PRP Records

Probable Primes Top 10000

(277054 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 ?
525126167^5794+5794^2616798466Hans Havermann01/2020
5252(6883*2^327047-1)/7798453Lelio R Paula05/2015
5253(71*10^98446+1)/998447Serge Batalov11/2010
525413^88363+9498432Lelio R Paula08/2016
525548^58543-47^5854398425Jean-Louis Charton11/2005
52566^126481+4198422Lelio R Paula08/2016
525778*10^98413-798415Robert Price05/2017
525822634^22263+22263^2263498404Hans Havermann07/2020
52597^116416+4698383Lelio R Paula08/2016
52607^116407-2498376Lelio R Paula07/2016
5261439^37228+37228^43998374Norbert Schneider08/2018
52622^326782-186067198372Enzo Doria03/2016
526317^79948+5898372Lelio R Paula08/2016
526422499^22602-22602^2249998368Norbert Schneider08/2020
52653^206143-9898356Lelio R Paula08/2016
52668*5^140705+798350Lelio R Paula11/2014
5267(2^326632+1662)/298326Stefano Morozzi09/2020
52682^326585+1198312Lelio R Paula12/2012
52692^326582-45916198311Enzo Doria05/2015
5271(2^326548+9)/598301Lelio R Paula10/2013
5270(2^326549+18)/1098301Stefano Morozzi03/2020
52722^326538+7165998298Enzo Doria04/2016
5273(2^326520+2082)/298293Stefano Morozzi09/2020
5274(2^326521+1002)/298293Stefano Morozzi09/2020
527515^83575-5898292Lelio R Paula08/2016
527610^98288+398289Robert Price03/2011
527710^98288-11701798288Patrick De Geest11/2011
5278(44*10^98284-719)/998285Robert Price12/2017
527923466^15419+15419^2346698277Hans Havermann02/2020
52802^326421-279757398263Enzo Doria04/2016
52812^326401+1609598257Lelio R Paula07/2016
52827^116240-116240^798235Norbert Schneider05/2017
528317^79826-7898222Lelio R Paula08/2016
52842^326268-80998217Yves Minet04/2011
528522659^21590+21590^2265998210Hans Havermann10/2019
528622268^22587-22587^2226898202Norbert Schneider08/2020
5287(418*10^98199+23)/998201Robert Price08/2017
528812*10^98198-798200Robert Price11/2017
528915^83496-7698199Lelio R Paula08/2016
5290(10223*2^326179+1)/612598190Lelio R Paula07/2014
52919*5^140471-498186Lelio R Paula11/2014
529222774^20455+20455^2277498175Hans Havermann07/2020
52932^326069-238398157Yves Minet10/2013
52942^325973+118598128Lelio R Paula07/2016
5295(25*2^325949-1)/1798121Lelio R Paula02/2014
52962^325945-184726998120Enzo Doria07/2015
52978*10^98111-6798112Robert Price10/2017
5298(2^325902+1138)/298106Stefano Morozzi09/2020
52992^325866+1598096Lelio R Paula12/2012
530022591^21952+21952^2259198079Hans Havermann02/2020
53012^325765+197430598066Enzo Doria06/2016
53022^325733-5869598056Lelio R Paula07/2016
53032^325717-364598051Lelio R Paula07/2016
5304(2^325704+718)/298047Stefano Morozzi09/2020
530523968^12293+12293^2396898021Hans Havermann11/2019
5306(23*2^325583-1)/2198011Lelio R Paula02/2014
5307(7*10^98007-13)/398008Robert Price06/2016
5308(2^325544+1110)/297999Stefano Morozzi09/2020
53092^325512-45995997989Enzo Doria05/2015
5310(2^325492+682)/297983Stefano Morozzi09/2020
5311(3^205354-8)/1797978Lelio R Paula09/2013
53122^325433+7681797966Enzo Doria05/2016
53135*10^97963+8197964Robert Price08/2017
53142^325390-10906197953Enzo Doria04/2014
531513^87921+2497940Lelio R Paula08/2016
5316961^32831-960^3283197926Jean-Louis Charton02/2011
531722600^21499+21499^2260097913Hans Havermann05/2020
53182^325215+1290997900Lelio R Paula07/2016
531922619^21286+21286^2261997898Hans Havermann04/2020
5320(85*10^97876-49)/997877Robert Price12/2020
53217*10^97874-6997875Robert Price01/2017
5323(17^79537+5^79537)/2297865Robert Price06/2013
532215^83212+2297865Lelio R Paula08/2016
53242^325087-10905797861Enzo Doria04/2014
53252^325074+187065797858Enzo Doria05/2016
53272^325066-211197855Yves Minet08/2013
5326CopelandErdos(97855)97855Eric W. Weisstein10/2015
532826660^4677+4677^2666097842Hans Havermann12/2019
532918^77944-8997841Lelio R Paula07/2016
5330119^47136+11897833Norbert Schneider09/2018
53316^125720-1766397830Enzo Doria02/2013
53322^324972-206997827Yves Minet05/2013
53332^324958-469197823Yves Minet05/2019
