
fermat sankhya

ganita saastramlo, vaatini modata adhyayanam chesina pierry dii fermat paeru meeda pettabadina fermat sankhya, eee roopam yokka saanukuula puurnaamkam.
ikkada "n" anedi pratikuulam kaani puurnaamkam. modati konni fermat sankhyalu
2 "k" + 1 prime ayithe, appudu "k" anedi 2 yokka power ayi undaali, alaage fermat sankhya; atuvanti praimlanu fermat primes antaaru. telisina ekaika fermat praimlu,,,,, mariyu; huristics ekkuva levani suuchistunnaayi.
praathamika lakshanaalu.
fermat sankhyalu eee krindi punaraavruta sambandhaalanu santrupti parustaih
n" ≤1 kosam,
kosam. eee sambandhaalalo prati okkati ganita prerana dwara niroopinchabadavacchu. rendava sameekaranam nundi, manam goldbatch siddhaantaanni (christian goldbatch paeru pettabadindi) oohinchavachhuh yea rendu fermat sankhyalu 1 kante ekkuva saadhaarana puurnaanka karakanni panchukovu. dheenini chuudataaniki, "f" i "mariyu" f "j" laku oka saadhaarana karakanni kaligi unnayani anukundam. appudu "a" rendintinee vibhajistundi
mariyu "f" "j"; anduvalla "a" vaati vyatyaasaanni vibhajistundi, 2. endukante, eee saktulu. idhi oka vairudhyam, endukante prati fermat sankhya spashtamgaa besigaa untundi. paryavasanamga, manam pradhana sankhyala anantaniki maroka rujuvunu pondutamu prati "f" n "kii, oka pradhana karakam" p "n" nuu enchukondi; appudu kramam anedi vibhina pradhana sankhyala yokka anantamaina kramam.
praadhamikata.
fermat sankhyalu mariyu fermat praimlanu modata pierry dii fermat adhyayanam chesaaru, vaaru anni fermat sankhyalu prime anie oohinchaaru. nijaaniki, modati aidu fermat sankhyalu "f" 0,..., f" 4 sulabhamgaa prime gaa chuupabadataayi. 1732loe leonhard euler fermat yokka oohanu khandinchaadu, athanu daanini choopinchaadu
f" "n" yokka prati karakam tappanisarigaa roopaanni kaligi undaalani (taruvaata lucas dwara meruguparachabadindi) euler niroopinchaadu ".
641 anedi "f" 5 yokka karakam anie 641 = 27 × 5 + 1 mariyu 641 = 24 + 54 samaanatvaala nundi oohinchavachhu. idhi modati samaanatvam nundi 27 × 5 shna − 1 (mode 641) mariyu anduvalla (nalgava saktiki penchadam) 228 × 54 shna 1 (mode 641) anie anusaristundi. marovaipu, rendava samaanatvam 54 shna − 24 (mode 641) anie suuchistumdi. eee sammelanaalu 232 shna −1 (mode 641) anie suuchistaayi.
taruvaata euler niroopinchina kaarakaala roopam gurinchi fermatku bahusha telusu, kabatti karakanni kanugonadaaniki suutigaa lekkinchadamlo athanu viphalamayyaadani aasaktikaramgaa anipistundi. oka saadhaarana vivarana emitante fermat ganana porapaatu chesindi.
f" "n" thoo telisina itara fermat praimlu laevu, conny pedda "" n "kosam fermat sankhyala gurinchi chaalaa takkuva telusu". nijaaniki, eee krindi vaatilo prati okkati bahiranga samasyah
veetilo, "f" n "yokka puurti karakalu matrame telisinappatikii," f "n" anedi mishramamgaa undani telisinappatikii, mariyu dheeniki telisina pradhana karakalu laevu. mishramamgaa telisina atipedda fermat sankhya "f" 182333954, mariyu daani pradhana karakam october 2020loe kanugonabadindi.
huristic vaadanalu.
huristics prakaram "f" 4 anedi chivari fermat prime.
