PRP Records

Probable Primes Top 10000

(290751 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 ?
850121713^17914+17914^2171392350Hans Havermann09/2020
85022^306672-10905992318Enzo Doria04/2014
8503(430463^16384+1)/292307Richard Fischer09/2020
85046^118604-1706392292Enzo Doria02/2013
850521969^15878+15878^2196992288Hans Havermann08/2020
850621690^17959+17959^2169092276Hans Havermann08/2020
8507(7613^23773-1)/761292273Serge Batalov08/2020
8508(31*2^306487-1)/229192260Lelio R Paula02/2014
85092^306467-183561192256Enzo Doria04/2015
85102^306433+7642792246Enzo Doria05/2016
85112^306430-11331392245Enzo Doria07/2014
8512(23*10^92244-59)/992245Robert Price03/2017
8513(47*2^306398+1)/138480392231Lelio R Paula04/2015
851421436^20043+20043^2143692217Hans Havermann09/2020
8515(25*10^92186+59)/392187Robert Price05/2016
85162^306213-28618392180Enzo Doria06/2015
851710^92178+6192179Robert Price04/2011
851810^92178-17550992178Patrick De Geest07/2013
85192^306200+118592176Lelio R Paula02/2016
8520(2^306171+1514)/292167Stefano Morozzi09/2020
85212^306153+1192162Lelio R Paula11/2012
8522(2^306141-7)/592157Lelio R Paula06/2013
852321725^17454+17454^2172592156Hans Havermann09/2020
8524(26*10^92152-23)/392153Robert Price08/2016
8525(2*10^92152+67)/392152Robert Price04/2017
852621368^20457+20457^2136892115Hans Havermann08/2020
8527(2^305996+3018)/292114Stefano Morozzi09/2020
85284*10^92099+3*7^9209992100Mike Oakes12/2010
852930504^1045+1045^3050492096Hans Havermann08/2020
853024334^6085+6085^2433492087Hans Havermann08/2020
8531(2^305898+2262)/292085Stefano Morozzi01/2021
8532(4591^25147-1)/459092083Serge Batalov08/2020
8533115^44684+11492081Norbert Schneider07/2018
8534(416771^16384+1)/292077Richard Fischer08/2020
8535(2^305867-2^152934+1)/59207511/2006
85362^305851-10949592071Enzo Doria04/2014
8537(416213^16384+1)/292067Richard Fischer08/2020
853912^85300+3592055Lelio R Paula06/2016
8538((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
854021732^17201+17201^2173292048Hans Havermann08/2020
85417*10^92043-3992044Robert Price07/2020
85423^192911+9292042Lelio R Paula04/2016
85432^305723-27627192032Enzo Doria07/2015
8544(2^305714+3738)/292029Stefano Morozzi09/2020
8545(2^305707+798)/292027Stefano Morozzi01/2021
8546(2^305682+3202)/292020Stefano Morozzi09/2020
85472^305676+9392018Donovan Johnson06/2008
85483^192819+491999Lelio R Paula04/2013
8549(38*10^91997-83)/9991997Ray Chandler07/2011
85502^305539+7291191977Enzo Doria04/2016
8551Phi(212014,10)91960Makoto Kamada04/2019
8552(2^305423+2666)/291942Stefano Morozzi09/2020
8553(2^305427-5)/129799821391934Lelio R Paula06/2013
855482077!4-12891928Robert Price11/2019
855585^47642+8491922Norbert Schneider10/2015
855610^91920+18765191921Patrick De Geest07/2013
855710^91920-3991920Robert Price05/2011
8558(3975^25537-1)/397491913Serge Batalov08/2020
8559(22*10^91903+41)/991904Robert Price02/2015
85612^305275-2791897Lelio R Paula11/2012
85603^192607-772691897Enzo Doria05/2014
8562(2^305243+2274)/291887Stefano Morozzi02/2021
8563(2^305220+1278)/291881Stefano Morozzi01/2021
8565(6958^23911-1)/695791874Serge Batalov08/2020
85649*10^91873-9191874Robert Price06/2021
8566(7*10^91856-61)/991856Erik Branger12/2009
8567(2^305107+1274)/291847Stefano Morozzi01/2021
8568(89*10^91839-53)/991840Robert Price11/2015
85691678^28479+28479^167891839Norbert Schneider08/2020
8570(2^304996+406)/291813Stefano Morozzi02/2021
85718*5^131351+791812Lelio R Paula10/2014
85723^192426-6891811Lelio R Paula04/2016
85732^304979-37560791808Harrison Mesh06/2022
85752^304973+11791807Lelio R Paula11/2012
8574(2^304974+234)/291807Stefano Morozzi09/2020
85762^304939-186372791796Enzo Doria03/2016
85772^304902+841591785Lelio R Paula02/2016
857818^73119+6191785Lelio R Paula06/2016
8579(78557*2^304740+1)/15991739Lelio R Paula06/2014
85802^304747+7135591738Lelio R Paula02/2016
8581(2^304738+2262)/291735Stefano Morozzi01/2021
85828*3^192251+591728Lelio R Paula08/2014
