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 ?
5501(2^343974+2670)/2103547Stefano Morozzi09/2020
55022^343971-5077103546Lelio R Paula09/2011
5503(7*10^103531+71)/3103532Robert Price05/2018
55042^343899+141103524Lelio R Paula08/2011
5505(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
55066^133029-67103517Lelio R Paula11/2016
5507(17*2^343877+1)/13625103515Lelio R Paula12/2013
550866*10^103507+7103509Robert Price07/2020
550926297^8614+8614^26297103485Hans Havermann09/2020
5510(2^343764+2658)/2103483Stefano Morozzi09/2020
551126499^8036+8036^26499103480Hans Havermann09/2020
5512(136*10^103474-1)/9103476Serge Batalov12/2014
55135^148014-24103458Lelio R Paula11/2016
551428316^4503+4503^28316103453Hans Havermann09/2020
5515(22*10^103450+53)/3103451Robert Price07/2019
55162^343604+9931103436Yves Minet01/2011
55172^343601-21189103435Enzo Doria06/2013
5518(10^103423+173)/3103423Robert Price05/2021
55192^343508-115229103407Enzo Doria06/2015
5520(509203*2^343491-1)/16147103403Lelio R Paula05/2015
55213^216685-113056103386Enzo Doria07/2014
552224829^14580+14580^24829103382Hans Havermann08/2020
552391355!4+1024103381Robert Price09/2019
552444^62903-43^62903103379Jean-Louis Charton08/2012
552511^99262-20103371Lelio R Paula12/2016
5526(509203*2^343357-1)/5103366Lelio R Paula05/2015
5527(2^343363+3570)/2103363Stefano Morozzi09/2020
55282^343356-2791889103361Enzo Doria03/2016
5529(25*10^103360-241)/9103361Robert Price05/2018
5530Phi(104989,10)/2939693103350Maksym Voznyy09/2015
553124826^14511+14511^24826103319Hans Havermann09/2020
55322^343182-171103309Lelio R Paula08/2011
5533(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
55342^343079-1835611103278Enzo Doria05/2015
55352^343063-1147103273Yves Minet06/2013
553624741^14930+14930^24741103271Hans Havermann09/2020
5537(16*10^103255-73)/3103256Robert Price07/2020
55389*6^132689+7103254Lelio R Paula11/2014
55392^342979-18085103247Enzo Doria05/2013
5540(16*10^103244-31)/3103245Robert Price03/2019
55412^342966-16995103244Lelio R Paula11/2016
554223797^21774+21774^23797103230Hans Havermann09/2020
554325388^11637+11637^25388103224Hans Havermann09/2020
5544(2^342876+2086)/2103216Stefano Morozzi09/2020
5545(16*10^103214-31)/3103215Robert Price03/2019
5547(37*10^103211+611)/9103212Robert Price11/2018
5546(238*10^103210-1)/3103212Robert Price04/2020
55485^147650+16103203Lelio R Paula11/2016
5549gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
55502^342817+2707067103199Enzo Doria03/2016
555143^63177-42103198Theodore Burton02/2007
55522^342805-21025103195Enzo Doria06/2013
555324129^18890+18890^24129103182Hans Havermann09/2020
5554(622*10^103171-1)/9103173Robert Price11/2021
55552^342714+12285103168Lelio R Paula11/2016
555618^82178-4481103156Enzo Doria03/2013
55572^342665-17349103153Enzo Doria05/2013
555830408^2467+2467^30408103150Hans Havermann09/2020
5559(2^342615+3090)/2103138Stefano Morozzi09/2020
55602^342612+175103137Lelio R Paula08/2011
55615*2^342585-3103130Lelio R Paula09/2014
5562(16*10^103127+77)/3103128Robert Price03/2019
5563(2^342527+3774)/2103111Stefano Morozzi02/2021
55642^342503-19209103104Enzo Doria05/2013
5565(2^342484+2586)/2103098Stefano Morozzi09/2020
55662^342476+51103096Lelio R Paula08/2011
55672^342460-18885103091Enzo Doria05/2013
5568(2^342442+862)/2103086Stefano Morozzi02/2021
5569(194*10^103074-17)/3103076Robert Price09/2020
55707^121968+82103075Lelio R Paula10/2016
55712^342392-108863103071Enzo Doria03/2014
5572(2^342389+806)/2103070Stefano Morozzi01/2021
55733^216014+28103065Lelio R Paula11/2016
55742^342353-108879103059Enzo Doria03/2014
557510^103055+276081103056Patrick De Geest12/2016
557610^103055-53103055Lelio R Paula11/2016
5577(58*10^103046+419)/9103047Robert Price05/2019
55787^121933+4103046Lelio R Paula11/2014
5579(71*10^103028-143)/9103029Robert Price10/2021
5580(2^342235+3618)/2103023Stefano Morozzi09/2020
558119^80560-68103017Lelio R Paula10/2016
55822^342209+76607103016Enzo Doria05/2016
5584328^40945+40945^328103013Norbert Schneider12/2014
