PRP Records

Probable Primes Top 10000

(297738 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 ?
625125549^24148+24148^25549111979Hans Havermann02/2021
62522^371970-459491111975Enzo Doria05/2015
625341^69427-40^69427111971Robert Price07/2012
6254(2^371782+358)/2111918Stefano Morozzi01/2021
625515*25^80056+446111915Eric Chen10/2023
6256(34*10^111902-547)/9111903Robert Price03/2021
6257(10^111902+71)/9111902Serge Batalov07/2015
6258(2^371625+1610)/2111870Stefano Morozzi09/2020
625929080^7027+7027^29080111865Hans Havermann01/2021
626031307^3730+3730^31307111820Hans Havermann02/2021
62612^371440-112865111815Enzo Doria06/2014
62622^371426-459161111811Enzo Doria05/2015
626325768^21771+21771^25768111779Hans Havermann02/2021
626428022^9747+9747^28022111777Hans Havermann02/2021
6265(94*10^111770+11)/3111772Robert Price04/2020
62662^371276-461267111766Enzo Doria07/2015
62676*10^111760+43111761Robert Price07/2020
626898079!4-1024111747Robert Price11/2019
6269(2^371186+3162)/2111738Stefano Morozzi09/2020
627010^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
62712^371098-113261111712Enzo Doria07/2014
6272(7*10^111706-61)/9111706Erik Branger01/2011
62732^371044+1869391111696Enzo Doria05/2016
627426310^17581+17581^26310111688Hans Havermann01/2021
627588^57416+87111645Norbert Schneider11/2015
62762^370829-109693111631Enzo Doria04/2014
627715^94906-2111619Lelio R Paula11/2013
627825835^20904+20904^25835111614Hans Havermann02/2021
6279(2^370726+1198)/2111600Stefano Morozzi09/2020
628027758^10479+10479^27758111597Hans Havermann02/2021
62812^370695-4627111591Yves Minet05/2019
62827*10^111579-87111580Robert Price06/2020
62832^370643-37111575Yves Minet01/2012
6284(2^370655-5)/2439111575Lelio R Paula03/2014
62852^370610-3911111565Yves Minet04/2017
6286(154*10^111549+17)/9111551Robert Price06/2022
628726200^18097+18097^26200111550Hans Havermann01/2021
6288286^45405+45405^286111532Norbert Schneider04/2015
62894*5^159563-9111531Lelio R Paula11/2014
62905*10^111528-21111529Robert Price12/2021
6291(4^185225+23)/3111517Robert Price10/2018
62922^370393-2797093111500Enzo Doria03/2016
6293(21*2^370382-1)/629111495Lelio R Paula03/2014
6294(2^370371+554)/2111493Stefano Morozzi09/2020
62956^143273-5111489Paul Bourdelais01/2021
62962^370292-2791979111469Enzo Doria03/2016
6297(14*10^111443-11)/3111444Robert Price08/2022
62982^370177-461551111435Enzo Doria07/2015
6299(2^370169+1706)/2111432Stefano Morozzi09/2020
6300109^54683-108111413Norbert Schneider02/2017
6302(83*10^111406-173)/9111407Robert Price04/2021
6301959^37362-37362^959111407Henri Lifchitz10/2024
6303(2^370043+1010)/2111394Stefano Morozzi09/2020
630432961^2396+2396^32961111392Hans Havermann10/2020
6305numbpart(10^10+76282)111391Serge Batalov04/2015
6306(19*10^111385+11)/3111386Robert Price07/2023
6307(23*10^111380-29)/3111381Robert Price03/2022
63082^369974+733111374Lelio R Paula05/2013
6309121^53470+120111367Norbert Schneider10/2018
63102^369915-286267111356Enzo Doria07/2015
6311(62*10^111347-629)/9111348Robert Price07/2021
63122^369855-1615111338Lelio R Paula05/2017
63137*10^111325+3111326Robert Price08/2015
631451^65176+2111293Lelio R Paula08/2013
63152^369643-1865767111274Enzo Doria03/2016
63162^369603+885111262Lelio R Paula05/2017
631725555^22564+22564^25555111252Hans Havermann10/2020
6318F(532391)/89441689/1425422598617111243Serge Batalov07/2024
6319L(532277)111240Renaud Lifchitz03/2004
6320105^55033-2111233Lelio R Paula10/2017
6321(35*10^111232-737)/9111233Robert Price07/2018
632226970^13307+13307^26970111227Hans Havermann10/2020
632325419^23716+23716^25419111210Hans Havermann10/2020
63249*10^111201-29111202Robert Price09/2019
63252^369392+29835111199Lelio R Paula05/2017
63263^233059+16111198Robert Price03/2020
63272^369354-3413111187Yves Minet12/2016
63282^369296-27111170Lelio R Paula02/2013
6329(2468^40960+1)/(2468^8192+1)111161Martin Hopf08/2024
63302^369239-109837111153Enzo Doria05/2014
63312^369224-291839111148Enzo Doria07/2015
63322^369216+2798881111146Enzo Doria04/2016
633326842^13817+13817^26842111137Hans Havermann11/2020
6334(5*10^111119-191)/3111120Robert Price05/2021
6335(29*10^111112-23)/3111113Robert Price03/2022
633610^111111+163849111112Patrick De Geest03/2017