8583(2^304693+3746)/291722Stefano Morozzi01/2021
85842^304674-8791717Lelio R Paula11/2012
8585(28*10^91715+701)/991716Robert Price11/2017
8586(2^304698+9)/136280995391715Lelio R Paula06/2013
8587(2^304671+1046)/291715Stefano Morozzi09/2020
8588(2^304667+3614)/291714Stefano Morozzi09/2020
8589(5*10^91707-119)/391708Robert Price04/2016
85902^304633-11277191704Enzo Doria06/2014
8591(395347^16384+1)/291701Richard Fischer06/2020
85929*10^91693+2391694Robert Price11/2017
85932^304578-1671391688Enzo Doria05/2013
85946^117824-1871391685Enzo Doria03/2013
8595(17^74509-1)/1691679Paul Bourdelais03/2010
8596(2^304551-7)/891223191673Lelio R Paula06/2013
8597(2^304532-3)/301391670Lelio R Paula06/2013
85982^304507-1664591666Enzo Doria04/2013
8599(29*2^304489+1)/3191661Lelio R Paula09/2013
860021221^20860+20860^2122191661Hans Havermann08/2020
86012^304471-183612791655Enzo Doria04/2015
86022^304433+3276991644Lelio R Paula02/2016
86032^304410-1662591637Enzo Doria04/2013
8604183^40500-291630Lelio R Paula10/2017
8605(2^304373+1850)/291626Stefano Morozzi02/2021
8606(203*10^91613+1)/391615Robert Price09/2017
86074*5^131052+791603Lelio R Paula10/2014
860921725^16458+16458^2172591601Hans Havermann08/2020
8608(2^304290+3270)/291601Stefano Morozzi02/2021
86102^304278-400191597Yves Minet04/2017
86112^304272-186637791595Enzo Doria03/2016
86122^304268+1968391594Lelio R Paula02/2016
861321718^16497+16497^2171891594Hans Havermann08/2020
861422759^10576+10576^2275991590Hans Havermann08/2020
8615(29*10^91584-119)/991585Robert Price12/2021
86162^304162-16191562Lelio R Paula11/2012
86175*7^108331+691552Lelio R Paula10/2014
86182^304082-278782191538Enzo Doria03/2016
86192^304015+6413391518David Broadhurst06/2002
8620(7*2^303963+1)/391503Lelio R Paula09/2013
8621(2^303945-9)/361791494Lelio R Paula06/2013
8622(384007^16384+1)/291494Richard Fischer05/2020
86232^303930+188052791493Enzo Doria10/2016
862424810^4859+4859^2481091464Hans Havermann08/2020
86252*10^91457+2991458Robert Price02/2021
86263^191684-6891457Lelio R Paula04/2016
8627(21*2^303813-1)/16991456Lelio R Paula02/2014
8628(298*10^91446+11)/391448Robert Price11/2020
862911^87797-12091432Enzo Doria07/2012
86302^303698-184723191423Enzo Doria07/2015
8631(38^28933-1)^2-291416Norbert Schneider06/2016
863225660^3643+3643^2566091388Hans Havermann08/2020
86332^303554+7729991379Enzo Doria05/2016
86342^303542+1270591376Lelio R Paula02/2016
863531^61269-291375Lelio R Paula09/2013
8636(2^303525+2774)/291370Stefano Morozzi01/2021
86372^303516-6487591368Lelio R Paula02/2016
8638(2^303497+1266)/291362Stefano Morozzi09/2020
8639(2^303497+3710)/291362Stefano Morozzi09/2020
8640(31*10^91352+257)/991353Robert Price12/2021
864121856^15121+15121^2185691349Hans Havermann09/2020
8642(24737*2^303428+1)/391345Lelio R Paula06/2014
8643(21181*2^303357+1)/3236191320Lelio R Paula06/2014
864423081^9046+9046^2308191319Hans Havermann09/2020
86452^303344-278696991316Enzo Doria03/2016
86466^117346+6591313Lelio R Paula05/2016
86472^303321+85591309Lelio R Paula02/2016
8648(2^303315+3746)/291307Stefano Morozzi01/2021
864912^84606+4791306Lelio R Paula06/2016
86502^303288+187431191299Enzo Doria06/2016
8651197^39788-291293Lelio R Paula10/2017
865211^87663-171091292Enzo Doria12/2012
8653(4*10^91284-61)/391285Robert Price12/2021
86552^303224+253391280Henri Lifchitz05/2005
8654(2^303226+1830)/291280Stefano Morozzi02/2021
86566^117302+14391279Lelio R Paula05/2016
86573^191306-11288091277Enzo Doria07/2014
8658(10052^22807-1)/1005191276Serge Batalov08/2020
86592^303207+1291591275Lelio R Paula02/2016
86602^303191-11125991270Enzo Doria05/2014
866181539!4+3291267Robert Price09/2019
8662(2^303116+3570)/291247Stefano Morozzi09/2020
866310^91230+9^(91230+1)91231Robert Price08/2016
866410^91230+792191231Patrick De Geest11/2016
866510^91230-91114191230Patrick De Geest11/2016
866610^91229+34879391230Patrick De Geest07/2019
866710^91229-247191229Patrick De Geest01/2019
86682996^26241+26241^299691228Norbert Schneider01/2020
