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 ?
6751(2^325704+718)/298047Stefano Morozzi09/2020
675223968^12293+12293^2396898021Hans Havermann11/2019
6753(23*2^325583-1)/2198011Lelio R Paula02/2014
6754(7*10^98007-13)/398008Robert Price06/2016
6755(2^325544+1110)/297999Stefano Morozzi09/2020
67562^325512-45995997989Enzo Doria05/2015
6757(2^325492+682)/297983Stefano Morozzi09/2020
6758(3^205354-8)/1797978Lelio R Paula09/2013
67592^325433+7681797966Enzo Doria05/2016
67605*10^97963+8197964Robert Price08/2017
67612^325390-10906197953Enzo Doria04/2014
6762(55*10^97940+323)/997941Robert Price10/2021
676313^87921+2497940Lelio R Paula08/2016
676410^97930-700000197930Robert Price06/2021
6765961^32831-960^3283197926Jean-Louis Charton02/2011
676622600^21499+21499^2260097913Hans Havermann05/2020
67672^325215+1290997900Lelio R Paula07/2016
676822619^21286+21286^2261997898Hans Havermann04/2020
6769(85*10^97876-49)/997877Robert Price12/2020
67707*10^97874-6997875Robert Price01/2017
67715*10^97869-6397870Robert Price04/2021
6773(17^79537+5^79537)/2297865Robert Price06/2013
677215^83212+2297865Lelio R Paula08/2016
67742^325087-10905797861Enzo Doria04/2014
67752^325074+187065797858Enzo Doria05/2016
67772^325066-211197855Yves Minet08/2013
6776CopelandErdos(97855)97855Eric W. Weisstein10/2015
677826660^4677+4677^2666097842Hans Havermann12/2019
677918^77944-8997841Lelio R Paula07/2016
6780119^47136+11897833Norbert Schneider09/2018
67816^125720-1766397830Enzo Doria02/2013
67822^324972-206997827Yves Minet05/2013
67832^324958-469197823Yves Minet05/2019
67842^324944-278831997818Enzo Doria03/2016
678522845^19112+19112^2284597807Hans Havermann10/2019
6786(2^324898+1270)/297804Stefano Morozzi09/2020
67884*10^97799-997800Erik Branger11/2013
67872^324882+57729457597800Lelio R Paula09/2016
67892^324863-186792197794Enzo Doria04/2016
67906^125662-1847397785Enzo Doria03/2013
679112^90604+1197779Lelio R Paula07/2016
6792(29*10^97751+49)/397752Robert Price09/2021
67935^139830+2497737Lelio R Paula04/2016
6794(2^324672+1198)/297736Stefano Morozzi09/2020
67952^324612+115597718Lelio R Paula07/2016
6796(2^324597+3542)/297714Stefano Morozzi09/2020
679719^76404-4497702Lelio R Paula07/2016
67982^324505-298397686Yves Minet04/2011
6799(144^45259+1)/14597684Paul Bourdelais08/2019
6800(31*2^324496-1)/4597683Lelio R Paula02/2014
68016^125488-1784397649Enzo Doria02/2013
6802(2^324350+3198)/297639Stefano Morozzi09/2020
68037^115515-297622Lelio R Paula09/2013
6804(89^50069-1)/8897603Paul Bourdelais08/2017
68056^125418-597595Lelio R Paula11/2014
6806(2^324193+3522)/297592Stefano Morozzi09/2020
6807(2^324172+666)/297586Stefano Morozzi09/2020
68082^324091+11154643597562Paul Bourdelais10/2021
68092^324076+115597557Lelio R Paula07/2016
6810(2^324074+9)/1397555Lelio R Paula10/2013
6811(55459*2^323993+1)/2197536Lelio R Paula07/2014
681213^87557-12^8755797534Jean-Louis Charton12/2008
68132^323946+7393997518Enzo Doria04/2016
68142^323937+186694797515Enzo Doria03/2016
68156^125290-1853397495Enzo Doria03/2013
6816(2^323870+1650)/297495Stefano Morozzi09/2020
68172^323845+10197488Lelio R Paula12/2012
681818^77662+6597487Lelio R Paula07/2016
681922634^20265+20265^2263497479Hans Havermann04/2020
68202^323772+7677197466Enzo Doria05/2016
68212^323765-11221397463Enzo Doria06/2014
682222730^19389+19389^2273097457Hans Havermann02/2020
68232^323720-655597450Lelio R Paula07/2016
68242^323694-186040197442Enzo Doria03/2016
682520^74886+397429Lelio R Paula06/2016
682624476^9561+9561^2447697427Hans Havermann01/2020
6827(2^323623+1766)/297420Stefano Morozzi09/2020
68293*10^97399+7397400Robert Price04/2016
68287^115252-5097400Lelio R Paula07/2016
6830224737#+39358197389Nicolas PALAU12/2016
6831(2^323468+3186)/297374Stefano Morozzi09/2020
6832(2^323456+538)/297370Stefano Morozzi09/2020
683323277^15236+15236^2327797365Hans Havermann07/2020
6835(26*10^97353+31)/397354Robert Price07/2016
6834(2^323403+3510)/297354Stefano Morozzi09/2020
