Twin Primes
Twin primes — pairs of primes separated by two — are common occurrences in number field propagation. They are exact divisors of Martini prime midpoints.
This page collects background, visualisations, and exploratory tools related to twin primes.
Background
Twin primes have fascinated mathematicians for centuries. In field systems, twins appear as stable irreducible structures.
This page illustrates features of twin primes and prime pairs and provides ways to explore them. This site is new and content will be added as time allows.
Visualisations
Mirror Pairs (Multiples of 3 to 500K)
Mirror Pairs (Multiples of 4 to 500K)
Mirror Pairs (Multiples of 5 to 500K)
Mirror Pairs (Multiples of 6 to 500K)
Mirror Pairs (Multiples of 7 to 500K)
Prime Midpoints Vase up to 5000
Large Twin Primes
Some examples of large twin prime pair midpoints which fell out of the field:
digits=1529: Twin Prime Midpoint at
41404489284792440978944812960950174213742581777513857628738698914467228337507267716861554272238446916707641346302906298597313206867453036247364161678848270623564344942263297959098916842909119927935501346476640416509185099528789796853116371658838345809678112949046647847247436947968283879888982868391804853059760178128227624528867498100953582968976684617375130375468133991380604631615955296992300539267163195821837587680675064382423780897808365981931320728310267398698801362757823910787938245822444317766098679373646155658809673108096905900734280591954228810996922776696814661004408036790874195021220082464541044183983400528397513099552098216275418492478252380441706315373773457420872030529334792279341055420466687935457112051386929427087775117267615894373178684108033838728360474584161970508988698416310091181283271284312704058717616379921262543554571484571500296958816061226057701881169358401653736585548429274299989424755402941562509512598000310448364130231920652934493205794174664321222280217391082334144302453065552523992112054318406942139071443929785918529402030055079453789106098923306697121119469743710929053442102960943079386093330001197579957284707424963071518088277528152482144698315439401741760015599841923382537016584147538321609849429486040322341134194267355407301300040307078224253212293203647562990885610697970609212475821680695273021293482896703139287654093599272198098936496059390410903385119253329687792207072467194920271135023936552899017317248645502223364035159907411056627486332603596800000000000000000000000 (primes at ±1)
digits=1227: Twin Prime Midpoint at
376667841661836058972452173996697786412792006036163740412950993117809617260022018968014611623096473011394354199225995909631341468147371277245037989087452011455037112705815984413349271027100161477738425032026174378678946988267915534463606923163305460506039590711180652978254400001379151004669798154781551896814185760630084282385934303298798526669806568354805076864425290384620983709888161879399757713516842506061053663563787686894454839524125792334029421585099177402656786751272932631204296110910852067937973341756103038820350651977791649610092363717979936437122903457549487099360575633055825963307692843692508032870736927012526127982692309285499220893925797013670921274869112069747613994351585036277288327666338745269481501941581486014557115328382691135500135997663381541302006865687380972920472762126885501584282280355795072353395503255308120683341822837715627139187621873646915096181632816529526847332183998000535858891291589128447443469917773807832825706988341019164774777918549138113204904720291513232680162912681156223928366686988123466723466271330575228556702368384926273035891927393697297087400064261646871816610124875763074789641323500515303995825899077149553364458184847864744349251697937639014400000000000000000000000 (primes at ±1)
digits=2253: Twin Prime Midpoint at
4894479346595065045372787919710709011570660654068702252601063571873541481745105643306218329599978318306414195204717327366986411057923310021896798361342486860875127063018864512250931138677700420407825002114411747561883595901159730703600933588189318881674753836829585001085509280789642899399115387461981223268847048641129547051553937297530999358654224068537815063585554482991924112877272627556057085513062436430090481723868215691783607894322131999632958381747515578544484857218512201959419985829664977243400543928319955513416945657939737290492039180514923560775094684308509983499970559738721775377165895000616811183644552136776014221520066918064689360579157654258021144725687678856001620437418407505458112740341266335037612406065150754382880150692718745783817656209071204393002139007752100266867699588306163321193355395878218318502293169760520068194680211305204343267130307643991145075941932116783337664204113043075216954747679807157141602536450723403518921316114174535872454386561555893109595774382954487963897789062435466040627697068233225072372412053174034382672889669540539186171885657813581536656913399452925369392043631672845698133858236929939648600631622239096984111399129781452738919548683166256157275091870461244834401311798938603374089427018941644935592859791830202437054309908189213121126888149785600822837346112040636163333748186847676546803268000082462020219846612245412303109194657942901366185906324668315930875443420523906176038135048639181889386666549192243752967444140561046537433883400391246808547942733091878153232382198741123080351261272353151933261353379689853291302531598008851936798859015271322814286976303025043704695935748422933329527858304418364565733233340359945335646746411602821391902492286188057207015546762851215525441133620617625221116175880413538787880553665922659417947181970888941012731319964410541947785305786347176029854950601739257866065718867451340943151111764379039265736983103535544675386619414354155454537254673718234498546518918808674181059982505441806628562668428855754958885067519826785407287041807654683071239145253114703721817909063380501678461135872541850813821172947164012644449426299046273372662000777664790069588699284900726478594106001259289513435711107670133589092042775228494797907297359067603029388188901822447632869834680014081468169047046813869557090192729483995915439744695986655756523719243974056254684348901246684322497835092116206717231221226422026391222638259733292678899323744121257568859961215694821217238223631347331304592199786546723313103134341267616217454494223751061289675591178701902165273115009692729303535781693929697531129546484112064452624800865773968794005621856967619085502935371208843522184214041451566588958042768040579494511289137888784309449505833124227198993579207804269473050977703443210617055004085770239863168216979080438339410945046644156428517572755097044568716452726255142704591130379649801705961022514187262213697237202775288316947010705064698964282475927049326848108169840474879465763889993956115307202649048824477891926131188009737423616823270958805964328939365495768039792234109253048382177296815027271972850327385865705616031319763876443079238335409460177016466687653460237468963820220141441866842527189371268986507117012106418488626996401411902788291743330524449252093237953590748521098727328916409279021350628630432079382666264233202909253146326404841917506364540551361331732792588557030629723919341203183210974644010443328814779064682643225998822382710386434941199778897602406591939466850467840000000000000000000000000000 (primes at ±1)
