PRP Records

Probable Primes Top 10000

(290751 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 ?
80013*10^95776-5995777Robert Price10/2017
8002(82970^19471-1)/8296995772Serge Batalov06/2022
8003193^41901-295768Lelio R Paula10/2017
8004(2^318124+2502)/295765Stefano Morozzi09/2020
8005(12900^23297-1)/1289995761Serge Batalov06/2022
80064*10^95752-7195753Robert Price11/2017
8007(16955^22639-1)/1695495743Serge Batalov06/2022
8008(81795^19489-1)/8179495740Serge Batalov06/2022
8009(2742^27847-1)/274195737Serge Batalov06/2022
8010(6072^25303-1)/607195726Serge Batalov06/2022
801123640^11197+11197^2364095721Hans Havermann12/2019
801210^95712-400000195712Robert Price07/2021
8013(60657^20011-1)/6065695706Serge Batalov06/2022
8014((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
8015(509203*2^317881-1)/5280595693Lelio R Paula04/2015
8016(26161^21661-1)/2616095687Serge Batalov06/2022
8017(2^317853+1086)/295683Stefano Morozzi09/2020
80184*10^95672+9195673Robert Price11/2017
80196*10^95665+4395666Robert Price07/2020
8020(20819^22153-1)/2081895663Serge Batalov06/2022
8021(64464^19891-1)/6446395658Serge Batalov06/2022
8022(934^32203-1)/93395652Serge Batalov06/2022
8023(11*10^95641-113)/395642Robert Price01/2017
8024(72330^19681-1)/7232995632Serge Batalov06/2022
8025(13224^23203-1)/1322395624Serge Batalov06/2022
8026(18211^22441-1)/1821095602Serge Batalov06/2022
8027(71975^19681-1)/7197495590Serge Batalov06/2022
8028(13*10^95588+11)/395589Robert Price05/2015
8029Phi(191188,10)/19118995587Maksym Voznyy11/2015
8030(13368^23167-1)/1336795585Serge Batalov06/2022
8031(25874^21661-1)/2587395583Serge Batalov06/2022
80323^200325+7095580Lelio R Paula05/2016
8033(25*10^95574-7)/995575Robert Price12/2014
8034(2^317485-3)/2131395569Lelio R Paula06/2013
80352^317464+3195567Lelio R Paula11/2012
8036(2^317451+2114)/295562Stefano Morozzi09/2020
80377^113073+8295558Lelio R Paula04/2016
8038(24728^21751-1)/2472795552Serge Batalov06/2022
8039(49764^20341-1)/4976395536Serge Batalov06/2022
8040(36155^20959-1)/3615495531Serge Batalov06/2022
8041(7725^24571-1)/772495526Serge Batalov06/2022
8042(20546^22147-1)/2054595510Serge Batalov06/2022
80432^317251+46595503Lelio R Paula03/2016
804419^74684+5895503Lelio R Paula06/2016
8045(2^317250-7)/33995500Lelio R Paula07/2013
80465*10^95498-2195499Robert Price12/2021
8047(21615^22031-1)/2161495495Serge Batalov06/2022
80486^122718-7995494Lelio R Paula05/2016
804922168^20291+20291^2216895485Hans Havermann10/2019
8050(77427^19531-1)/7742695481Serge Batalov06/2022
8051(13026^23203-1)/1302595472Serge Batalov06/2022
80522^317141-11049195469Enzo Doria05/2014
8053(2^317097+3014)/295456Stefano Morozzi09/2020
80542^317094+7630995455Enzo Doria05/2016
80552^317085+9595453Lelio R Paula11/2012
8056(17*10^95451-377)/995452Robert Price11/2017
80572^317057-10955195444Enzo Doria04/2014
80583^200026+2895437Lelio R Paula05/2016
80592^317024+9395434Donovan Johnson06/2008
8060(86*10^95428-437)/995429Robert Price03/2021