633710^111111-312911111111Patrick De Geest03/2017
63382^369092-216923111108Enzo Doria05/2014
63392^369081-55111105Lelio R Paula02/2013
6340(2^369047+3618)/2111094Stefano Morozzi09/2020
634188^57124-87111077Norbert Schneider11/2015
63422^368980+753111075Lelio R Paula05/2013
63432^368946-3623111064Yves Minet03/2017
63442^368929+29835111059Lelio R Paula05/2017
63454^184463-3^184463111058Jean-Louis Charton12/2004
6346111^54298+110111057Norbert Schneider04/2017
6347(4*10^111032-7)/3111033Ray Chandler04/2011
6348(29*10^111020-41)/3111021Tyler Busby03/2024
634935799^1262+1262^35799111015Hans Havermann10/2020
6350(298*10^111004+11)/3111006Robert Price11/2020
635127648^10349+10349^27648111004Hans Havermann11/2020
635228899^6932+6932^28899110997Hans Havermann11/2020
6353(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
63542^368641-460303110972Enzo Doria06/2015
63552^368619-109087110966Enzo Doria04/2014
6356(74*10^110961+313)/9110962Robert Price06/2019
635725258^24711+24711^25258110956Hans Havermann11/2020
6358(2^368539+1290)/2110941Stefano Morozzi01/2021
63593*2^368489+7110927Lelio R Paula09/2014
6360(14*10^110922+61)/3110923Robert Price12/2018
636197411!4-2110913Robert Price07/2017
6362(301*10^110903+23)/9110905Robert Price06/2021
6363(9179*2^368330-1)/35110881Lelio R Paula05/2015
636425830^19619+19619^25830110880Hans Havermann10/2020
6365(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
636626022^18191+18191^26022110850Hans Havermann10/2020
6367(2^368211+2250)/2110843Stefano Morozzi01/2021
6368(37*10^110813+251)/9110814Robert Price09/2021
63692^368050-64875110795Lelio R Paula05/2017
63702^368048+25110794Lelio R Paula02/2013
6371(2^368017+2262)/2110784Stefano Morozzi02/2021
637269^60239-2110771Lelio R Paula10/2013
6373(23*2^367952+1)/15717110762Lelio R Paula03/2014
63742^367924-69110757Lelio R Paula02/2013
6375(23*10^110738+61)/3110739Robert Price01/2022
6376(2^367779+3750)/2110713Stefano Morozzi01/2021
63772^367709-109723110692Enzo Doria04/2014
63782^367687+213413110685Enzo Doria09/2023
6379(3*2^367644-1)/107110671Lelio R Paula03/2014
6380(2^367626+3514)/2110667Stefano Morozzi09/2020
6381(1288676*34^72242-455)/33110642Eric Chen03/2023
6382(23*2^367398+1)/57963110595Lelio R Paula03/2014
6383140^51515-139110558Norbert Schneider04/2019
63842^367215+1879223110543Enzo Doria09/2016
638525782^19375+19375^25782110534Hans Havermann10/2020
638626117^17058+17058^26117110526Hans Havermann10/2020
63872^367141+41110521Lelio R Paula02/2013
63882^367126+29835110516Lelio R Paula05/2017
6389(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6390(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6391(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6392(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6393(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6394(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6395(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6396(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6397(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6398(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6399(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
64003*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
64013*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
64023*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
64033*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
64043*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
64053*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
64063*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
64077*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
64087*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
64097*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
64107*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
64117*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
64127*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
64137*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
64147*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
64157*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
64167*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
64177*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
