
shinzel kii parikalpana aich

ganit mein, schingel kii parikalpana aich sankhya siddhant key vishay mein sabse prasiddh khuli samasyaon mein seey ack haye. yeh vyaapak roop seey khule anumaanon kaa ack bahut hii vyaapak saamaanyikaran haye jaise kii judvaan pramukh anuman. parikalpana kaa naam andrez schingel key naam parr rakhaa gayaa haye. 
bayaan.
parikalpana kaa daavaa haye kii sakaratmak pramukh gunank vaale purnankon parr gair-sthir aparivartaniya bahupadon key pratyek seemit sangrah sootra key liye, "nimnalikhit sharton mein seey ack" mein haih
doosari shart sootra _ 11 jaise seton dwara santusht hoti haye, kyonki sootra _ 12 hamesha 2 seey vibhaajya hotaa haye. yeh dekhana aasaan haye kii yeh sthiti "pahali" sthiti koo sahee honey seey rokti haye. shinzel kii parikalpana anivarya roop seey daavaa karati haye kii sthiti 2 "ekmatra" tarika haye joe sthiti 1 koo pakadane mein whiffle hoe sakati haye.
yeh nirdhaarit karane key liye koee prabhaavi takneek gyaat naheen haye kii kyaa "pahali" sthiti bahupadon key diye gaye sett key liye haye, lekin doosari jaanch karane key liye seedhi haih sootra _ 13 aur sootra _ 15 key sootra _ 14 kramik moolyon key sabse badey samanya bhaajak kii ganana karein. koee bhee seemit antar key saath bahirveshan karke dekh sakata haye kii yeh bhaajak sootra _ 15 key anya sabhi moolyon koo bhee vibhajit karega.
shinzel kii parikalpana pahale key bunyakovsky anuman parr, ack ekal bahupad key liye, aur kaee raikhik bahupad key liye hardy-littlewood anuman aur dickson key anuman parr adharit haye. yeh badale mein ballebaaz-seeng anuman dwara vistaarit haye.
udaaharan.
sootra _ 17 key saath ack saral udaaharan key roop mein,
koee nishchit abhaajya bhaajak naheen haye. isaliye humm ummeed karate hain kii anant roop seey kaee abhaajya hain
halanki yeh saabit naheen huaa haye. yeh landau key anumaanon mein seey ack thaa aur euler key paas vaapas jaataa haye, jinhone 1752 mein goldback koo likhe ack patra mein dekhaa kii sootra _ 19 aksar sootra _ 21 seey 1500 taka key liye pramukh hotaa haye.
ack anya udaaharan key roop mein, sootra _ 23 aur sootra _ 24 key saath sootra _ 22 lein. parikalpana taba anant roop seey kaee judvaan abhaajya key astitva kaa sanket detee haye, joe ack buniyaadi aur kukhyaat khuli samasya haye.
roop.
jaisa kii prishth 188 mein shinzel aur sierpinsky dwara saabit kiya gayaa haye 
yeh nimnalikhit key barabar haih yadi sthiti 2 naheen pakadati haye, tou cumm seey cumm ack sakaratmak purnank sootra _ 21 maujood haye jaise kii sabhi sootra _ 26 ack saath abhaajya honge, sakaratmak pramukh gunank key saath aparivartaniya abhinn bahupad sootra _ 27 key kissy bhee vikalp key liye.
yadi pramukh gunank nakaratmak they, tou humm nakaratmak abhaajya moolyon kii ummeed curr sakate hain; yeh ack haanirahit pratibandh haye.
purnank-moolya vaale bahupadon (jaise sootra _ 28, joe sabhi purnank sootra _ 29 key liye purnank maan letaa haye, bhale hii gunank purnank naa houn) key bajaay purnank gunank vaale bahupadon koo pratibandhit karane kaa shayed koee vaastavik kaaran naheen haye.
pichhale parinam.
ekal raikhik kaa vishesh mamla
bahupad ankganitiya pragati parr dirichlet kii pramey haye, joe ankganitiya pragati key sabse mahatvapurna parinamon mein seey ack haye.
sankhya siddhant. vaastav mein, yeh vishesh mamla shinzel kii parikalpana kaa ekmatra gyaat udaaharan haye. humm naheen karate
sootra _ 30 seey adhik degree key kissy bhee diye gaye bahupad key liye dhaaran karane key liye parikalpana koo jaanen, naa hii kissy bhee pranali key liye
ack seey adhik bahupad.
