ano. Nekuda kweizvi, dzidziso yeprime nhamba ichiri imwe yenyaya dzakatsvakurudzwa zvakanyanya uye dzinonakidza kuvadzidzi vemasvomhu, vadzidzisi, nevaongorori kusvika nhasi.