558312^95454-91103013Lelio R Paula10/2016
558525833^9716+9716^25833103009Hans Havermann01/2019
5586(893*10^103004+7)/9103006Robert Price06/2021
558765^56809-64^56809102990Robert Price08/2013
55885^147338-6102985Lelio R Paula11/2014
55892^342084-112739102978Enzo Doria06/2014
55909*6^132330+7102974Lelio R Paula11/2014
55912^342034-16737102963Enzo Doria05/2013
5592(9787*2^342011-1)/25102959Lelio R Paula05/2015
5593(3^215802-5)/124343756102956Lelio R Paula12/2013
55942^341991-17421102950Enzo Doria05/2013
55952^341969-112225102943Enzo Doria06/2014
5596(9787*2^341864-1)/3102915Lelio R Paula05/2015
55972^341859+1869413102910Enzo Doria05/2016
559810^102909+61102910Lelio R Paula11/2016
559910^102909-67049102909Patrick De Geest12/2016
560023814^20935+20935^23814102898Hans Havermann02/2019
560128345^4264+4264^28345102888Hans Havermann02/2019
560225665^10204+10204^25665102886Hans Havermann02/2019
560326288^8181+8181^26288102860Hans Havermann02/2019
56042^341659+1836773102850Enzo Doria03/2016
56052^341608-110639102835Enzo Doria05/2014
560610^102824+49102825Lelio R Paula11/2016
560710^102824-168011102824Patrick De Geest12/2016
560811^98708-8102794Lelio R Paula10/2016
56092^341466+4429102792Lelio R Paula09/2011
56102^341460-107102790Lelio R Paula08/2011
5611(2^341388+47)/21014943102761Lelio R Paula12/2013
56122^341355+21102759Lelio R Paula08/2011
56132^341246+40755102726Lelio R Paula11/2016
5614(2^341256-5)/991699102723Lelio R Paula12/2013
56157^121547+78102720Lelio R Paula10/2016
56162^341223-461197102719Enzo Doria06/2015
561727838^4893+4893^27838102711Hans Havermann03/2019
56192^341190-20577102709Enzo Doria06/2013
5618(27*2^341212+1)/84674449102709Lelio R Paula12/2013
56206^131976-65102698Lelio R Paula10/2016
56212^341134+2533102692Henri Lifchitz09/2005
562213^92184-54102688Lelio R Paula10/2016
56232^341116-20873102687Enzo Doria06/2013
56242^341094-19953102680Enzo Doria06/2013
562523761^20950+20950^23761102676Hans Havermann03/2019
56262^341053+129102668Lelio R Paula08/2011
5628(31*2^341006-1)/3102655Lelio R Paula03/2014
56277^121471+94102655Lelio R Paula10/2016
56302^341004-173102653Lelio R Paula08/2011
562920^78901+3102653Lelio R Paula10/2016
5631(2^341001+1674)/2102652Stefano Morozzi09/2020
56325^146853-52102646Lelio R Paula10/2016
56332^340969-216931102642Enzo Doria05/2014
5634122^49196+121102641Norbert Schneider10/2018
56352^340952+1870021102637Enzo Doria05/2016
56365*2^340940-3102634Lelio R Paula08/2014
5637(6^131891+1)/7102631Paul Bourdelais01/2010
5638(11*10^102629-23)/3102630Robert Price09/2021
563925876^9239+9239^25876102615Hans Havermann02/2019
5640(4*10^102612+83)/3102613Robert Price02/2018
564175^54717+74102598Norbert Schneider01/2015
5642(17*10^102597+13)/3102598Robert Price01/2019
56432^340806-20393102593Enzo Doria06/2013
5644(2^340790+5)/138267102583Lelio R Paula12/2013
56456^131821+77102577Lelio R Paula10/2016
5646(203*10^102561-11)/3102563Robert Price12/2020
56472^340688-29102558Henri Lifchitz05/2005
56482^340685-109101102557Enzo Doria04/2014
564965^56567-64102552Norbert Schneider11/2014
565026230^8121+8121^26230102550Hans Havermann03/2019
5651(8*10^102541+49)/3102542Robert Price05/2020
5652(536*10^102533-23)/9102535Robert Price02/2020
56532^340547-108897102515Enzo Doria03/2014
5654(2^340536+778)/2102512Stefano Morozzi09/2020
565525592^10119+10119^25592102500Hans Havermann02/2019
56567^121268+82102484Lelio R Paula10/2016
5657(6883*2^340443-1)/162401102483Lelio R Paula05/2015
56582^340434-5955102481Lelio R Paula11/2016
5659(7*10^102480-19)/3102481Robert Price10/2020
5660(2^340381+47)/7102465Lelio R Paula12/2013
5661111^50095+110102461Norbert Schneider04/2017
56622^340291-20301102438Enzo Doria06/2013
566312^94915+89102431Lelio R Paula10/2016
5664(106*10^102422+17)/3102424Robert Price04/2021
566524466^15349+15349^24466102417Hans Havermann03/2019
56662^340212+111546435102415Paul Bourdelais10/2021
56672^340208-20373102413Enzo Doria06/2013
56686^131598-17273102404Enzo Doria02/2013
5669(2^340132+1182)/2102390Stefano Morozzi09/2020
