PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
700150^56543-4996065Norbert Schneider09/2018
70022^319107-10955596061Enzo Doria04/2014
7003(3*2^319114-1)/262796060Lelio R Paula02/2014
70042^319098-11215796059Enzo Doria06/2014
700515^81673+9496055Lelio R Paula07/2016
70062^319074+187174996051Enzo Doria05/2016
700725670^5517+5517^2567096050Hans Havermann06/2020
70086*10^96037+1996038Robert Price11/2021
70092^319007-11211196031Enzo Doria06/2014
70102^318946-142196013Yves Minet01/2013
701122830^16003+16003^2283095982Hans Havermann02/2020
70122^318834-11041195979Enzo Doria05/2014
70132^318831-196595978Lelio R Paula03/2016
7014(5*10^95976+7)/395977Erik Branger03/2014
701522871^15696+15696^2287195962Hans Havermann01/2020
7016(2^318760+858)/295957Stefano Morozzi02/2021
701723167^13860+13860^2316795953Hans Havermann01/2020
70185*3^201089-895945Lelio R Paula08/2014
70192^318711-13995942Lelio R Paula11/2012
70202^318635-116795919Lelio R Paula03/2016
702115^81555+1695917Lelio R Paula07/2016
7022(37*10^95895+377)/995896Robert Price10/2017
7023(22699*2^318527+1)/2195890Lelio R Paula07/2014
70242^318496-9730595877Lelio R Paula03/2016
702522129^21496+21496^2212995871Hans Havermann07/2020
70272^318466+1501595868Lelio R Paula03/2016
702624847^7216+7216^2484795868Hans Havermann07/2020
702823706^11065+11065^2370695866Hans Havermann07/2020
70296^123187-17312995859Mike Oakes04/2011
70302^318423-48795855Yves Minet03/2012
7031(2^318359+678)/295836Stefano Morozzi09/2020
7032(10223*2^318350+1)/156395834Lelio R Paula07/2014
7033(2^318267+2550)/295808Stefano Morozzi09/2020
70344*10^95799+1395800Robert Price02/2021
703545369!2+102495787Robert Price02/2015
70363^200758-8695786Lelio R Paula05/2016
7037(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
7038(2^318171+2030)/295779Stefano Morozzi09/2020
70393*10^95776-5995777Robert Price10/2017
7040193^41901-295768Lelio R Paula10/2017
7041(2^318124+2502)/295765Stefano Morozzi09/2020
70424*10^95752-7195753Robert Price11/2017
704323640^11197+11197^2364095721Hans Havermann12/2019
704410^95712-400000195712Robert Price07/2021
7045((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
7046(509203*2^317881-1)/5280595693Lelio R Paula04/2015
7047(2^317853+1086)/295683Stefano Morozzi09/2020
70484*10^95672+9195673Robert Price11/2017
70496*10^95665+4395666Robert Price07/2020
7050(11*10^95641-113)/395642Robert Price01/2017
7051(13*10^95588+11)/395589Robert Price05/2015
7052Phi(191188,10)/19118995587Maksym Voznyy11/2015
70533^200325+7095580Lelio R Paula05/2016
7054(25*10^95574-7)/995575Robert Price12/2014
7055(2^317485-3)/2131395569Lelio R Paula06/2013
70562^317464+3195567Lelio R Paula11/2012
7057(2^317451+2114)/295562Stefano Morozzi09/2020
70587^113073+8295558Lelio R Paula04/2016
70592^317251+46595503Lelio R Paula03/2016
706019^74684+5895503Lelio R Paula06/2016
7061(2^317250-7)/33995500Lelio R Paula07/2013
70625*10^95498-2195499Robert Price12/2021
70636^122718-7995494Lelio R Paula05/2016
706422168^20291+20291^2216895485Hans Havermann10/2019
70652^317141-11049195469Enzo Doria05/2014
7066(2^317097+3014)/295456Stefano Morozzi09/2020
70672^317094+7630995455Enzo Doria05/2016
70682^317085+9595453Lelio R Paula11/2012
7069(17*10^95451-377)/995452Robert Price11/2017
70702^317057-10955195444Enzo Doria04/2014
70713^200026+2895437Lelio R Paula05/2016
70722^317024+9395434Donovan Johnson06/2008
7073(86*10^95428-437)/995429Robert Price03/2021
707410^95427+19259195428Patrick De Geest05/2021
70772^316999+160595427Lelio R Paula03/2016
7076(2^317000+3210)/295427Stefano Morozzi09/2020
707510^95427-1000195427Robert Price02/2021
70782^316995-11042795426Enzo Doria05/2014
707922300^18987+18987^2230095410Hans Havermann06/2020
70812^316937+17795408Lelio R Paula11/2012
70804*10^95407+9195408Robert Price11/2017
70822^316908+191595399Lelio R Paula03/2016
70832^316894+9995395Lelio R Paula11/2012
7084(2^316887+2546)/295393Stefano Morozzi09/2020
