PRP Records

Probable Primes Top 10000

(280932 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 ?
57517^116240-116240^798235Norbert Schneider05/2017
575217^79826-7898222Lelio R Paula08/2016
57532^326268-80998217Yves Minet04/2011
575422659^21590+21590^2265998210Hans Havermann10/2019
575522268^22587-22587^2226898202Norbert Schneider08/2020
5756(418*10^98199+23)/998201Robert Price08/2017
575712*10^98198-798200Robert Price11/2017
575815^83496-7698199Lelio R Paula08/2016
5759(10223*2^326179+1)/612598190Lelio R Paula07/2014
57609*5^140471-498186Lelio R Paula11/2014
576122774^20455+20455^2277498175Hans Havermann07/2020
57622^326069-238398157Yves Minet10/2013
57632^325973+118598128Lelio R Paula07/2016
5764(25*2^325949-1)/1798121Lelio R Paula02/2014
57652^325945-184726998120Enzo Doria07/2015
57668*10^98111-6798112Robert Price10/2017
5767(2^325902+1138)/298106Stefano Morozzi09/2020
57682^325866+1598096Lelio R Paula12/2012
576922591^21952+21952^2259198079Hans Havermann02/2020
57702^325765+197430598066Enzo Doria06/2016
57712^325733-5869598056Lelio R Paula07/2016
57722^325717-364598051Lelio R Paula07/2016
5773(2^325704+718)/298047Stefano Morozzi09/2020
577423968^12293+12293^2396898021Hans Havermann11/2019
5775(23*2^325583-1)/2198011Lelio R Paula02/2014
5776(7*10^98007-13)/398008Robert Price06/2016
5777(2^325544+1110)/297999Stefano Morozzi09/2020
57782^325512-45995997989Enzo Doria05/2015
5779(2^325492+682)/297983Stefano Morozzi09/2020
5780(3^205354-8)/1797978Lelio R Paula09/2013
57812^325433+7681797966Enzo Doria05/2016
57825*10^97963+8197964Robert Price08/2017
57832^325390-10906197953Enzo Doria04/2014
578413^87921+2497940Lelio R Paula08/2016
5785961^32831-960^3283197926Jean-Louis Charton02/2011
578622600^21499+21499^2260097913Hans Havermann05/2020
57872^325215+1290997900Lelio R Paula07/2016
578822619^21286+21286^2261997898Hans Havermann04/2020
5789(85*10^97876-49)/997877Robert Price12/2020
57907*10^97874-6997875Robert Price01/2017
57915*10^97869-6397870Robert Price04/2021
5793(17^79537+5^79537)/2297865Robert Price06/2013
579215^83212+2297865Lelio R Paula08/2016
57942^325087-10905797861Enzo Doria04/2014
57952^325074+187065797858Enzo Doria05/2016
57972^325066-211197855Yves Minet08/2013
5796CopelandErdos(97855)97855Eric W. Weisstein10/2015
579826660^4677+4677^2666097842Hans Havermann12/2019
579918^77944-8997841Lelio R Paula07/2016
5800119^47136+11897833Norbert Schneider09/2018
58016^125720-1766397830Enzo Doria02/2013
58022^324972-206997827Yves Minet05/2013
58032^324958-469197823Yves Minet05/2019
58042^324944-278831997818Enzo Doria03/2016
580522845^19112+19112^2284597807Hans Havermann10/2019
5806(2^324898+1270)/297804Stefano Morozzi09/2020
58084*10^97799-997800Erik Branger11/2013
58072^324882+57729457597800Lelio R Paula09/2016
58092^324863-186792197794Enzo Doria04/2016
58106^125662-1847397785Enzo Doria03/2013
581112^90604+1197779Lelio R Paula07/2016
58125^139830+2497737Lelio R Paula04/2016
5813(2^324672+1198)/297736Stefano Morozzi09/2020
58142^324612+115597718Lelio R Paula07/2016
5815(2^324597+3542)/297714Stefano Morozzi09/2020
581619^76404-4497702Lelio R Paula07/2016
58172^324505-298397686Yves Minet04/2011
5818(144^45259+1)/14597684Paul Bourdelais08/2019
5819(31*2^324496-1)/4597683Lelio R Paula02/2014
58206^125488-1784397649Enzo Doria02/2013
5821(2^324350+3198)/297639Stefano Morozzi09/2020
58227^115515-297622Lelio R Paula09/2013
5823(89^50069-1)/8897603Paul Bourdelais08/2017
58246^125418-597595Lelio R Paula11/2014
5825(2^324193+3522)/297592Stefano Morozzi09/2020
5826(2^324172+666)/297586Stefano Morozzi09/2020
58272^324076+115597557Lelio R Paula07/2016
5828(2^324074+9)/1397555Lelio R Paula10/2013
5829(55459*2^323993+1)/2197536Lelio R Paula07/2014
583013^87557-12^8755797534Jean-Louis Charton12/2008
58312^323946+7393997518Enzo Doria04/2016
58322^323937+186694797515Enzo Doria03/2016
58346^125290-1853397495Enzo Doria03/2013
5833(2^323870+1650)/297495Stefano Morozzi09/2020