683623756^12519+12519^2375697342Hans Havermann07/2020
683710^97335-400000197335Robert Price07/2021
6838(637*10^97331+11)/997333Robert Price10/2021
683923991^11402+11402^2399197332Hans Havermann07/2020
684061^54517-60^5451797331Jean-Louis Charton09/2005
6841(38*10^97329+187)/997330Robert Price11/2017
684286455!4+897319Robert Price09/2019
684322591^20310+20310^2259197316Hans Havermann06/2020
684425101^7520+7520^2510197297Hans Havermann05/2020
6845p(19982)#/2-102497293Robert Price09/2017
6846(65*10^97288+277)/997289Robert Price08/2021
68476^125021-8597286Lelio R Paula08/2016
68482^323164-4735597283Lelio R Paula07/2016
6849(3^203902+4)/3605101515797276Lelio R Paula09/2013
68512^323054-655597249Lelio R Paula07/2016
685022822^18247+18247^2282297249Hans Havermann02/2020
68529*10^97247-2997248Robert Price05/2017
685324382^9735+9735^2438297244Hans Havermann02/2020
6854(31*10^97242+41)/997243Robert Price04/2015
6855GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
685612^90098-4197233Lelio R Paula07/2016
68572^322928-21692997212Enzo Doria05/2014
68583*10^97205-6197206Robert Price04/2021
6859(7*2^322896-1)/5797201Lelio R Paula02/2014
6860(35*10^97194-341)/997195Robert Price08/2021
6861(2^322897+5)/314610748997193Lelio R Paula10/2013
6862(2^322789+2214)/297169Stefano Morozzi09/2020
68632^322725+7576197150Enzo Doria04/2016
6864(13*2^322686+1)/11997138Lelio R Paula11/2013
686522402^21639+21639^2240297118Hans Havermann07/2020
686623399^14128+14128^2339997108Hans Havermann06/2020
6867(2^322525+2606)/297090Stefano Morozzi09/2020
6868(41*10^97085+373)/997086Robert Price04/2017
6869(2^322473+854)/297074Stefano Morozzi02/2021
68702^322413+7797056Lelio R Paula12/2012
68712^322406+17797054Lelio R Paula12/2012
6872(14*10^97044+31)/997045Robert Price02/2015
68732^322302+25525597023Lelio R Paula07/2016
68742^322196-11309396991Enzo Doria07/2014
6875(2^322169+2690)/296983Stefano Morozzi09/2020
68769*10^96968-4796969Robert Price11/2021
687723109^15668+15668^2310996943Hans Havermann07/2020
68782^322000-186146996932Enzo Doria03/2016
68792^321971-11274796923Enzo Doria06/2014
688023754^12023+12023^2375496917Hans Havermann07/2020
688111^93062-9296915Lelio R Paula06/2016
6882(2^321922+2214)/296908Stefano Morozzi09/2020
6883(2^321900+2086)/296902Stefano Morozzi09/2020
6884(11*2^321841-7)/1596884Renaud Lifchitz03/2011
68853^203051+3496880Lelio R Paula05/2016
68862*10^96867-5196868Robert Price11/2017
6887(2^321779+2618)/296865Stefano Morozzi09/2020
6888(64*10^96863-1)/2796864Serge Batalov05/2010
68892^321716-278693996847Enzo Doria03/2016
689022496^20181+20181^2249696844Hans Havermann03/2020
68912^321701-11305396842Enzo Doria07/2014
68922^321700-2863596842Lelio R Paula06/2016
6893(5*2^321691-1)/2796838Lelio R Paula02/2014
68946*10^96835+1396836Robert Price10/2021
68956^124433-12443396828Robert Price01/2014
68962^321631+6996821Lelio R Paula12/2012
6897(13*2^321606+1)/11996813Lelio R Paula11/2013
6898(46*10^96798-1)/996799Serge Batalov10/2014
6899(59*10^96798+31)/996799Robert Price09/2015
6900(2^321536+2062)/296792Stefano Morozzi09/2020
6901223319#+23122396790Makoto Morimoto02/2016
69022^321519-2863596787Lelio R Paula06/2016
69032^321487-186723796778Enzo Doria03/2016
69042^321461-6396770Lelio R Paula12/2012
69052^321439+12396763Lelio R Paula12/2012
69062^321434+70996762Lelio R Paula02/2013
6907(2^321415+554)/296756Stefano Morozzi09/2020
690814^84413+8996749Lelio R Paula07/2016
6909(28*10^96743+71)/996744Serge Batalov12/2008
691013^86847+9696743Lelio R Paula06/2016
69119*2^321336-796733Lelio R Paula08/2014
6912(209*10^96722-17)/396724Robert Price05/2017
69132^321237-461596702Yves Minet05/2019
69142^321187-115996687Yves Minet11/2012
69152^321182-185008196686Enzo Doria08/2015
691623359^13768+13768^2335996680Hans Havermann06/2020
69172^321116-11282996666Enzo Doria06/2014
69182^321108-10949996664Enzo Doria04/2014
69192^321098+279385996661Enzo Doria03/2016