53342^324944-278831997818Enzo Doria03/2016
533522845^19112+19112^2284597807Hans Havermann10/2019
5336(2^324898+1270)/297804Stefano Morozzi09/2020
53384*10^97799-997800Erik Branger11/2013
53372^324882+57729457597800Lelio R Paula09/2016
53392^324863-186792197794Enzo Doria04/2016
53406^125662-1847397785Enzo Doria03/2013
534112^90604+1197779Lelio R Paula07/2016
53425^139830+2497737Lelio R Paula04/2016
5343(2^324672+1198)/297736Stefano Morozzi09/2020
53442^324612+115597718Lelio R Paula07/2016
5345(2^324597+3542)/297714Stefano Morozzi09/2020
534619^76404-4497702Lelio R Paula07/2016
53472^324505-298397686Yves Minet04/2011
5348(144^45259+1)/14597684Paul Bourdelais08/2019
5349(31*2^324496-1)/4597683Lelio R Paula02/2014
53506^125488-1784397649Enzo Doria02/2013
5351(2^324350+3198)/297639Stefano Morozzi09/2020
53527^115515-297622Lelio R Paula09/2013
5353(89^50069-1)/8897603Paul Bourdelais08/2017
53546^125418-597595Lelio R Paula11/2014
5355(2^324193+3522)/297592Stefano Morozzi09/2020
5356(2^324172+666)/297586Stefano Morozzi09/2020
53572^324076+115597557Lelio R Paula07/2016
5358(2^324074+9)/1397555Lelio R Paula10/2013
5359(55459*2^323993+1)/2197536Lelio R Paula07/2014
536013^87557-12^8755797534Jean-Louis Charton12/2008
53612^323946+7393997518Enzo Doria04/2016
53622^323937+186694797515Enzo Doria03/2016
53646^125290-1853397495Enzo Doria03/2013
5363(2^323870+1650)/297495Stefano Morozzi09/2020
53652^323845+10197488Lelio R Paula12/2012
536618^77662+6597487Lelio R Paula07/2016
536722634^20265+20265^2263497479Hans Havermann04/2020
53682^323772+7677197466Enzo Doria05/2016
53692^323765-11221397463Enzo Doria06/2014
537022730^19389+19389^2273097457Hans Havermann02/2020
53712^323720-655597450Lelio R Paula07/2016
53722^323694-186040197442Enzo Doria03/2016
537320^74886+397429Lelio R Paula06/2016
537424476^9561+9561^2447697427Hans Havermann01/2020
5375(2^323623+1766)/297420Stefano Morozzi09/2020
53773*10^97399+7397400Robert Price04/2016
53767^115252-5097400Lelio R Paula07/2016
5378224737#+39358197389Nicolas PALAU12/2016
5379(2^323468+3186)/297374Stefano Morozzi09/2020
5380(2^323456+538)/297370Stefano Morozzi09/2020
538123277^15236+15236^2327797365Hans Havermann07/2020
5383(26*10^97353+31)/397354Robert Price07/2016
5382(2^323403+3510)/297354Stefano Morozzi09/2020
538423756^12519+12519^2375697342Hans Havermann07/2020
538523991^11402+11402^2399197332Hans Havermann07/2020
538661^54517-60^5451797331Jean-Louis Charton09/2005
5387(38*10^97329+187)/997330Robert Price11/2017
538886455!4+897319Robert Price09/2019
538922591^20310+20310^2259197316Hans Havermann06/2020
539025101^7520+7520^2510197297Hans Havermann05/2020
5391p(19982)#/2-102497293Robert Price09/2017
53926^125021-8597286Lelio R Paula08/2016
53932^323164-4735597283Lelio R Paula07/2016
5394(3^203902+4)/3605101515797276Lelio R Paula09/2013
53952^323054-655597249Lelio R Paula07/2016
539622822^18247+18247^2282297249Hans Havermann02/2020
53979*10^97247-2997248Robert Price05/2017
539824382^9735+9735^2438297244Hans Havermann02/2020
5399(31*10^97242+41)/997243Robert Price04/2015
5400GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
540112^90098-4197233Lelio R Paula07/2016
54022^322928-21692997212Enzo Doria05/2014
5403(7*2^322896-1)/5797201Lelio R Paula02/2014
5404(2^322897+5)/314610748997193Lelio R Paula10/2013
5405(2^322789+2214)/297169Stefano Morozzi09/2020
54062^322725+7576197150Enzo Doria04/2016
5407(13*2^322686+1)/11997138Lelio R Paula11/2013
540822402^21639+21639^2240297118Hans Havermann07/2020
540923399^14128+14128^2339997108Hans Havermann06/2020
5410(2^322525+2606)/297090Stefano Morozzi09/2020
5411(41*10^97085+373)/997086Robert Price04/2017
54122^322413+7797056Lelio R Paula12/2012
54132^322406+17797054Lelio R Paula12/2012
5414(14*10^97044+31)/997045Robert Price02/2015
54152^322302+25525597023Lelio R Paula07/2016
54162^322196-11309396991Enzo Doria07/2014
5417(2^322169+2690)/296983Stefano Morozzi09/2020