pradhana sankhya siddhaantam "n" chuttoo tagina viramamlo yaadruchchika puurnaamkam sambhaavyata 1/ln "n" thoo pradhanamani suuchistumdi. oka fermat sankhya daani parimaanam yokka yaadruchchika puurnaamkam vale adhe sambhaavyatatoo prime anie huristicnu upayogiste, mariyu aaa "f" 5,..., f" 32 mishramamgaa untaayi, appudu "f" 4 (ledhaa samanamga, "f" 32 daati) daati fermat praimla sankhyanu anchanaa veyali 
f" 4 daati oka fermat prime unde sambhaavyataku eee sankhyanu eguva sarihaddugaa ardham chesukovacchu.
eee vaadana khachitamaina rujuvu kaadu. oka vishayam emitante, fermat sankhyalu yaadrucchikamgaa pravartistaayani idhi bhaavistundi, conny fermat sankhyala karakalu pratyeka lakshanaalanu kaligi untaayi. boklan mariyu conway marinta khachitamaina vislaeshanhanu prachurinchaaru, maroka fermat prime undataaniki sambhaavyata oka biliyanlo okati kante takkuvagaa undani suuchistumdi.
samaanamaina paristhitulu.
suutram _ 9 anedi "n" va fermat sankhyagaa undanivvandi. pepin pareeksha ilaa perkondi,
vyakteekarana suutram _ 12 nuu maadyulo suutram _ 10 nuu punaraavruta chaturasram dwara anchanaa veyavachu. idhi pareekshanu vegavantamaina bahupadi-samaya algorithamgaa chestundi. conny fermat sankhyalu entha vaegamgaa perugutunnaayi antey vaatilo konni matrame sahetukamaina samayam mariyu sthalamlo pareekshinchabadataayi.
praadhamikata kosam fermat sankhyala karakalu vanti roopam yokka sankhyalaku konni pareekshalu unnaayi.
okavela, appudu paina perkonna jacobi chihnam ellappuduu −1 kuu samanamga untundi, mariyu proth siddhaantam yokka eee pratyeka kesunu peppins test antaaru. konni fermat sankhyala samarasyanni niroopinchadaaniki pepin pareeksha mariyu proth siddhaantam computerlalo amalu cheyabadinappatiki, yea pareeksha kooda nirdishtamaina chinna karakam ivvadu. vaastavaaniki, nirdishta pradhana karakalu mariyu 24 gurinchi teliyadu.
kaarakatvam.
fermat sankhyala parimaanam kaaranamgaa, karakanni nirnayinchadam ledhaa praadhamikatanu tanikhi cheyadam kooda kashtam. pepin pareeksha fermat sankhyala praadhamikataku avasaramaina mariyu taginanta sharatu istundi mariyu aadhunika computerla dwara amalu cheyavachu. deerghavruttaakaara vakrata paddhati anedi sankhyala yokka chinna pradhana bhaajakaalanu kanugonadaaniki vegavantamaina paddhati. distributed computing project "fermatserch" fermat sankhyala yokka konni kaarakaalanu kanugondi. vives gallot yokka proth.pedda fermat sankhyala kaarakaalanu kanugonadaaniki exe upayoginchabadindi. paina perkonna phalitaanni merugupariche edward lucas, 1878loe fermat sankhya suutram _ 10looni prati karakam, kaneesam "n" thoo, suutram _ 19 roopamlo undani niroopinchaadu (modati sankhyanu chudandi), ikkada "k" anedi saanukuula puurnaamkam. swayamgaa, idhi telisina fermat praimla yokka praadhamikatanu niroopinchadaanni sulabhataram chestundi.
modati pannendu fermat sankhyala karakalu
, kevalam "f" 0 nundi "f" 11 varaku matrame puurtigaa karakamga unnaayi. distributed computing project fermat serch anedi fermat sankhyala yokka kotta kaarakaala kosam vetukutondi. anni fermat kaarakaala samiti OEIS loe (ledhaa, kramabaddheekarinchabadindi) untundi.
fermat sankhyala yokka eee krindi karakalu 1950 kii mundu telisinavi (appati nundi, digital computerlu marinni kaarakaalanu kanugonadamlo sahayapaddayi):
fermat sankhyala yokka 362 pradhana karakalu telisinavi, mariyu 318 fermat sankhyalu mishramamgaa telisinavi. prati samvatsaram aneka kotta fermat karakalu kanugonabaddayi.
suudoe praimlu mariyu fermat sankhyalu.
