PRP Records

Probable Primes Top 10000

(291192 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 ?
80012^324944-278831997818Enzo Doria03/2016
800222845^19112+19112^2284597807Hans Havermann10/2019
8003(2^324898+1270)/297804Stefano Morozzi09/2020
80054*10^97799-997800Erik Branger11/2013
80042^324882+57729457597800Lelio R Paula09/2016
80062^324863-186792197794Enzo Doria04/2016
80076^125662-1847397785Enzo Doria03/2013
800812^90604+1197779Lelio R Paula07/2016
8009(29*10^97751+49)/397752Robert Price09/2021
8010(37108^21391-1)/3710797741Serge Batalov06/2022
80115^139830+2497737Lelio R Paula04/2016
8012(2^324672+1198)/297736Stefano Morozzi09/2020
8013(101*10^97724+7)/997726Robert Price02/2022
80142^324612+115597718Lelio R Paula07/2016
8015(2^324597+3542)/297714Stefano Morozzi09/2020
801619^76404-4497702Lelio R Paula07/2016
8017(5939^25889-1)/593897694Serge Batalov06/2022
80192^324505-298397686Yves Minet04/2011
8018(7740^25121-1)/773997686Serge Batalov06/2022
8020(144^45259+1)/14597684Paul Bourdelais08/2019
8021(31*2^324496-1)/4597683Lelio R Paula02/2014
8022(11234^24109-1)/1123397651Serge Batalov06/2022
80236^125488-1784397649Enzo Doria02/2013
8024(2^324350+3198)/297639Stefano Morozzi09/2020
8025(75638^20011-1)/7563797624Serge Batalov06/2022
80267^115515-297622Lelio R Paula09/2013
8027(15672^23269-1)/1567197613Serge Batalov06/2022
8028(89^50069-1)/8897603Paul Bourdelais08/2017
80296^125418-597595Lelio R Paula11/2014
8030(2^324193+3522)/297592Stefano Morozzi09/2020
8031(2422^28837-1)/242197587Serge Batalov06/2022
8032(2^324172+666)/297586Stefano Morozzi09/2020
80332^324091+11154643597562Paul Bourdelais10/2021
80342^324076+115597557Lelio R Paula07/2016
8035(2^324074+9)/1397555Lelio R Paula10/2013
8036(11*10^97539-71)/397540Robert Price04/2022
8037(55459*2^323993+1)/2197536Lelio R Paula07/2014
803813^87557-12^8755797534Jean-Louis Charton12/2008
80392^323946+7393997518Enzo Doria04/2016
80402^323937+186694797515Enzo Doria03/2016
8041(98339^19531-1)/9833897508Serge Batalov06/2022
80436^125290-1853397495Enzo Doria03/2013
8042(2^323870+1650)/297495Stefano Morozzi09/2020
80442^323845+10197488Lelio R Paula12/2012
804518^77662+6597487Lelio R Paula07/2016
804622634^20265+20265^2263497479Hans Havermann04/2020
8047(5533^26041-1)/553297467Serge Batalov06/2022
80482^323772+7677197466Enzo Doria05/2016
80492^323765-11221397463Enzo Doria06/2014
805022730^19389+19389^2273097457Hans Havermann02/2020
80512^323720-655597450Lelio R Paula07/2016
80522^323694-186040197442Enzo Doria03/2016
805320^74886+397429Lelio R Paula06/2016
805424476^9561+9561^2447697427Hans Havermann01/2020
8055(2^323623+1766)/297420Stefano Morozzi09/2020
8056(3250^27739-1)/324997413Serge Batalov06/2022
80583*10^97399+7397400Robert Price04/2016
80577^115252-5097400Lelio R Paula07/2016
8059(4715^26513-1)/471497392Serge Batalov06/2022
8060224737#+39358197389Nicolas PALAU12/2016
8061(2^323468+3186)/297374Stefano Morozzi09/2020
8062(2^323456+538)/297370Stefano Morozzi09/2020