digits=2297: Twin Prime Midpoint at
63909733203084033675246313541020317305224973658654389396412702113830276057902073151086594113453183495923466450985730615354580380950321018142522399724977012966783822596064756290268497435223601037852653753086412078496294089316240163793313001536689211139098442741901420612330891315802564603122350926300448820507665830296827620190490793569848167669595671869693311728711400864561922460641187941682378288147754800080165866834456857985589191369654872769735552631022294690467034623055940746007341416920157046185695538245706971792637860323050317073437640144325669979041934049934732855738927950892602275827679556836281012209102939822450181035426359012267007434585841781563726940444552083542292658692252201288631273247053397882221144682982725545240380413506817492838195160185570866931608487672828679014284058943015101098074000664220898497219757448841156993788964459605833937717061010981507475446425243655218054198770305212447319296397666877885281294606469571408451216882399461147780453246236152346234339692076854395885718721228040473253622207885839331962221489680275434770561640726408690668766079641136951953614264833307447032435349172989466101056012488104962699062410050763839206490231369753419177436466898331338271935372589382355623658269404166400250847922825341747663979772170960995664206439656610489486235271983987104223070084007987797327896965477899542699285442712813105888349510249861175092152699914364580047839668757406189412888830759667473338079502266648359795841251881676588294473055327084351734248461014769379692047539355872513795900366287068314131198380310876649079278847630455785574329064347628628077075123815624111256071603848036941963898485141121610173209963266740391853844012263249941833455146719811355379064082868096469002670871117072396527330167695012481445859737647874675417419860132258093581898776228651529023972433297128119669669497358271258041080374039031534931369274796226274359837739515217747491787215648372247083638001855248722723573849154197657725495462990993169469209519425903260345802263907432647051554742071269988513665307854036662401608292599186301612022881963658224445959637470211632980295031989819076691292405931108105749132075172502300746398608611627775686246681781703785864690326806367630590714599255681203056367238119424000000000000000000000000000000000000000000000000000000 (primes at ±1)
digits=3324: Twin Prime Midpoint at
279427696381901674173849921351737944943944163689282847271189042108260841504814640355950172894997713592004093895669586020488116648450471402075631112224985366529939339543742042640197560370058153050653828830101938131270573882204848231545937979104384952506487650547996835635931424149272586275908565767975535237673828258541264189816440052486316766564688887357244357097972951031839575454108601309598896932307502135581384135102129716777793685451658966917919132443039705001087394982764499287752957486494404688807499385485448200928880565900307885233952709407356911160072299410546396310407104603167203405927232135577364101852895269077900538417803181516873044666247204971754172710727889109473854780010380491552881350259461747260896184599067284622017872395444326343975521487322410505396985142463143942648622010795191374852299231903365318620116884305784282448900193357812024832944896851357889193370142948873415385675714860229023812423012772645837359471289079173828945056412060809229579278537605153720150545949032593566311618286870289341252951883902965868062362153573727127404567794343413004285875442603451175910116419180944248804230213983324724097686171253452283197174623703760896417816203581421672184684890527529327224877983660339875370946521324973276041967880525567357713146407514541265261197174529205726520792881641860228631697152499909953409962833513791603695916131873150578230184348415168018401946802530918337045704162295203728259442949249418562023540564636417103838133491028754533270084613671341590702836152512277508754345587683075365577699894402264595869338179928336558263291320075908339705027667375266702933987526277504865438039613718027975393585226549222625446581820496786434998897457588173238754801265466467347511378548805236859981567788563812373639049087719756216533539620046066514308941713649809588149456317895428334694684075608130499790653066314813059655727744873967191569186021836997287481906352386241264728980431581180057251248134497252767697858593272449420980768746015787586917785192237601946054149357338459563446188696673184449388329739579152601702665960202304027883641621899515698259692735699088993338902825926865307426434406593017379586900693734533088793223681540126602626898806980426025368230082968539265211933280566822801409257630503655013142508443445774019802634274892685668225753826056530894766061414142774385889631347214024935811145427412639664989454195941703451949046980048001903470705129574561605530176802844667197697729396417707751170035069755261238880007903290653464043886008994569675421738010703318100011163742545022573085901579647234977429139165017404060057172747502688821235909022600724629425518868800500746699151897415273863750601198998743522089112831551217684803416531681133241631769755321223998775877504843201707578659406105580470706453847624861129915228825388191601266779185504203572628510048098957483111195611704228900077618024082294226390210632158730536275183360667628999521291371646560297617348911103655123650201425501437415277680454745410546781709786439271149257366939084970548314099560014019990936441801366418397521650233927219126258340941951190147156275608574280892665915779035873954909974969936017990060313292780307539267293783934224048138498887222457238480091631721636084472851135653548927772857991168000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (primes at ±1)