schingel kii parikalpana key lagbhag pramukh anumaanon kaa prayaas kaee ganitvidon dwara kiya gayaa haye; unamen seey, vishesh roop seey,
chain kii pramey bataati haye kii aseem roop seey kaee abhaajya sankhya sootra _ 2 maujood hain jaise kii sootra _ 32 yaa tou ack abhaajya yaa ardh-abhaajya haye. 
aur ivanic ney saabit kiya kii anant roop seey kaee purnank sootra _ 2 maujood hain jinake liye sootra _ 34 yaa tou ack abhaajya yaa ardh-prime haye. skorobogatov aur sophos ney saabit curr diyaa haye kii kissy bhee nishchit degree key lagbhag sabhi bahupad schingel kii parikalpana koo santusht karate hain. 
yadi ack kaalpanik sambhaavit ghanatva chhalani haye, tou dee. aar. aar. chhalani kaa upayog ganitiya punaravritti dwara sabhi mamalon mein schingel kii parikalpana aich koo saabit curr sakata haye.
sambhaavanaaen aur anuprayog.
parikalpana shayed vishleshanatmak sankhya siddhant mein vartamaan vidhiyon key saath sulabh naheen haye, lekin abb aksar sashart parinamon koo saabit karane key liye upayog kiya jaataa haye, udaaharan key liye diophantine jyaamiti mein. yeh sambandh jeane-luis colliot-thelen aur jeane-jacks sansuk key kaaran haye. iss sambandh mein aage kii vyakhyaon aur sandarbhon key liye
swinnerton-dier key nott dekhein.
anumanatmak parinam prakriti mein itna majboot honey key kaaran, yeh sambhav haye kii yeh bahut adhik honey kii ummeed key liye dikhaaya jaa sakata haye.
goldback anuman koo shamil karane key liye vistaar.
parikalpana goldback key anuman koo shamil naheen karati haye, lekin ack nikatata seey sambandhit sanskaran (parikalpana hn) kartaa haye. isake liye ack atirikt bahupad sootra _ 35 kii aavashyakta hoti haye, joe goldback samasya mein kewal sootra _ 36 hoga, jisake liye
ack abhaajya sankhya bhee honey chaahiye. ise hulberstom aur richart, "chaalani vidhiyon" mein uddhrit kiya gayaa haye. yahaan anuman ack kathan kaa roop letaa haye "jaba n paryaapt roop seey badaa hotaa haye", aur sthiti key adheen hotaa haye.
koee nishchit bhaajak"> 1 naheen haye. tou hamein "n" key astitva kii aavashyakta honey chaahiye jaise kii "n" − "f" ("n") sakaratmak aur ack abhaajya sankhya donon haye; aur sabhi "fi" ("n") abhaajya sankhyaon key saath.
inn anumaanon key kaee mamle gyaat naheen hain; lekin ack vistrit matratmak siddhant (ballebaaz-seeng anuman) haye.
sthaaniya vishleshan.
koee nishchit abhaajya bhaajak naa honey kii sthiti vishuddh roop seey sthaaniya haye (kewal abhaajya parr nirbhar karati haye, arthaat). dusare shabdon mein, aparivartaniya purnank-moolya vaale bahupadon kaa ack seemit samooh 
binaa kissy "sthaaniya baadha" key anant roop seey kaee pramukh moolyon koo lene key liye anant roop seey kaee pramukh moolyon koo lene kaa anuman lagaaya jaataa haye.
ack analogue joe whiffle hoe jaataa haye.
ack seemit kshetra parr ack-charr bahupad valay dwara pratisthaapit purnankon key saath anuroop anuman "galat" haye. udaaharan key liye, huns ney 1962 mein (parikalpana aich seey asambandhit karanon seey) ullekh kiya kii bahupad
f" 2 ["u"] ring parr irreducible haye aur iska koee nishchit prime polynomial devisor naheen haye (aakhirkaar, "x" = 0 aur "x" = 1 parr isake maan apekshaakrit prime polynomial hain) lekin isake sabhi maan "x" key roop mein "f" 2 ["u"] parr chalate hain, joe samagr hain. isi tarah key udaaharan "f" 2 key saath kissy bhee seemit kshetra dwara pratisthaapit kiye jaa sakate hain; parikalpana key uchit sutrikaran mein baadhaaen "f" ["u"] parr, jahan "f" ack seemit kshetra haye, abb kewal "sthaaniya" naheen haye, balki ack naee "vaishvik" baadha hoti haye jisamen koee shaastriya samanantar naheen haye, yeh maanate hue kii parikalpana h vaastav mein sahee haye.