70852*10^95374-2195375Robert Price09/2020
70866^122547+1195361Lelio R Paula05/2016
70872^316771+8287595358Lelio R Paula03/2016
7088(2^316765+3102)/295356Stefano Morozzi09/2020
7089(23*10^95326+1)/395327Serge Batalov05/2009
70901*10^95326+5795327Robert Price03/2011
709110^95326-39368795326Patrick De Geest09/2013
7092(3^199803+4)/47953995325Lelio R Paula04/2013
70932^316654-10948195323Enzo Doria04/2014
70948*10^95316+5195317Robert Price05/2017
7095(50^56099+43^56099)/9395309Serge Batalov12/2016
7096(23*2^316559+1)/392595292Lelio R Paula09/2013
7098(71*10^95277-539)/995278Robert Price11/2017
709723422^11691+11691^2342295278Hans Havermann10/2019
709919^74503-5695271Lelio R Paula06/2016
710011^91475-438095262Enzo Doria01/2013
7101(62*10^95251-611)/995252Robert Price05/2017
7102(2^316321-509203)/6937795218Lelio R Paula06/2013
710326541^3868+3868^2654195216Hans Havermann07/2020
7104(79*10^95214-43)/995215Erik Branger11/2013
7105(7176^24691-1)/717595202Anonymous11/2020
7106(9*2^316233-1)/175195194Lelio R Paula02/2014
71075*2^316213+995191Lelio R Paula08/2014
71082*10^95188-9195189Robert Price04/2020
71092^316205-184816395188Enzo Doria07/2015
71102^316185-278791395182Enzo Doria04/2016
7111(2^316174+3538)/295178Stefano Morozzi09/2020
7112(9787*2^316142-1)/395172Lelio R Paula04/2015
71132^316140-595168Henri Lifchitz02/2006
7114(15185*2^316117-1)/395165Lelio R Paula04/2015
7115(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
71162^316069+7681795147Enzo Doria05/2016
7117(199*10^95134-7)/395136Robert Price02/2017
71182^316027-9730595134Lelio R Paula03/2016
71192^316006-279805195128Enzo Doria04/2016
712024994^6397+6397^2499495127Hans Havermann02/2020
71222^315921-279760395102Enzo Doria04/2016
7121(2^315921+1314)/295102Stefano Morozzi02/2021
71232*10^95095+6395096Robert Price10/2017
71242^315857+129995083Lelio R Paula03/2016
7125(2^315858+2598)/295083Stefano Morozzi09/2020
712714^82955-4395078Lelio R Paula06/2016
7126(8*10^95078-269)/995078Robert Price09/2021
7128(23*10^95074-101)/395075Robert Price04/2021
71292^315827-93307595074Paul Bourdelais04/2021
7130(2*10^95072-17)/395072Robert Price08/2014
7131(286*10^95059-1)/395061Robert Price11/2020
7132(2^315779+1610)/295059Stefano Morozzi09/2020
71332^315775-11154643595058Paul Bourdelais10/2021
713421938^21513+21513^2193895051Hans Havermann09/2020
71352^315727+6595044Lelio R Paula11/2012
71362^315725+188575795043Enzo Doria03/2017
713723277^12058+12058^2327795000Hans Havermann09/2020
71381*10^94983+2194984Robert Price03/2011
713910^94983-71794983Patrick De Geest08/2013
714017^77187-8294975Lelio R Paula07/2016
71413*10^94964+3794965Robert Price10/2017
7142(2^315481-1017)/2062728594962Lelio R Paula06/2013
71432^315423-11032994952Enzo Doria05/2014
714411^91169-723094943Enzo Doria02/2013
71457*10^94938+6194939Robert Price02/2017
71462^315351+102594931Lelio R Paula03/2016
71472^315350-11225394930Enzo Doria06/2014
7148(2^315343+1766)/294928Stefano Morozzi09/2020
7149(2^315343+3066)/294928Stefano Morozzi09/2020
7152((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
71512^315268+794906Lelio R Paula10/2012
715011^91133+6294906Lelio R Paula05/2016
7153(2^315264+1558)/294904Stefano Morozzi09/2020
715430^64244+4194897Lelio R Paula08/2012
7155(151*10^94885-7)/994887Robert Price07/2017
71564^157583+2214794875Mike Oakes01/2011
71572^315098+12394854Lelio R Paula11/2012
71583^198791-3494848Robert Price11/2013
71593*2^315067+794846Lelio R Paula08/2014
7160(9*2^315057+1)/7394841Lelio R Paula09/2013
716122576^15875+15875^2257694836Hans Havermann09/2020
7162(16*10^94822+53)/394823Robert Price12/2016
71638*6^121849-794818Lelio R Paula10/2014
7164(85*10^94802+473)/994803Robert Price03/2017
716521767^21852-21852^2176794790Norbert Schneider06/2020
71662^314870-10876194786Enzo Doria03/2014
71675*2^314841-394778Lelio R Paula08/2014
7168(2^314842+550)/294777Stefano Morozzi09/2020