806323277^15236+15236^2327797365Hans Havermann07/2020
8065(26*10^97353+31)/397354Robert Price07/2016
8064(2^323403+3510)/297354Stefano Morozzi09/2020
806623756^12519+12519^2375697342Hans Havermann07/2020
806710^97335+27164197336Patrick De Geest09/2022
806910^97335-400000197335Robert Price07/2021
806810^97335-9819397335Patrick De Geest09/2022
8070(637*10^97331+11)/997333Robert Price10/2021
807123991^11402+11402^2399197332Hans Havermann07/2020
807261^54517-60^5451797331Jean-Louis Charton09/2005
8073(38*10^97329+187)/997330Robert Price11/2017
8074(31147^21661-1)/3114697328Serge Batalov06/2022
807586455!4+897319Robert Price09/2019
807622591^20310+20310^2259197316Hans Havermann06/2020
80772^323261-43117397312Harrison Mesh06/2022
8078(3996^27017-1)/399597302Serge Batalov06/2022
807925101^7520+7520^2510197297Hans Havermann05/2020
8080(233*10^97294+7)/397296Robert Price03/2022
8081p(19982)#/2-102497293Robert Price09/2017
8082(65*10^97288+277)/997289Robert Price08/2021
80836^125021-8597286Lelio R Paula08/2016
80842^323164-4735597283Lelio R Paula07/2016
8085(3^203902+4)/3605101515797276Lelio R Paula09/2013
80862^323054-655597249Lelio R Paula07/2016
808722822^18247+18247^2282297249Hans Havermann02/2020
80889*10^97247-2997248Robert Price05/2017
808924382^9735+9735^2438297244Hans Havermann02/2020
8090(31*10^97242+41)/997243Robert Price04/2015
8091GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
809212^90098-4197233Lelio R Paula07/2016
80932^322928-21692997212Enzo Doria05/2014
8094(16731^23017-1)/1673097209Serge Batalov06/2022
80953*10^97205-6197206Robert Price04/2021
8096(7*2^322896-1)/5797201Lelio R Paula02/2014
8097(35*10^97194-341)/997195Robert Price08/2021
8098(4872^26357-1)/487197194Serge Batalov06/2022
8099(2^322897+5)/314610748997193Lelio R Paula10/2013
8100(796*10^97183-31)/997185Robert Price07/2022
8101(2^322789+2214)/297169Stefano Morozzi09/2020
81022^322725+7576197150Enzo Doria04/2016
8103(13*2^322686+1)/11997138Lelio R Paula11/2013
8104(2175^29101-1)/217497121Serge Batalov06/2022
810522402^21639+21639^2240297118Hans Havermann07/2020
810623399^14128+14128^2339997108Hans Havermann06/2020
8107(2892^28057-1)/289197108Serge Batalov06/2022
8108(9578^24391-1)/957797104Serge Batalov06/2022
8109(2^322525+2606)/297090Stefano Morozzi09/2020
8110(9563^24391-1)/956297087Serge Batalov06/2022
8111(41*10^97085+373)/997086Robert Price04/2017
8112(2^322473+854)/297074Stefano Morozzi02/2021
81132^322413+7797056Lelio R Paula12/2012
81142^322406+17797054Lelio R Paula12/2012
8115(349^38167-1)/34897050Serge Batalov06/2022
8116(14*10^97044+31)/997045Robert Price02/2015
81172^322302+25525597023Lelio R Paula07/2016
8118(1302^31147-1)/130197008Serge Batalov06/2022
81192^322196-11309396991Enzo Doria07/2014
8120(2^322169+2690)/296983Stefano Morozzi09/2020
8121(49*10^96980+221)/996981Robert Price02/2022
81229*10^96968-4796969Robert Price11/2021
8123(5895^25717-1)/589496962Serge Batalov06/2022
8124(27473^21841-1)/2747296946Serge Batalov06/2022
812523109^15668+15668^2310996943Hans Havermann07/2020