2 "p"-1 roopam yokka mishrama sankhyala maadirigaane, prati mishrama fermat sankhya bays 2kii balamaina suudoe prime. dheeniki kaaranam bays 2kii anni balamaina suudoe praimlu kooda fermat suudoe praimlu-i.ii.,
anni fermat sankhyalaku.
1904loe, sipollah kaneesam rendu vibhina pradhana ledhaa mishrama fermat sankhyala suutram _ 21 suutram _ 22 yokka gunakaaram suutram _ 23 ayithe matrame bays 2kii fermat sudoprimega untundani choopinchindi.
fermat sankhyala gurinchi itara siddhaantaalu.
 \rite) ^ {2} \equiv2 ^ {1 + 2 ^ {n-1}} \p.</ganitam>
2 yokka besi shakti anedi "p" anae chaturasra avashesha maadyulo kabatti, adhi kooda 2.
fermat sankhya anedi khachitamaina sankhya ledhaa snehapoorvaka sankhyala jatalo bhaagam kakudadu. 
fermat sankhyala yokka anni pradhana bhajakala paraspara shreni convergent. 
prime ayithe, atuvanti puurnaamkam "m" untundi. sameekaranam
aaa vishayamlo unchandi.
fermat sankhya "f" n "yokka atipedda pradhana karakam" p "(" f "n") gaa undanivvandi. appudu,
nirmaanaatmaka bahubhujaalato sambandham.
carle friedrich gaas thana "discusitions arthematic" loe gassian kaalaala siddhaantaanni abhivruddhi chesi, saadhaarana bahubhujaala nirmaanaaniki tagina sharatu roopondinchaadu. eee paristhiti kooda avasaramani gaas paerkonnaadu, conny eppuduu rujuvunu prachurinchaledu. pierry vantgel 1837loe avasaraniki puurti rujuvunu icchaaru. phalitamgaa gaas-vantgel siddhaantam anie pilustaaruh
oka dhanaatmaka puurnaamkam "n" anedi paina perkonna roopamlo untundi, daani tuttient "φ" ("n") anedi 2 yokka power ayithe matrame.
fermat sankhyala yokka anuvartanaalu.
sudorandum sankhyala utpatti.
fermat praimlu mukhyamgaa 1,, paridhiloo unna sankhyala nakilee-yaadruchchika shrenulanu roopondinchadamlo upayogapadataayi..., n", ikkada "n" anedi 2 yokka shakti. upayoginche atyanta saadhaarana paddhati emitante, 1 mariyu madhya edainaa vittana viluvanu teesukovadam, ikkada "p" anedi fermat prime. ippudu dheenini "a" sankhyatho guninchandi, idhi "p" yokka varga muulam kante peddadi mariyu idhi aadima muula maadyulo "p" (i.ii., idhi quadratic avasheshaalu kaadu). appudu phalitaanni maadyulo "p" gaa teesukondi. phalitamgaa rng kii kotta viluva vastundi.