58352^323845+10197488Lelio R Paula12/2012
583618^77662+6597487Lelio R Paula07/2016
583722634^20265+20265^2263497479Hans Havermann04/2020
58382^323772+7677197466Enzo Doria05/2016
58392^323765-11221397463Enzo Doria06/2014
584022730^19389+19389^2273097457Hans Havermann02/2020
58412^323720-655597450Lelio R Paula07/2016
58422^323694-186040197442Enzo Doria03/2016
584320^74886+397429Lelio R Paula06/2016
584424476^9561+9561^2447697427Hans Havermann01/2020
5845(2^323623+1766)/297420Stefano Morozzi09/2020
58473*10^97399+7397400Robert Price04/2016
58467^115252-5097400Lelio R Paula07/2016
5848224737#+39358197389Nicolas PALAU12/2016
5849(2^323468+3186)/297374Stefano Morozzi09/2020
5850(2^323456+538)/297370Stefano Morozzi09/2020
585123277^15236+15236^2327797365Hans Havermann07/2020
5853(26*10^97353+31)/397354Robert Price07/2016
5852(2^323403+3510)/297354Stefano Morozzi09/2020
585423756^12519+12519^2375697342Hans Havermann07/2020
585523991^11402+11402^2399197332Hans Havermann07/2020
585661^54517-60^5451797331Jean-Louis Charton09/2005
5857(38*10^97329+187)/997330Robert Price11/2017
585886455!4+897319Robert Price09/2019
585922591^20310+20310^2259197316Hans Havermann06/2020
586025101^7520+7520^2510197297Hans Havermann05/2020
5861p(19982)#/2-102497293Robert Price09/2017
58626^125021-8597286Lelio R Paula08/2016
58632^323164-4735597283Lelio R Paula07/2016
5864(3^203902+4)/3605101515797276Lelio R Paula09/2013
58652^323054-655597249Lelio R Paula07/2016
586622822^18247+18247^2282297249Hans Havermann02/2020
58679*10^97247-2997248Robert Price05/2017
586824382^9735+9735^2438297244Hans Havermann02/2020
5869(31*10^97242+41)/997243Robert Price04/2015
5870GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
587112^90098-4197233Lelio R Paula07/2016
58722^322928-21692997212Enzo Doria05/2014
5873(7*2^322896-1)/5797201Lelio R Paula02/2014
5874(2^322897+5)/314610748997193Lelio R Paula10/2013
5875(2^322789+2214)/297169Stefano Morozzi09/2020
58762^322725+7576197150Enzo Doria04/2016
5877(13*2^322686+1)/11997138Lelio R Paula11/2013
587822402^21639+21639^2240297118Hans Havermann07/2020
587923399^14128+14128^2339997108Hans Havermann06/2020
5880(2^322525+2606)/297090Stefano Morozzi09/2020
5881(41*10^97085+373)/997086Robert Price04/2017
5882(2^322473+854)/297074Stefano Morozzi02/2021
58832^322413+7797056Lelio R Paula12/2012
58842^322406+17797054Lelio R Paula12/2012
5885(14*10^97044+31)/997045Robert Price02/2015
58862^322302+25525597023Lelio R Paula07/2016
58872^322196-11309396991Enzo Doria07/2014
5888(2^322169+2690)/296983Stefano Morozzi09/2020
588923109^15668+15668^2310996943Hans Havermann07/2020
58902^322000-186146996932Enzo Doria03/2016
58912^321971-11274796923Enzo Doria06/2014
589223754^12023+12023^2375496917Hans Havermann07/2020
589311^93062-9296915Lelio R Paula06/2016
5894(2^321922+2214)/296908Stefano Morozzi09/2020
5895(2^321900+2086)/296902Stefano Morozzi09/2020
5896(11*2^321841-7)/1596884Renaud Lifchitz03/2011
58973^203051+3496880Lelio R Paula05/2016
58982*10^96867-5196868Robert Price11/2017
5899(2^321779+2618)/296865Stefano Morozzi09/2020
5900(64*10^96863-1)/2796864Serge Batalov05/2010
59012^321716-278693996847Enzo Doria03/2016
590222496^20181+20181^2249696844Hans Havermann03/2020
59042^321701-11305396842Enzo Doria07/2014
59032^321700-2863596842Lelio R Paula06/2016
5905(5*2^321691-1)/2796838Lelio R Paula02/2014
59066^124433-12443396828Robert Price01/2014
59072^321631+6996821Lelio R Paula12/2012
5908(13*2^321606+1)/11996813Lelio R Paula11/2013
5909(46*10^96798-1)/996799Serge Batalov10/2014
5910(59*10^96798+31)/996799Robert Price09/2015
5911(2^321536+2062)/296792Stefano Morozzi09/2020
5912223319#+23122396790Makoto Morimoto02/2016
59132^321519-2863596787Lelio R Paula06/2016
59142^321487-186723796778Enzo Doria03/2016
59152^321461-6396770Lelio R Paula12/2012
59162^321439+12396763Lelio R Paula12/2012
59172^321434+70996762Lelio R Paula02/2013
5918(2^321415+554)/296756Stefano Morozzi09/2020