81262^322000-186146996932Enzo Doria03/2016
81272^321971-11274796923Enzo Doria06/2014
812823754^12023+12023^2375496917Hans Havermann07/2020
812911^93062-9296915Lelio R Paula06/2016
8130(37871^21169-1)/3787096914Serge Batalov06/2022
8131(2^321922+2214)/296908Stefano Morozzi09/2020
8132(2^321900+2086)/296902Stefano Morozzi09/2020
8133(11*2^321841-7)/1596884Renaud Lifchitz03/2011
81343^203051+3496880Lelio R Paula05/2016
81352*10^96867-5196868Robert Price11/2017
8136(2^321779+2618)/296865Stefano Morozzi09/2020
8137(64*10^96863-1)/2796864Serge Batalov05/2010
81382^321716-278693996847Enzo Doria03/2016
813922496^20181+20181^2249696844Hans Havermann03/2020
81402^321701-11305396842Enzo Doria07/2014
81412^321700-2863596842Lelio R Paula06/2016
8142(5*2^321691-1)/2796838Lelio R Paula02/2014
81436*10^96835+1396836Robert Price10/2021
81446^124433-12443396828Robert Price01/2014
81452^321631+6996821Lelio R Paula12/2012
8146(27109^21841-1)/2710896820Serge Batalov06/2022
8147(13*2^321606+1)/11996813Lelio R Paula11/2013
8148(5052^26141-1)/505196809Serge Batalov06/2022
8149(46*10^96798-1)/996799Serge Batalov10/2014
8150(59*10^96798+31)/996799Robert Price09/2015
8151(2^321536+2062)/296792Stefano Morozzi09/2020
8152223319#+23122396790Makoto Morimoto02/2016
81532^321519-2863596787Lelio R Paula06/2016
81542^321487-186723796778Enzo Doria03/2016
81552^321461-6396770Lelio R Paula12/2012
8156(16053^23011-1)/1605296770Serge Batalov06/2022
81572^321439+12396763Lelio R Paula12/2012
81582^321434+70996762Lelio R Paula02/2013
8159(2^321415+554)/296756Stefano Morozzi09/2020
816014^84413+8996749Lelio R Paula07/2016
8161(28*10^96743+71)/996744Serge Batalov12/2008
816213^86847+9696743Lelio R Paula06/2016
81639*2^321336-796733Lelio R Paula08/2014
8164(209*10^96722-17)/396724Robert Price05/2017
8165(54163^20431-1)/5416296710Serge Batalov06/2022
81662^321237-461596702Yves Minet05/2019
8167(27273^21799-1)/2727296691Serge Batalov06/2022
81682^321187-115996687Yves Minet11/2012
81692^321182-185008196686Enzo Doria08/2015
817123359^13768+13768^2335996680Hans Havermann06/2020
8170(65630^20071-1)/6562996680Serge Batalov06/2022
81722^321116-11282996666Enzo Doria06/2014
81732^321108-10949996664Enzo Doria04/2014
81742^321098+279385996661Enzo Doria03/2016
8175(2^321100+1170)/296661Stefano Morozzi09/2020
81762^321057+409796648Lelio R Paula06/2016
8177(4435*29^66081-4)/796640Curtis Bright05/2015
817822743^17750+17750^2274396640Hans Havermann04/2020
817922882^16679+16679^2288296612Hans Havermann02/2020
818023452^13163+13163^2345296608Hans Havermann02/2020
8181(1042^32009-1)/104196596Serge Batalov06/2022
8182(85*10^96594-373)/996595Robert Price05/2021
8183(2^320863+666)/296590Stefano Morozzi09/2020
8184p(19849)#/2-6496581Robert Price04/2017
81852^320817+18996576Lelio R Paula12/2012
81862^320816-468596576Yves Minet05/2019
8188(361*10^96567-163)/996569Robert Price10/2017
8187(19*10^96568+137)/396569Robert Price03/2022
81892^320788-11032796567Enzo Doria05/2014
8190(3065^27697-1)/306496561Serge Batalov06/2022
