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 ?
65012^306153+1192162Lelio R Paula11/2012
6502(2^306141-7)/592157Lelio R Paula06/2013
650321725^17454+17454^2172592156Hans Havermann09/2020
6504(26*10^92152-23)/392153Robert Price08/2016
6505(2*10^92152+67)/392152Robert Price04/2017
650621368^20457+20457^2136892115Hans Havermann08/2020
6507(2^305996+3018)/292114Stefano Morozzi09/2020
65084*10^92099+3*7^9209992100Mike Oakes12/2010
650930504^1045+1045^3050492096Hans Havermann08/2020
651024334^6085+6085^2433492087Hans Havermann08/2020
6511(2^305898+2262)/292085Stefano Morozzi01/2021
6512(4591^25147-1)/459092083Serge Batalov08/2020
6513115^44684+11492081Norbert Schneider07/2018
6514(416771^16384+1)/292077Richard Fischer08/2020
6515(2^305867-2^152934+1)/59207511/2006
65162^305851-10949592071Enzo Doria04/2014
6517(416213^16384+1)/292067Richard Fischer08/2020
651912^85300+3592055Lelio R Paula06/2016
6518((10^46026-1)*1000/9+739)*10^46026+(10^46026-1)/992055Hans Havermann05/2019
652021732^17201+17201^2173292048Hans Havermann08/2020
65217*10^92043-3992044Robert Price07/2020
65223^192911+9292042Lelio R Paula04/2016
65232^305723-27627192032Enzo Doria07/2015
6524(2^305714+3738)/292029Stefano Morozzi09/2020
6525(2^305707+798)/292027Stefano Morozzi01/2021
6526(2^305682+3202)/292020Stefano Morozzi09/2020
65272^305676+9392018Donovan Johnson06/2008
65283^192819+491999Lelio R Paula04/2013
6529(38*10^91997-83)/9991997Ray Chandler07/2011
65302^305539+7291191977Enzo Doria04/2016
6531Phi(212014,10)91960Makoto Kamada04/2019
6532(2^305423+2666)/291942Stefano Morozzi09/2020
6533(2^305427-5)/129799821391934Lelio R Paula06/2013
653482077!4-12891928Robert Price11/2019
653585^47642+8491922Norbert Schneider10/2015
653610^91920+18765191921Patrick De Geest07/2013
653710^91920-3991920Robert Price05/2011
6538(3975^25537-1)/397491913Serge Batalov08/2020
6539(22*10^91903+41)/991904Robert Price02/2015
65412^305275-2791897Lelio R Paula11/2012
65403^192607-772691897Enzo Doria05/2014
6542(2^305243+2274)/291887Stefano Morozzi02/2021
6543(2^305220+1278)/291881Stefano Morozzi01/2021
6544(6958^23911-1)/695791874Serge Batalov08/2020
6545(7*10^91856-61)/991856Erik Branger12/2009
6546(2^305107+1274)/291847Stefano Morozzi01/2021
6547(89*10^91839-53)/991840Robert Price11/2015
65481678^28479+28479^167891839Norbert Schneider08/2020
6549(2^304996+406)/291813Stefano Morozzi02/2021
65508*5^131351+791812Lelio R Paula10/2014
65513^192426-6891811Lelio R Paula04/2016
65532^304973+11791807Lelio R Paula11/2012
6552(2^304974+234)/291807Stefano Morozzi09/2020
65542^304939-186372791796Enzo Doria03/2016
65552^304902+841591785Lelio R Paula02/2016
655618^73119+6191785Lelio R Paula06/2016
6557(78557*2^304740+1)/15991739Lelio R Paula06/2014
65582^304747+7135591738Lelio R Paula02/2016
6559(2^304738+2262)/291735Stefano Morozzi01/2021
65608*3^192251+591728Lelio R Paula08/2014
6561(2^304693+3746)/291722Stefano Morozzi01/2021
65622^304674-8791717Lelio R Paula11/2012
6563(28*10^91715+701)/991716Robert Price11/2017
6565(2^304698+9)/136280995391715Lelio R Paula06/2013
6564(2^304671+1046)/291715Stefano Morozzi09/2020
6566(2^304667+3614)/291714Stefano Morozzi09/2020