7169(2^314787+2630)/294761Stefano Morozzi09/2020
71706^121772+11394758Lelio R Paula05/2016
7171(2^314740+3642)/294746Stefano Morozzi09/2020
71726^121756-1625394745Enzo Doria02/2013
71732^314718-11279394740Enzo Doria06/2014
71742^314697-184729394734Enzo Doria07/2015
717522836^14065+14065^2283694727Hans Havermann09/2020
71772^314548-24994689Yves Minet02/2012
71765^135469+4294689Lelio R Paula04/2016
7178gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
717925773^4712+4712^2577394670Hans Havermann08/2020
7180(2^314485+3614)/294670Stefano Morozzi09/2020
7181(2*10^94604+547)/994604Robert Price10/2017
7182(2^314164+2562)/294573Stefano Morozzi09/2020
71833*2^314152+594570Lelio R Paula08/2014
71842*6^121530-594570Lelio R Paula10/2014
71857*10^94563+8794564Robert Price11/2016
71862^314114-10967794558Enzo Doria04/2014
7187(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
71882^314059+7658394542Enzo Doria05/2016
71892^314041-403594536Lelio R Paula03/2016
7190(2^314028+3102)/294532Stefano Morozzi09/2020
7191(2^314012+618)/294527Stefano Morozzi09/2020
7192(7*2^314003-11)/1594524Renaud Lifchitz03/2011
719311^90760-471094517Enzo Doria01/2013
719421675^21796+21796^2167594507Norbert Schneider04/2020
71952^313942+10028024506594506Paul Bourdelais10/2021
7196(7*2^313926-1)/14882194497Lelio R Paula02/2014
719794*10^94493-394495Robert Price11/2016
7198(1000547^15749+1)/100054894492Faysal YAtim12/2008
7199(2^313859+2706)/294481Stefano Morozzi09/2020
7200(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
72017^111792-3294476Lelio R Paula04/2016
7202(2^313800+822)/294463Stefano Morozzi01/2021
72039*10^94462-4794463Robert Price11/2021
720411*10^94460+394462Robert Price07/2021
7205(202*10^94441-1)/394443Robert Price05/2020
720611^90680-585094434Enzo Doria01/2013
7207(752^32833-1)/75194432Michael Stocker05/2020
72082^313675-11012594426Enzo Doria04/2014
7209(2999*29^64556-2427)/494410Curtis Bright05/2015
72102^313609-11222594406Enzo Doria06/2014
72112^313584+7290194399Enzo Doria04/2016
7212(2^313567+1310)/294393Stefano Morozzi02/2021
7213(2^313562+730)/294392Stefano Morozzi09/2020
72142^313510-11286594376Enzo Doria06/2014
72157*10^94373+8794374Robert Price11/2016
7216(9^98897+8^98897)/1794371Robert Price12/2012
72172^313453-11470394359Enzo Doria04/2015
72188*10^94357-5194358Robert Price10/2017
721925903^4392+4392^2590394356Hans Havermann09/2020
722031706^945+945^3170694340Hans Havermann09/2020
7221(379*10^94337-1)/994339Robert Price08/2017
72222^313344-313344+194326Robert Price10/2014
7223(2^313313+3662)/294317Stefano Morozzi09/2020
722420^72481-4994300Lelio R Paula05/2016
7225(34*10^94293-259)/994294Robert Price12/2021
722644725!2+12894289Robert Price03/2015
72274*10^94286+994287Robert Price05/2015
722817^76621+2494279Lelio R Paula07/2016
722926274^3875+3875^2627494279Hans Havermann09/2020
72304*10^94270-3394271Robert Price04/2021
72312^313156-11285994270Enzo Doria06/2014
72326^121130-5994258Lelio R Paula05/2016
72333^197542+2894252Robert Price11/2013
7234(2^313076+3550)/294245Stefano Morozzi09/2020
7235(3^197521+2)/5165594237Lelio R Paula04/2013
72362^313045-595594236Lelio R Paula03/2016
723722099^18358+18358^2209994227Hans Havermann08/2020
7238(67*10^94212+23)/994213Ray Chandler02/2011
72392^312909-186520394195Enzo Doria03/2016
724025013^5830+5830^2501394191Hans Havermann09/2020
72412^312848-14994177Lelio R Paula11/2012
7242(2^312819+3278)/294168Stefano Morozzi02/2021
72434^156403-7759794164Mike Oakes04/2011
724418^75004-8594151Lelio R Paula06/2016
724519^73622-4894145Lelio R Paula06/2016
7246(11^90397-3^90397)/894138Robert Price04/2011
7247(3^197287+5)/1694129Lelio R Paula04/2013
724824220^7691+7691^2422094119Hans Havermann09/2020
724912^87212-3794118Lelio R Paula06/2016
725011^90376+7694117Lelio R Paula05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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