806110^95427+19259195428Patrick De Geest05/2021
80642^316999+160595427Lelio R Paula03/2016
8063(2^317000+3210)/295427Stefano Morozzi09/2020
806210^95427-1000195427Robert Price02/2021
80652^316995-11042795426Enzo Doria05/2014
8066(69841^19699-1)/6984095420Serge Batalov06/2022
8067(59242^19993-1)/5924195415Serge Batalov06/2022
806922300^18987+18987^2230095410Hans Havermann06/2020
8068(9478^23993-1)/947795410Serge Batalov06/2022
80702^316937+17795408Lelio R Paula11/2012
80714*10^95407+9195408Robert Price11/2017
80722^316908+191595399Lelio R Paula03/2016
80732^316894+9995395Lelio R Paula11/2012
8074(2^316887+2546)/295393Stefano Morozzi09/2020
80752*10^95374-2195375Robert Price09/2020
80766^122547+1195361Lelio R Paula05/2016
80772^316771+8287595358Lelio R Paula03/2016
8078(15609^22741-1)/1560895358Serge Batalov06/2022
8079(2^316765+3102)/295356Stefano Morozzi09/2020
8080(2267^28411-1)/226695329Serge Batalov06/2022
8081(824^32693-1)/82395328Serge Batalov06/2022
8082(23*10^95326+1)/395327Serge Batalov05/2009
80831*10^95326+5795327Robert Price03/2011
808410^95326-39368795326Patrick De Geest09/2013
8085(3^199803+4)/47953995325Lelio R Paula04/2013
80862^316654-10948195323Enzo Doria04/2014
80878*10^95316+5195317Robert Price05/2017
8088(50^56099+43^56099)/9395309Serge Batalov12/2016
8089(23*2^316559+1)/392595292Lelio R Paula09/2013
8091(71*10^95277-539)/995278Robert Price11/2017
809023422^11691+11691^2342295278Hans Havermann10/2019
809219^74503-5695271Lelio R Paula06/2016
8093(5038^25733-1)/503795267Serge Batalov06/2022
809411^91475-438095262Enzo Doria01/2013
8095(62*10^95251-611)/995252Robert Price05/2017
8096(160090^18301-1)/16008995240Serge Batalov06/2022
8097(173205^18181-1)/17320495238Serge Batalov06/2022
8098(158710^18313-1)/15870995234Serge Batalov06/2022
8099(9979^23813-1)/997895227Serge Batalov06/2022
8100(57376^20011-1)/5737595223Serge Batalov06/2022
8101(2^316321-509203)/6937795218Lelio R Paula06/2013
810226541^3868+3868^2654195216Hans Havermann07/2020
8103(79*10^95214-43)/995215Erik Branger11/2013
8104(7176^24691-1)/717595202Anonymous11/2020
8105(9*2^316233-1)/175195194Lelio R Paula02/2014
81065*2^316213+995191Lelio R Paula08/2014
81072*10^95188-9195189Robert Price04/2020
81082^316205-184816395188Enzo Doria07/2015
81092^316185-278791395182Enzo Doria04/2016
8110(2^316174+3538)/295178Stefano Morozzi09/2020
8111(9787*2^316142-1)/395172Lelio R Paula04/2015
81122^316140-595168Henri Lifchitz02/2006
8113(15185*2^316117-1)/395165Lelio R Paula04/2015
8114(34*10^95153-7)/9/19/1915795149Makoto Morimoto05/2016
81152^316069+7681795147Enzo Doria05/2016
8116(199*10^95134-7)/395136Robert Price02/2017
81172^316027-9730595134Lelio R Paula03/2016
81182^316006-279805195128Enzo Doria04/2016
811924994^6397+6397^2499495127Hans Havermann02/2020
81212^315921-279760395102Enzo Doria04/2016
8120(2^315921+1314)/295102Stefano Morozzi02/2021
81222*10^95095+6395096Robert Price10/2017
81232^315857+129995083Lelio R Paula03/2016
8124(2^315858+2598)/295083Stefano Morozzi09/2020