81912^320764+79396560Lelio R Paula02/2013
8192(2^320752+1842)/296556Stefano Morozzi02/2021
8193(48331^20611-1)/4833096542Serge Batalov06/2022
8194(50595^20521-1)/5059496529Serge Batalov06/2022
8195(9179*2^320652-1)/22196528Lelio R Paula05/2015
819623288^13947+13947^2328896517Hans Havermann07/2020
81972^320616-7879596516Lelio R Paula03/2016
81982^320612-46193996514Enzo Doria07/2015
8199(21245^22303-1)/2124496507Serge Batalov06/2022
820010^96504+98765432196505Robert Price12/2019
820110^96504+7188796505Patrick De Geest02/2020
820222654^18195+18195^2265496505Hans Havermann07/2020
820310^96504-13927796504Patrick De Geest02/2020
8204(218^41263-1)/21796490Serge Batalov06/2022
8205(47220^20641-1)/4721996474Serge Batalov06/2022
82065*2^320431+796461Lelio R Paula08/2014
820719^75431-9096458Lelio R Paula06/2016
8208(11853^23677-1)/1185296452Serge Batalov06/2022
8209(2^320386+2814)/296446Stefano Morozzi02/2021
8210(2^320370+3)/6796440Lelio R Paula10/2013
82113*10^96431-1796432Robert Price03/2021
82122^320309+187147796423Enzo Doria05/2016
8213(10412^24001-1)/1041196421Serge Batalov06/2022
8214tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
8215(29*10^96407-23)/396408Robert Price03/2022
8216(21*2^320252-1)/189596404Lelio R Paula02/2014
82172^320232-17396400Lelio R Paula12/2012
8218175^42975-296395Lelio R Paula10/2017
8219(2^320170+2718)/296381Stefano Morozzi09/2020
822010^96377+19991196378Patrick De Geest12/2016
822110^96377-2000196377Robert Price11/2016
8222(18079^22639-1)/1807896374Serge Batalov06/2022
82242^320124-279044996367Enzo Doria03/2016
822310^96366+1919796367Patrick De Geest08/2021
822610^96366-1000000000196366Robert Price04/2021
822510^96366-28736796366Patrick De Geest08/2021
8227(26351^21799-1)/2635096365Serge Batalov06/2022
822822488^19255+19255^2248896351Hans Havermann11/2019
822923248^13939+13939^2324896346Hans Havermann11/2019
8230(5928^25537-1)/592796345Serge Batalov06/2022
82322^320043-10877596343Enzo Doria04/2014
823124989^7168+7168^2498996343Hans Havermann11/2019
823310^96338+42493996339Patrick De Geest03/2016
823410^96338-928196338Robert Price09/2015
8235(8527^24509-1)/852696336Serge Batalov06/2022
8236(3*2^320008+1)/796332Lelio R Paula09/2013
8237(2444^28433-1)/244396331Serge Batalov06/2022
8238(48690^20551-1)/4868996327Serge Batalov06/2022
8239(61935^20101-1)/6193496318Serge Batalov06/2022
824025699^5596+5596^2569996317Hans Havermann07/2020
8241(11*10^96298+529)/996299Robert Price09/2021
824326502^4297+4297^2650296287Hans Havermann07/2020
8242(54180^20341-1)/5417996287Serge Batalov06/2022
82442^319838+425796281Lelio R Paula03/2016
82452^319830-1699596279Lelio R Paula03/2016
82466^123713+14396268Lelio R Paula05/2016
8247(28*10^96265-97)/396266Robert Price07/2016
8248(3799^26893-1)/379896265Serge Batalov06/2022
8250103^47825-10296264Norbert Schneider10/2016
8249(54041^20341-1)/5404096264Serge Batalov06/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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