86692^303249-49495391228Harrison Mesh06/2022
867110^91225+527191226Patrick De Geest01/2019
86702816^26445+26445^281691226Norbert Schneider02/2020
86736^117232-1742391225Enzo Doria02/2013
867210^91225-14721991225Patrick De Geest07/2019
86747*10^91215+391216Erik Branger11/2009
867510^91215+23061191216Patrick De Geest07/2019
867610^91215-453991215Patrick De Geest01/2019
8677(2^303007+606)/291214Stefano Morozzi09/2020
86789*10^91212-4791213Robert Price11/2021
8679(2^302998+3102)/291212Stefano Morozzi09/2020
868010^91210+242191211Patrick De Geest01/2019
868110^91210-173791210Patrick De Geest01/2019
868297*10^91205-391207Robert Price01/2017
86832^302979-16118191206Enzo Doria04/2013
8684(166*10^91199-7)/391201Robert Price11/2020
86852^302949+8191197Henri Lifchitz02/2007
868610^91194+20036191195Patrick De Geest07/2019
86884*6^117192-591194Lelio R Paula10/2014
868710^91194-866391194Patrick De Geest01/2019
86892^302918+9991188Lelio R Paula11/2012
869010^91186+26811191187Patrick De Geest07/2019
869110^91186-776391186Patrick De Geest01/2019
869210^91181+55047191182Patrick De Geest07/2019
8693(26*10^91181-83)/391182Robert Price12/2021
869410^91181-136791181Patrick De Geest01/2019
869510^91178+7188391179Patrick De Geest07/2019
869610^91178-471991178Patrick De Geest01/2019
869724686^4935+4935^2468691173Hans Havermann08/2020
869810^91165+304391166Patrick De Geest01/2019
869910^91165-39941391165Patrick De Geest07/2019
870010^91156+386191157Patrick De Geest01/2019
870110^91156-23149791156Patrick De Geest07/2019
87022^302797+186958791151Enzo Doria05/2016
8703265^37614+37614^26591148Norbert Schneider01/2015
87047^107852+8291146Lelio R Paula04/2016
8705(38*10^91144-11)/991145Robert Price05/2015
8706(55*10^91142+377)/991143Robert Price10/2017
870710^91128+996191129Patrick De Geest01/2019
8709249^38030+38030^24991128Norbert Schneider01/2015
870810^91128-18915391128Patrick De Geest07/2019
8710(2^302718+2814)/291127Stefano Morozzi02/2021
87116^117094-21104991117Mike Oakes05/2011
871221353^18472+18472^2135391103Hans Havermann05/2020
87142^302602-186718191093Enzo Doria03/2016
871310^91092+5612791093Patrick De Geest07/2019
871510^91092-910791092Patrick De Geest01/2019
8716(1017*2^302592-1)/5391091Lelio R Paula04/2015
871715^77445-1691083Lelio R Paula07/2016
871821656^16053+16053^2165691076Hans Havermann05/2020
87192^302505+8191064Henri Lifchitz02/2007
87202^302496-11234991061Enzo Doria06/2014
8721(2^302475+1790)/291054Stefano Morozzi01/2021
872217^73999-7291052Lelio R Paula07/2016
872310^91047+933191048Patrick De Geest01/2019
872410^91047-67116991047Patrick De Geest07/2019
872510^91044+207791045Patrick De Geest01/2019
872610^91044-13635991044Patrick De Geest07/2019
872710^91041+934991042Patrick De Geest01/2019
872810^91041-782391041Patrick De Geest01/2019
872910^91040+407791041Patrick De Geest01/2019
873010^91040-11942191040Patrick De Geest07/2019
873110^91037+276991038Patrick De Geest01/2019
873210^91037-2264991037Patrick De Geest07/2019
8733(16*10^91032+41)/391033Robert Price10/2017
873410^91023+5803991024Patrick De Geest07/2019
873510^91023-647191023Patrick De Geest01/2019
873610^91018+787391019Patrick De Geest01/2019
873710^91018-33317791018Patrick De Geest07/2019
873810^91017+6876791018Patrick De Geest07/2019
873910^91017-42832791017Patrick De Geest07/2019
874010^91016+7311191017Patrick De Geest07/2019
874110^91016-797391016Patrick De Geest01/2019
87421949^27666+27666^194991016Norbert Schneider04/2020
87432^302332+57729457591012Lelio R Paula08/2016
874410^91004+907391005Patrick De Geest01/2019
874510^91004-49151991004Patrick De Geest07/2019
874610^91003+7426991004Patrick De Geest07/2019
874710^91003-390391003Patrick De Geest01/2019
87482^302274+7420990994Enzo Doria04/2016
874910^90991+8114790992Patrick De Geest07/2019
875010^90991-627990991Patrick De Geest01/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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