812614^82955-4395078Lelio R Paula06/2016
8125(8*10^95078-269)/995078Robert Price09/2021
8127(23*10^95074-101)/395075Robert Price04/2021
81282^315827-93307595074Paul Bourdelais04/2021
8129(2*10^95072-17)/395072Robert Price08/2014
8130(286*10^95059-1)/395061Robert Price11/2020
8131(2^315779+1610)/295059Stefano Morozzi09/2020
81322^315775-11154643595058Paul Bourdelais10/2021
813321938^21513+21513^2193895051Hans Havermann09/2020
81342^315727+6595044Lelio R Paula11/2012
81352^315725+188575795043Enzo Doria03/2017
813623277^12058+12058^2327795000Hans Havermann09/2020
81371*10^94983+2194984Robert Price03/2011
813810^94983-71794983Patrick De Geest08/2013
813917^77187-8294975Lelio R Paula07/2016
81403*10^94964+3794965Robert Price10/2017
8141(2^315481-1017)/2062728594962Lelio R Paula06/2013
81422^315423-11032994952Enzo Doria05/2014
814311^91169-723094943Enzo Doria02/2013
81447*10^94938+6194939Robert Price02/2017
81452^315351+102594931Lelio R Paula03/2016
81462^315350-11225394930Enzo Doria06/2014
8147(2^315343+1766)/294928Stefano Morozzi09/2020
8148(2^315343+3066)/294928Stefano Morozzi09/2020
8151((1001327^(15817)+1)/1001328)94906Faysal YAtim10/2010
81502^315268+794906Lelio R Paula10/2012
814911^91133+6294906Lelio R Paula05/2016
8152(2^315264+1558)/294904Stefano Morozzi09/2020
815330^64244+4194897Lelio R Paula08/2012
8154(151*10^94885-7)/994887Robert Price07/2017
81554^157583+2214794875Mike Oakes01/2011
81562^315098+12394854Lelio R Paula11/2012
81573^198791-3494848Robert Price11/2013
81583*2^315067+794846Lelio R Paula08/2014
8159(9*2^315057+1)/7394841Lelio R Paula09/2013
816022576^15875+15875^2257694836Hans Havermann09/2020
8161(16*10^94822+53)/394823Robert Price12/2016
81628*6^121849-794818Lelio R Paula10/2014
8163(85*10^94802+473)/994803Robert Price03/2017
816421767^21852-21852^2176794790Norbert Schneider06/2020
81652^314870-10876194786Enzo Doria03/2014
81665*2^314841-394778Lelio R Paula08/2014
8167(2^314842+550)/294777Stefano Morozzi09/2020
816811738^23289-23289^1173894777Norbert Schneider05/2022
8169(2^314787+2630)/294761Stefano Morozzi09/2020
81706^121772+11394758Lelio R Paula05/2016
8171(2^314740+3642)/294746Stefano Morozzi09/2020
81726^121756-1625394745Enzo Doria02/2013
81732^314718-11279394740Enzo Doria06/2014
81742^314697-184729394734Enzo Doria07/2015
817522836^14065+14065^2283694727Hans Havermann09/2020
81772^314548-24994689Yves Minet02/2012
81765^135469+4294689Lelio R Paula04/2016
8178gcd(V(1137755),5*F(227551)*(F(227551)-1)+1)94676Serge Batalov04/2015
817925773^4712+4712^2577394670Hans Havermann08/2020
8180(2^314485+3614)/294670Stefano Morozzi09/2020
8181(2*10^94604+547)/994604Robert Price10/2017
8182(2^314164+2562)/294573Stefano Morozzi09/2020
81833*2^314152+594570Lelio R Paula08/2014
81842*6^121530-594570Lelio R Paula10/2014
81857*10^94563+8794564Robert Price11/2016
81862^314114-10967794558Enzo Doria04/2014
8187(218389#+240867)/(3*11*811)94557Makoto Morimoto10/2017
81882^314059+7658394542Enzo Doria05/2016