idhi computer sainslo upayogakaramgaa untundi, endukante chaalaa dayta structurelalo 2 "x" saadhyamaina viluvalatho sabhyulu untaaru. udaaharanaku, oka bite 256 (28) saadhyamayye viluvalanu kaligi untundi (0-255). anduvalla, yaadruchchika viluvalatho bite ledhaa baitlanu nimpadaaniki, 1-256 viluvalanu utpatti chese yaadruchchika sankhya generatornu upayoginchavacchu, avtput viluva-1nii teesukune bite. eee kaaranamgaa chaalaa pedda fermat praimlu dayta encryptionlo pratyeka aasaktini kaligi untaayi. eee paddhati nakilee viluvalanu matrame utpatti chestundi, endukante punaraavruttula tarvaata, kramam punaraavrutamavutundi. sarigga enchukooni gunakam anedi kramam kante mundugaane punaraavrutamayye avakaasam undhi.
saadhaaraneekarinchina fermat sankhyalu.
a", "b" thoo kuudina suutram _ 26 yokka edainaa sahaarthika puurnaamkaala sankhyalanu saadhaaraneekarinchina fermat sankhyalu antaaru. p" anedi 1 (mode 4) kuu samanamga unte matrame besi prime "p" anedi saadhaaraneekarinchina fermat sankhya. (ikkada memu kesunu matrame pariganistaamu, kabatti!+ 1 </math>}} oka prati udaaharana kaadu.)
eee roopam yokka sambhaavya praimku udaaharana 1215131072 + 242131072 (kellen shenton kanugonnaru).
saadhaarana fermat sankhyalatho saaruupyata dwara, formula _ 27 yokka saadhaaraneekarinchina fermat sankhyalanu "f" n "(" a ") gaa vrayadam saadhaaranam. udaaharanaku, eee sangnaamaanamlo, 100,000,001 sankhya "f" 3 (10) gaa vraayabadutundi. eee krindi vaatilo manam eee roopam yokka praimlaku parimitam avtamu, formula _ 27, atuvanti praimlanu "fermat primes bays" a "anie pilustaaru. vaastavaaniki, "a" sarri ayithene eee praimlu untaayi.
manaku avasaramaite, anantamaina aneka saadhaaraneekarinchina fermat praimlu "fn" ("a") unnaya anie landou yokka nalgava samasya adugutundi.
saadhaaraneekarinchina fermat praimlu.
vaati praadhamikatanu niroopinchadamlo soulabhyam kaaranamgaa, iteevali samvatsaraalalo saadhaaraneekarinchina fermat praimlu sankhya siddhaanta rangamlo parisoedhanaku oka amsamgaa marai. nedu telisina atipedda praimlu chaalaa varaku saadhaaraneekarinchina fermat praimlu.
saadhaaraneekarinchina fermat sankhyalu sarri kosam matrame prime kaavacchu, endukante besi ayithe prati saadhaaraneekarinchina fermat sankhya 2thoo bhaaginchabadutundi. suutram _ 30 thoo unna atichinna pradhana sankhya suutram _ 29 suutram _ 31, ledhaa 3032 + 1. antekakunda, besi bays kosam "sagam saadhaaraneekarinchina fermat sankhyalanu" nirvachinchavacchu, sagam saadhaaraneekarinchina fermat sankhya "a" (besi "a" kosam) suutram _ 32, mariyu prati besi bays kosam parimitamgaa aneka sagam saadhaaraneekarinchina fermat praimlu matrame untaayani kooda aasinchaali.
athi chinna bays "b" antey "b" 2 "n" + 1 prime gaa untundi
athi chinna "k" antey (2 "n") "k" + 1 anedi prime
sthira suutram _ 36kii suutram _ 29 pradhanamgaa unde sthaavaraala sankhyanu anchanaa vaeyadaaniki marinta vistrutamaina siddhaantaanni upayoginchavacchu. suutram _ 36 1 penchinanduna saadhaaraneekarinchina fermat praimla sankhya daadaapu sagaaniki taggutundani anchanaa veyavachu.
telisina atipedda saadhaaraneekarinchina fermat praimlu.
krinda ivvabadinavi 5 atipedda saadhaarana fermat praimla jabita. mottam top-5 nii prime grid prajectlo paalgonevaaru kanugonnaru.
pradhana pageelalo prastuta 100 saadhaarana fermat praimlanu chudavachu.