64187*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
64197*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
64207*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
64217*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
6422(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
6423(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
6424(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
6425(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
6426(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
6427(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
6428(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
6429(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
6430(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
6431(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
6432(11*10^110496+49)/3110497Robert Price07/2018
643325447^21958+21958^25447110481Hans Havermann11/2020
6434(31*2^366976+1)/7110472Lelio R Paula03/2014
64357*10^110468-23110469Robert Price07/2019
64365*3^231464-2^231464110438Jon Grantham08/2023
64372^366853+5711110434Lelio R Paula05/2017
6438(21181*2^366833+1)/3110432Lelio R Paula07/2014
64392^366816+315110423Lelio R Paula05/2017
64402^366775-2787037110411Enzo Doria03/2016
6441(112*10^110405-1)/3110407Serge Batalov12/2014
64422^366751+2797553110404Enzo Doria03/2016
644325276^23331+23331^25276110404Hans Havermann10/2020
64442^366748+255110403Lelio R Paula05/2017
64452^366738-2985110400Yves Minet09/2014
6446(23*2^366739+1)/74575110396Lelio R Paula03/2014
6447(2^366722+1314)/2110395Stefano Morozzi02/2021
64482^366716+1871791110393Enzo Doria05/2016
6449(239*23^81066-349)/22110391Eric Chen08/2023
64502^366695+1334025110387Henri Lifchitz10/2024
64512^366649+1871687110373Enzo Doria05/2016
64522^366629-351205110367Enzo Doria06/2015
6453(31*10^110363+257)/9110364Robert Price12/2021
6454(17*19^86292-215)/18110347Eric Chen01/2023
64562^366558+1874479110345Enzo Doria06/2016
645525132^24581+24581^25132110345Hans Havermann10/2020
6457(2^366539+770)/2110339Stefano Morozzi09/2020
645826368^15285+15285^26368110331Hans Havermann10/2020
6459(23*10^110290+19)/3110291Robert Price07/2019
646018^87853-4409110280Enzo Doria03/2013
646128490^7419+7419^28490110267Hans Havermann11/2020
64622^366218-23110243Lelio R Paula02/2013
6463(21*2^366193-1)/197110235Lelio R Paula03/2014
64642^366178-343991110231Enzo Doria07/2015
646512^102123-11110210Riley Fisher09/2023
646625777^18798+18798^25777110174Hans Havermann10/2020
64672^365944+1871341110161Enzo Doria05/2016
64682^365838-461267110129Enzo Doria07/2015
646930152^4491+4491^30152110126Hans Havermann11/2020
64702^365802+23359110118Enzo Doria10/2023
647110^110111+464019110112Patrick De Geest05/2021
647210^110111-40001110111Robert Price01/2021
64732^365763-6555110106Lelio R Paula04/2017
6474(2^365689+2^182845+1)/511008311/2006
64752^365666-459161110077Enzo Doria05/2015
64763*10^110076-7110077Robert Price08/2015
647713^98785-72110041Lelio R Paula03/2017
6479(25^78707+1)/26110027Robert Price06/2013
6478(7*10^110027-277)/9110027Robert Price02/2022
6480(16*10^110014-73)/3110015Robert Price07/2020
6481(7*10^110006-151)/9110006Robert Price02/2018
64826^141361-7110001Lelio R Paula11/2014
648310^110000+8029681110001Hayden Chesnut11/2024
648410^110000+2044477110001Hayden Chesnut11/2024
648510^110000+76407110001Hayden Chesnut11/2024
648610^110000+167311110001Hayden Chesnut11/2024
648720^84536+81109984Lelio R Paula03/2017
64885*2^365347-9109982Lelio R Paula09/2014
64899*6^141303+7109957Lelio R Paula11/2014
649027635^9522+9522^27635109953Hans Havermann11/2020
649178^58099+77109929Norbert Schneider02/2015
64922*10^109928-7109929Robert Price10/2015
649330580^3933+3933^30580109927Hans Havermann11/2020
649426380^14689+14689^26380109926Hans Havermann11/2020
6495(2^365161+1130)/2109925Stefano Morozzi09/2020
6496(27*2^365137-1)/2021109916Lelio R Paula03/2014
649729^75157-30109910Anonymous09/2024
6498(4441*29^75152-24)/7109905Curtis Bright05/2015
6499(2^365087+7)/6015109899Lelio R Paula01/2014
6500(2^365069+3774)/2109897Stefano Morozzi02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 12 2024 22:37 (Time in France)

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