5670(2^340133+1166)/2102390Stefano Morozzi09/2020
56712^340115-21181102385Enzo Doria06/2013
5672(55459*2^340090+1)/1591102379Lelio R Paula07/2014
5673(2^340064+3630)/2102370Stefano Morozzi09/2020
567489^52511-88^52511102365Robert Price06/2015
56753^214539-112756102362Enzo Doria07/2014
567623159^23450-23450^23159102353Norbert Schneider12/2019
56772^340000-19877102351Enzo Doria06/2013
56782^339990-114845102348Enzo Doria05/2015
5679(3^214516-2)/51383102346Lelio R Paula12/2013
568020^78661-99102341Lelio R Paula09/2016
56812^339951-19585102336Enzo Doria05/2013
5682(13*2^339943+1)/45102333Lelio R Paula12/2013
5683(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
56845*10^102323-91102324Robert Price03/2021
56862^339889+29327102317Yves Minet06/2010
5685(167*10^102315-17)/3102317Robert Price03/2020
568726348^7641+7641^26348102314Hans Havermann03/2019
5688Phi(239414,10)/6333218543102303Makoto Kamada08/2019
56892^339834-109493102301Enzo Doria04/2014
5690(16*10^102299-19)/3102300Robert Price02/2019
5691(11^98221-5^98221)/6102286Robert Price01/2013
56923^214365+1820102279Lelio R Paula10/2016
569331978^1579+1579^31978102278Hans Havermann03/2019
5694(11*2^339705-1)/183102261Lelio R Paula03/2014
56952^339694-16995102259Lelio R Paula09/2016
5696(56*10^102255+691)/9102256Robert Price05/2019
5697122^49008+121102249Norbert Schneider10/2018
5698(2^339652+3178)/2102246Stefano Morozzi09/2020
56997^120985-38102245Lelio R Paula10/2016
570010^102244+122961102245Patrick De Geest12/2016
570110^102244-27102244Lelio R Paula09/2016
57027^120982-62102242Lelio R Paula10/2016
5703(2^339640+2670)/2102242Stefano Morozzi09/2020
57044*6^131382-5102236Lelio R Paula11/2014
5705(2^339607+3290)/2102232Stefano Morozzi02/2021
57062^339586-1091102226Yves Minet11/2012
570711^98161-3072000102225Enzo Doria12/2012
57089*7^120961-4102225Lelio R Paula11/2014
57095*3^214250+2102224Serge Batalov10/2010
571012^94713-59102213Lelio R Paula10/2016
571112^94705+89102204Lelio R Paula10/2016
57122^339407-177102172Lelio R Paula08/2011
57134*10^102163-57102164Robert Price10/2018
57142^339355+65102157Lelio R Paula07/2011
5715(28*10^102142-31)/3102143Robert Price12/2019
5716(2^339323+47)/880715102141Lelio R Paula12/2013
5717(2^339268+1758)/2102130Stefano Morozzi09/2020
5718s(178551)102122Robert Price05/2020
5719(797*10^102112-23)/9102114Robert Price01/2022
5720(2^339175+2790)/2102102Stefano Morozzi02/2021
57232^339168+21102100Lelio R Paula07/2011
57222^339167-108807102100Enzo Doria03/2014
5721(2^339169+42)/2102100Stefano Morozzi09/2020
57242^339156+163102097Lelio R Paula08/2011
5725(2^339149+746)/2102094Stefano Morozzi09/2020
5726(25*10^102076-67)/3102077Robert Price06/2019
57272^339081-4543102074Yves Minet03/2019
57282*10^102062+77102063Robert Price08/2020
572924327^15668+15668^24327102053Hans Havermann02/2019
573010^102052-7000001102052Robert Price06/2021
57312^339000-175635102050Stefano Morozzi12/2021
57322^339000-151667102050Stefano Morozzi12/2021
57332^338999+79289102049Stefano Morozzi01/2022
57342^338975+28355102042Stefano Morozzi01/2022
573625080^11711+11711^25080102041Hans Havermann02/2019
57352^338972+152343102041Stefano Morozzi12/2021
57372^338968+53461102040Stefano Morozzi01/2022
57382^338963-127455102039Stefano Morozzi12/2021
5740(2^338982-7)/1754517102038Lelio R Paula12/2013
57392^338960+53935102038Stefano Morozzi01/2022
57412^338954-177003102036Stefano Morozzi12/2021
57422^338954+154207102036Stefano Morozzi01/2022
57432^338950+175077102035Stefano Morozzi12/2021
57442^338951-51687102035Stefano Morozzi12/2021
57452^338943+127103102033Stefano Morozzi12/2021
57462^338940+78607102032Stefano Morozzi01/2022
57472^338939+151569102031Stefano Morozzi12/2021
57482^338931+2349102029Stefano Morozzi12/2021
57492^338928+2367102028Stefano Morozzi12/2021
57502^338927+52779102028Stefano Morozzi01/2022


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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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