541823109^15668+15668^2310996943Hans Havermann07/2020
54192^322000-186146996932Enzo Doria03/2016
54202^321971-11274796923Enzo Doria06/2014
542123754^12023+12023^2375496917Hans Havermann07/2020
542211^93062-9296915Lelio R Paula06/2016
5423(2^321922+2214)/296908Stefano Morozzi09/2020
5424(2^321900+2086)/296902Stefano Morozzi09/2020
5425(11*2^321841-7)/1596884Renaud Lifchitz03/2011
54263^203051+3496880Lelio R Paula05/2016
54272*10^96867-5196868Robert Price11/2017
5428(2^321779+2618)/296865Stefano Morozzi09/2020
5429(64*10^96863-1)/2796864Serge Batalov05/2010
54302^321716-278693996847Enzo Doria03/2016
543122496^20181+20181^2249696844Hans Havermann03/2020
54322^321701-11305396842Enzo Doria07/2014
54332^321700-2863596842Lelio R Paula06/2016
5434(5*2^321691-1)/2796838Lelio R Paula02/2014
54356^124433-12443396828Robert Price01/2014
54362^321631+6996821Lelio R Paula12/2012
5437(13*2^321606+1)/11996813Lelio R Paula11/2013
5438(46*10^96798-1)/996799Serge Batalov10/2014
5439(59*10^96798+31)/996799Robert Price09/2015
5440(2^321536+2062)/296792Stefano Morozzi09/2020
5441223319#+23122396790Makoto Morimoto02/2016
54422^321519-2863596787Lelio R Paula06/2016
54432^321487-186723796778Enzo Doria03/2016
54442^321461-6396770Lelio R Paula12/2012
54452^321439+12396763Lelio R Paula12/2012
54462^321434+70996762Lelio R Paula02/2013
5447(2^321415+554)/296756Stefano Morozzi09/2020
544814^84413+8996749Lelio R Paula07/2016
5449(28*10^96743+71)/996744Serge Batalov12/2008
545013^86847+9696743Lelio R Paula06/2016
54519*2^321336-796733Lelio R Paula08/2014
5452(209*10^96722-17)/396724Robert Price05/2017
54532^321237-461596702Yves Minet05/2019
54542^321187-115996687Yves Minet11/2012
54552^321182-185008196686Enzo Doria08/2015
545623359^13768+13768^2335996680Hans Havermann06/2020
54572^321116-11282996666Enzo Doria06/2014
54582^321108-10949996664Enzo Doria04/2014
54592^321098+279385996661Enzo Doria03/2016
5460(2^321100+1170)/296661Stefano Morozzi09/2020
54612^321057+409796648Lelio R Paula06/2016
5463(4435*29^66081-4)/796640Curtis Bright05/2015
546222743^17750+17750^2274396640Hans Havermann04/2020
546422882^16679+16679^2288296612Hans Havermann02/2020
546523452^13163+13163^2345296608Hans Havermann02/2020
5466(2^320863+666)/296590Stefano Morozzi09/2020
5467p(19849)#/2-6496581Robert Price04/2017
54692^320817+18996576Lelio R Paula12/2012
54682^320816-468596576Yves Minet05/2019
5470(361*10^96567-163)/996569Robert Price10/2017
54712^320788-11032796567Enzo Doria05/2014
54722^320764+79396560Lelio R Paula02/2013
5473(9179*2^320652-1)/22196528Lelio R Paula05/2015
547423288^13947+13947^2328896517Hans Havermann07/2020
54752^320616-7879596516Lelio R Paula03/2016
54762^320612-46193996514Enzo Doria07/2015
547710^96504+98765432196505Robert Price12/2019
547810^96504+7188796505Patrick De Geest02/2020
547922654^18195+18195^2265496505Hans Havermann07/2020
548010^96504-13927796504Patrick De Geest02/2020
54815*2^320431+796461Lelio R Paula08/2014
548219^75431-9096458Lelio R Paula06/2016
5483(2^320370+3)/6796440Lelio R Paula10/2013
54842^320309+187147796423Enzo Doria05/2016
5485tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
5486(21*2^320252-1)/189596404Lelio R Paula02/2014
54872^320232-17396400Lelio R Paula12/2012
5488175^42975-296395Lelio R Paula10/2017
5489(2^320170+2718)/296381Stefano Morozzi09/2020
549010^96377+19991196378Patrick De Geest12/2016
549110^96377-2000196377Robert Price11/2016
54922^320124-279044996367Enzo Doria03/2016
549322488^19255+19255^2248896351Hans Havermann11/2019
549423248^13939+13939^2324896346Hans Havermann11/2019
54962^320043-10877596343Enzo Doria04/2014
549524989^7168+7168^2498996343Hans Havermann11/2019
549710^96338+42493996339Patrick De Geest03/2016
549810^96338-928196338Robert Price09/2015
5499(3*2^320008+1)/796332Lelio R Paula09/2013
550025699^5596+5596^2569996317Hans Havermann07/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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