81892^314041-403594536Lelio R Paula03/2016
8190(2^314028+3102)/294532Stefano Morozzi09/2020
8191(2^314012+618)/294527Stefano Morozzi09/2020
8192(7*2^314003-11)/1594524Renaud Lifchitz03/2011
819311^90760-471094517Enzo Doria01/2013
819421675^21796+21796^2167594507Norbert Schneider04/2020
81952^313942+10028024506594506Paul Bourdelais10/2021
8196(7*2^313926-1)/14882194497Lelio R Paula02/2014
819794*10^94493-394495Robert Price11/2016
8198(1000547^15749+1)/100054894492Faysal YAtim12/2008
8199(2^313859+2706)/294481Stefano Morozzi09/2020
8200(F(3*75345)^2+L(3*75345)^2)/494477Henri Lifchitz10/2017
82017^111792-3294476Lelio R Paula04/2016
8202(2^313800+822)/294463Stefano Morozzi01/2021
82039*10^94462-4794463Robert Price11/2021
820411*10^94460+394462Robert Price07/2021
8205(202*10^94441-1)/394443Robert Price05/2020
820611^90680-585094434Enzo Doria01/2013
8207(752^32833-1)/75194432Michael Stocker05/2020
82082^313675-11012594426Enzo Doria04/2014
8209(2999*29^64556-2427)/494410Curtis Bright05/2015
82102^313609-11222594406Enzo Doria06/2014
82112^313584+7290194399Enzo Doria04/2016
8212(2^313567+1310)/294393Stefano Morozzi02/2021
8213(2^313562+730)/294392Stefano Morozzi09/2020
82142^313510-11286594376Enzo Doria06/2014
82157*10^94373+8794374Robert Price11/2016
8216(9^98897+8^98897)/1794371Robert Price12/2012
82172^313453-11470394359Enzo Doria04/2015
82188*10^94357-5194358Robert Price10/2017
821925903^4392+4392^2590394356Hans Havermann09/2020
822031706^945+945^3170694340Hans Havermann09/2020
8221(379*10^94337-1)/994339Robert Price08/2017
82222^313344-313344+194326Robert Price10/2014
8223(2^313313+3662)/294317Stefano Morozzi09/2020
822420^72481-4994300Lelio R Paula05/2016
8225(34*10^94293-259)/994294Robert Price12/2021
822644725!2+12894289Robert Price03/2015
82274*10^94286+994287Robert Price05/2015
822817^76621+2494279Lelio R Paula07/2016
822926274^3875+3875^2627494279Hans Havermann09/2020
82304*10^94270-3394271Robert Price04/2021
82312^313156-11285994270Enzo Doria06/2014
8232(49*10^94262-211)/994263Robert Price06/2022
82336^121130-5994258Lelio R Paula05/2016
82343^197542+2894252Robert Price11/2013
8235(2^313076+3550)/294245Stefano Morozzi09/2020
8236(3^197521+2)/5165594237Lelio R Paula04/2013
82372^313045-595594236Lelio R Paula03/2016
823822099^18358+18358^2209994227Hans Havermann08/2020
8239(67*10^94212+23)/994213Ray Chandler02/2011
82402^312909-186520394195Enzo Doria03/2016
824125013^5830+5830^2501394191Hans Havermann09/2020
82422^312848-14994177Lelio R Paula11/2012
8243(2^312819+3278)/294168Stefano Morozzi02/2021
82444^156403-7759794164Mike Oakes04/2011
824518^75004-8594151Lelio R Paula06/2016
824619^73622-4894145Lelio R Paula06/2016
8247(11^90397-3^90397)/894138Robert Price04/2011
8248(3^197287+5)/1694129Lelio R Paula04/2013
8249(23*10^94123-29)/394124Robert Price03/2022
825024220^7691+7691^2422094119Hans Havermann09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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