6920(2^321100+1170)/296661Stefano Morozzi09/2020
69212^321057+409796648Lelio R Paula06/2016
6922(4435*29^66081-4)/796640Curtis Bright05/2015
692322743^17750+17750^2274396640Hans Havermann04/2020
692422882^16679+16679^2288296612Hans Havermann02/2020
692523452^13163+13163^2345296608Hans Havermann02/2020
6926(85*10^96594-373)/996595Robert Price05/2021
6927(2^320863+666)/296590Stefano Morozzi09/2020
6928p(19849)#/2-6496581Robert Price04/2017
69292^320817+18996576Lelio R Paula12/2012
69302^320816-468596576Yves Minet05/2019
6931(361*10^96567-163)/996569Robert Price10/2017
69322^320788-11032796567Enzo Doria05/2014
69332^320764+79396560Lelio R Paula02/2013
6934(2^320752+1842)/296556Stefano Morozzi02/2021
6935(9179*2^320652-1)/22196528Lelio R Paula05/2015
693623288^13947+13947^2328896517Hans Havermann07/2020
69372^320616-7879596516Lelio R Paula03/2016
69382^320612-46193996514Enzo Doria07/2015
693910^96504+98765432196505Robert Price12/2019
694010^96504+7188796505Patrick De Geest02/2020
694122654^18195+18195^2265496505Hans Havermann07/2020
694210^96504-13927796504Patrick De Geest02/2020
69435*2^320431+796461Lelio R Paula08/2014
694419^75431-9096458Lelio R Paula06/2016
6945(2^320386+2814)/296446Stefano Morozzi02/2021
6946(2^320370+3)/6796440Lelio R Paula10/2013
69473*10^96431-1796432Robert Price03/2021
69482^320309+187147796423Enzo Doria05/2016
6949tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
6950(21*2^320252-1)/189596404Lelio R Paula02/2014
69512^320232-17396400Lelio R Paula12/2012
6952175^42975-296395Lelio R Paula10/2017
6953(2^320170+2718)/296381Stefano Morozzi09/2020
695410^96377+19991196378Patrick De Geest12/2016
695510^96377-2000196377Robert Price11/2016
69562^320124-279044996367Enzo Doria03/2016
695710^96366+1919796367Patrick De Geest08/2021
695910^96366-1000000000196366Robert Price04/2021
695810^96366-28736796366Patrick De Geest08/2021
696022488^19255+19255^2248896351Hans Havermann11/2019
696123248^13939+13939^2324896346Hans Havermann11/2019
69632^320043-10877596343Enzo Doria04/2014
696224989^7168+7168^2498996343Hans Havermann11/2019
696410^96338+42493996339Patrick De Geest03/2016
696510^96338-928196338Robert Price09/2015
6966(3*2^320008+1)/796332Lelio R Paula09/2013
696725699^5596+5596^2569996317Hans Havermann07/2020
6968(11*10^96298+529)/996299Robert Price09/2021
696926502^4297+4297^2650296287Hans Havermann07/2020
69702^319838+425796281Lelio R Paula03/2016
69712^319830-1699596279Lelio R Paula03/2016
69726^123713+14396268Lelio R Paula05/2016
6973(28*10^96265-97)/396266Robert Price07/2016
6974103^47825-10296264Norbert Schneider10/2016
6975(2^319777+2082)/296263Stefano Morozzi09/2020
6976(2^319771+3686)/296261Stefano Morozzi09/2020
69772^319713-8196244Lelio R Paula11/2012
6978(55459*2^319706+1)/2016796242Lelio R Paula07/2014
697922834^16393+16393^2283496238Hans Havermann05/2020
69808*10^96236+2796237Robert Price09/2021
698112^89153-4396213Lelio R Paula06/2016
6982(2*10^96195-59)/396195Robert Price05/2017
69839*10^96194-7796195Robert Price08/2020
69842^319545+14796193Lelio R Paula11/2012
698523357^13128+13128^2335796189Hans Havermann02/2020
698625952^5073+5073^2595296160Hans Havermann12/2019
6987(50^56597+1)/5196155Robert Price03/2014
698822313^20374+20374^2231396149Hans Havermann12/2019
698922279^20668+20668^2227996141Hans Havermann11/2019
6990(41*10^96137-59)/996138Robert Price10/2017
69912^319353-11034396135Enzo Doria05/2014
699211^92309-4296130Lelio R Paula05/2016
699314^83869-13^8386996125Jean-Louis Charton01/2009
6994(7*10^96112+143)/396113Robert Price04/2016
699526731^3940+3940^2673196112Hans Havermann07/2020
699622640^17583+17583^2264096109Hans Havermann07/2020
69972^319237+6583596100Lelio R Paula03/2016
69982^319194-184196087Yves Minet03/2013
699923949^10280+10280^2394996084Hans Havermann07/2020
700020^73847-3196078Lelio 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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