591914^84413+8996749Lelio R Paula07/2016
5920(28*10^96743+71)/996744Serge Batalov12/2008
592113^86847+9696743Lelio R Paula06/2016
59229*2^321336-796733Lelio R Paula08/2014
5923(209*10^96722-17)/396724Robert Price05/2017
59242^321237-461596702Yves Minet05/2019
59252^321187-115996687Yves Minet11/2012
59262^321182-185008196686Enzo Doria08/2015
592723359^13768+13768^2335996680Hans Havermann06/2020
59282^321116-11282996666Enzo Doria06/2014
59292^321108-10949996664Enzo Doria04/2014
59312^321098+279385996661Enzo Doria03/2016
5930(2^321100+1170)/296661Stefano Morozzi09/2020
59322^321057+409796648Lelio R Paula06/2016
5933(4435*29^66081-4)/796640Curtis Bright05/2015
593422743^17750+17750^2274396640Hans Havermann04/2020
593522882^16679+16679^2288296612Hans Havermann02/2020
593623452^13163+13163^2345296608Hans Havermann02/2020
5937(2^320863+666)/296590Stefano Morozzi09/2020
5938p(19849)#/2-6496581Robert Price04/2017
59402^320817+18996576Lelio R Paula12/2012
59392^320816-468596576Yves Minet05/2019
5941(361*10^96567-163)/996569Robert Price10/2017
59422^320788-11032796567Enzo Doria05/2014
59432^320764+79396560Lelio R Paula02/2013
5944(2^320752+1842)/296556Stefano Morozzi02/2021
5945(9179*2^320652-1)/22196528Lelio R Paula05/2015
594623288^13947+13947^2328896517Hans Havermann07/2020
59472^320616-7879596516Lelio R Paula03/2016
59482^320612-46193996514Enzo Doria07/2015
594910^96504+98765432196505Robert Price12/2019
595010^96504+7188796505Patrick De Geest02/2020
595122654^18195+18195^2265496505Hans Havermann07/2020
595210^96504-13927796504Patrick De Geest02/2020
59535*2^320431+796461Lelio R Paula08/2014
595419^75431-9096458Lelio R Paula06/2016
5955(2^320386+2814)/296446Stefano Morozzi02/2021
5956(2^320370+3)/6796440Lelio R Paula10/2013
59573*10^96431-1796432Robert Price03/2021
59582^320309+187147796423Enzo Doria05/2016
5959tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
5960(21*2^320252-1)/189596404Lelio R Paula02/2014
59612^320232-17396400Lelio R Paula12/2012
5962175^42975-296395Lelio R Paula10/2017
5963(2^320170+2718)/296381Stefano Morozzi09/2020
596410^96377+19991196378Patrick De Geest12/2016
596510^96377-2000196377Robert Price11/2016
59662^320124-279044996367Enzo Doria03/2016
596722488^19255+19255^2248896351Hans Havermann11/2019
596823248^13939+13939^2324896346Hans Havermann11/2019
59702^320043-10877596343Enzo Doria04/2014
596924989^7168+7168^2498996343Hans Havermann11/2019
597110^96338+42493996339Patrick De Geest03/2016
597210^96338-928196338Robert Price09/2015
5973(3*2^320008+1)/796332Lelio R Paula09/2013
597425699^5596+5596^2569996317Hans Havermann07/2020
597526502^4297+4297^2650296287Hans Havermann07/2020
59762^319838+425796281Lelio R Paula03/2016
59772^319830-1699596279Lelio R Paula03/2016
59786^123713+14396268Lelio R Paula05/2016
5979(28*10^96265-97)/396266Robert Price07/2016
5980103^47825-10296264Norbert Schneider10/2016
5981(2^319777+2082)/296263Stefano Morozzi09/2020
5982(2^319771+3686)/296261Stefano Morozzi09/2020
59832^319713-8196244Lelio R Paula11/2012
5984(55459*2^319706+1)/2016796242Lelio R Paula07/2014
598522834^16393+16393^2283496238Hans Havermann05/2020
598612^89153-4396213Lelio R Paula06/2016
5988(2*10^96195-59)/396195Robert Price05/2017
59879*10^96194-7796195Robert Price08/2020
59892^319545+14796193Lelio R Paula11/2012
599023357^13128+13128^2335796189Hans Havermann02/2020
599125952^5073+5073^2595296160Hans Havermann12/2019
5992(50^56597+1)/5196155Robert Price03/2014
599322313^20374+20374^2231396149Hans Havermann12/2019
599422279^20668+20668^2227996141Hans Havermann11/2019
5995(41*10^96137-59)/996138Robert Price10/2017
59962^319353-11034396135Enzo Doria05/2014
599711^92309-4296130Lelio R Paula05/2016
599814^83869-13^8386996125Jean-Louis Charton01/2009
5999(7*10^96112+143)/396113Robert Price04/2016
600026731^3940+3940^2673196112Hans Havermann07/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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