[math-fun] record polynomial for primes, 70 and 118 values.

1 Oct 2020

      Hello,

  I have been working on the idea of producing
a polynomial that gives primes. I have found this
expression,
  if c =

1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\ 

000000000000000000000000000000000000000000000000000000000000000000000000000000001556808232856463140\ 

060524522424280772934429200613394089802373785244587288947728630209290312111238140972072983869588571\ 

830870498647900351444778386216146076636515297094962921999030102707899655875083040665145525741443694\ 

679398437806398341541385226365101056503219529413038357761603719148231623498218255233850813147568998\ 

744093447755692241415245289626420200959624751354414736085310934015664680524107510074349656822480162\ 

844410900000000000000000000006345174532890027939294089368385587928671551372984708501441585620418908\ 

704346095361979911978459546006902805287612053866464609018035122943293118288150470557741929174121124\ 

290158771911527759861726269584165754859588606741441445142853262133802425477033893100601759975564856\ 

010884639189352574717896440249667645304974867391425986281906375105044471660347105158250104363991834\ 

652263421461752834975705269597512556117680247632410969440028501070105083651713662403142442324953222\ 

225461614957943694687384105246348009815340760743692542284884699931895728286412542979603098044884198\ 

867262644327255465732046886424762403984621514353794473387936916290029911549331529954509625933626714\ 

214956674379391784430822602413846681316909794084400273637943424856690207465817148161052758912779700\ 

994744869116506018623229585002806564436851770494944385807359855293872240395791047188062073418411994\ 

344296873461271952410865026038448423723192039177383879070574428090707165141606873722573750361413628\ 

118939617030810117859967828092642486835827304995753842763548295039042203138474167878091109846423833\ 

375302339937989596168347847772485744109449547853544023508997274222527142776574434316734525917951119\ 

963956001777673781864527502261570125603162371258224293816247417631732394744100802942101015408972089\ 

551902455081699086722777589571816095705739686859606854254953133788523318655544571643416019528317460\ 

445413625249324735829

Then { c*n^599 } will produce 70 primes in a row. { } is
the nearest integer function from n = 2 to 71.

Pushing the argument further, we can compute another c

c:=1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\ 

000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\ 

000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\ 

000000000000000000000000000000000000000000000000000000000000000000000000420808913403862852286037439\ 

407207843280000454871709619989894140740709325325252736588820344022475410602235657175990218497430264\ 

507047719507377755195716569424888020122974216275756432352375373324176830942254809073810657745081913\ 

603888834668238535298596378009711467814200413802525979955404026071836372488037677429251875416844528\ 

065861840386027884753763707042193371171062601284648726970657466685180064833875657919373385253912481\ 

027773992391561048642338757691327360781626065347664616770332572923617311886082595296236132142036996\ 

417631450188411788269401899358010244184959963090467560534373012929594222867337833389724761101476675\ 

265940651881737969147941607553518894806698237842174373575406499207457956921830241573813363914109602\ 

358518386220031857824704794430689335145845120578114984070186291502181713823988558402910508064322733\ 

386664486830182828399818696846253725628343900000000000000000000000000000000000000000000000084175367\ 

076263959877259166560848274081827502629329509901369386601926351191550840426061007096278515366265573\ 

952742294088796839541191179807808635987650890468860605139264215146106576144341811285085551240005000\ 

227988558319987250361379891704780432636060689056700626535379944795660666700454584856310206434590094\ 

563862726354995211336248348977032053078689859896535496416742714456066139307160173240122478999781218\ 

197906243111555919375402725879595014949858452214458311548245169558232561733182222402280681701375871\ 

793674008212637679797212418300296261196701357686395359413115610049111887480023065235108355761846794\ 

154242861989506511616703890355282922203837990655338427540314744201707762522718995260468275097894687\ 

992658082255204558477493326827178073388363120958685523709670974720969561623848267686506891223902113\ 

356465938801122508318610403664836118814508451633512182695560344508500322312812467848420047540700118\ 

756996471899350068204423209609398912635469407815389181128071148265623479744625601961828151165458057\ 

147404102417248338590636605285714210912430034480012999178228996360603231909255738065132728968316201\ 

942832143187208766136927730107179702837907838280367350477002598486254090817302319631003233911930910\ 

326471343720878750834773567638442701853950231270477449195094392125036285692593745404976928391598493\ 

120102332751565874902239824210432449599913477786262806371486887301944497146993921610645697910752375\ 

471592158629224985009940446389322350619119669969165095587552413272311756200137164763698462482237842\ 

085305489252071338731483772934377614611471560053211589913596117355646404568766829712511199143649379\ 

532868420835646628215546104322304046559478794811449490815559145536588643275429191044262263030906449\ 

008533040348061447967481937845138943509232559583664683731050066160246941104648886339886131997547626\ 

564120786805439643038360743772486321929905049774075239032391693139009562591896452809951937070106931\ 

642757393826901443265817325728278062434238566608603447589227610334941793131104068971110670780632223\ 

501992904396028760342780374806446000650380882469871510606798126329459070489028928886613221959394681\ 

050313121338162899918203136695650902893260267066828147220878717494110655700034933423554789843042459\ 

788022312976819102949452912553641155543969632606853848755713600338142981448378093170817347349572333\ 

952846367305250612191724450242639374172385705018208921153877985055819331461598505096730761179995331\ 

035421322004624870914956170836838658721047385074001034842012584599289337696078080593315480435697028\ 

797774107860521215331382017992014682105116071846031465281846724781837631731709033583747490253551521\ 

803421554038976456384199449968082545362824346045297834204279214326015137442652491792514695344393933\ 

611548475720971484567438167471354078436388186768821886590160600734921902666008892973993959127619935\ 

979220653987693039715708896453055494647408765542658440234527096823567561970767330545161066354821607\ 

244431370845177234625939025174648851026905740292276726858715610711059412344054491438441794529481070\ 

832085773331946632572075193269154720991959262777548164921202141769518765360369196200318903302241851\ 

418383237112822078939390705199644185307459995247776965884156912985571438965918094406295259053539143\ 

012557100340081332145565524386009208260466781433220908290351633667375248793342095089544887182663796\ 

959414821279536006717126997713929475971075504116872033184698268145793823163522155260021118497275248\ 

218585277043570493808327959903835073039657749082814079252504658007442530811406763989164961498255778\ 

804250702976093118870182366132160978707672267041810251065555501606510564729290105611727839326557928\ 

121443797072417029288704025364542736049982739791265476935477664530256067268014661044783782058238843\ 

329500015341452854520505118062087287565683882017664

{ c*n^1229 } is prime for n = 2 .. 119.

  There is probably a lower degree polynomial which would produce more 
primes
, the one found here is the simplest possible expression.

Details of this algorithm are here,.
https://vixra.org/pdf/2009.0116v3.pdf

Best regards,
Simon Plouffe