6567(5*10^91707-119)/391708Robert Price04/2016
65682^304633-11277191704Enzo Doria06/2014
6569(395347^16384+1)/291701Richard Fischer06/2020
65709*10^91693+2391694Robert Price11/2017
65712^304578-1671391688Enzo Doria05/2013
65726^117824-1871391685Enzo Doria03/2013
6573(17^74509-1)/1691679Paul Bourdelais03/2010
6574(2^304551-7)/891223191673Lelio R Paula06/2013
6575(2^304532-3)/301391670Lelio R Paula06/2013
65762^304507-1664591666Enzo Doria04/2013
6577(29*2^304489+1)/3191661Lelio R Paula09/2013
657821221^20860+20860^2122191661Hans Havermann08/2020
65792^304471-183612791655Enzo Doria04/2015
65802^304433+3276991644Lelio R Paula02/2016
65812^304410-1662591637Enzo Doria04/2013
6582183^40500-291630Lelio R Paula10/2017
6583(2^304373+1850)/291626Stefano Morozzi02/2021
6584(203*10^91613+1)/391615Robert Price09/2017
65854*5^131052+791603Lelio R Paula10/2014
658721725^16458+16458^2172591601Hans Havermann08/2020
6586(2^304290+3270)/291601Stefano Morozzi02/2021
65882^304278-400191597Yves Minet04/2017
65892^304272-186637791595Enzo Doria03/2016
65902^304268+1968391594Lelio R Paula02/2016
659121718^16497+16497^2171891594Hans Havermann08/2020
659222759^10576+10576^2275991590Hans Havermann08/2020
65932^304162-16191562Lelio R Paula11/2012
65945*7^108331+691552Lelio R Paula10/2014
65952^304082-278782191538Enzo Doria03/2016
65962^304015+6413391518David Broadhurst06/2002
6597(7*2^303963+1)/391503Lelio R Paula09/2013
6598(2^303945-9)/361791494Lelio R Paula06/2013
6599(384007^16384+1)/291494Richard Fischer05/2020
66002^303930+188052791493Enzo Doria10/2016
660124810^4859+4859^2481091464Hans Havermann08/2020
66022*10^91457+2991458Robert Price02/2021
66033^191684-6891457Lelio R Paula04/2016
6604(21*2^303813-1)/16991456Lelio R Paula02/2014
6605(298*10^91446+11)/391448Robert Price11/2020
660611^87797-12091432Enzo Doria07/2012
66072^303698-184723191423Enzo Doria07/2015
6608(38^28933-1)^2-291416Norbert Schneider06/2016
660925660^3643+3643^2566091388Hans Havermann08/2020
66102^303554+7729991379Enzo Doria05/2016
66112^303542+1270591376Lelio R Paula02/2016
661231^61269-291375Lelio R Paula09/2013
6613(2^303525+2774)/291370Stefano Morozzi01/2021
66142^303516-6487591368Lelio R Paula02/2016
6615(2^303497+1266)/291362Stefano Morozzi09/2020
6616(2^303497+3710)/291362Stefano Morozzi09/2020
661721856^15121+15121^2185691349Hans Havermann09/2020
6618(24737*2^303428+1)/391345Lelio R Paula06/2014
6619(21181*2^303357+1)/3236191320Lelio R Paula06/2014
662023081^9046+9046^2308191319Hans Havermann09/2020
66212^303344-278696991316Enzo Doria03/2016
66226^117346+6591313Lelio R Paula05/2016
66232^303321+85591309Lelio R Paula02/2016
6624(2^303315+3746)/291307Stefano Morozzi01/2021
662512^84606+4791306Lelio R Paula06/2016
66262^303288+187431191299Enzo Doria06/2016
6627197^39788-291293Lelio R Paula10/2017
662811^87663-171091292Enzo Doria12/2012
66292^303224+253391280Henri Lifchitz05/2005
6630(2^303226+1830)/291280Stefano Morozzi02/2021
66316^117302+14391279Lelio R Paula05/2016
66323^191306-11288091277Enzo Doria07/2014
6633(10052^22807-1)/1005191276Serge Batalov08/2020
66342^303207+1291591275Lelio R Paula02/2016
66352^303191-11125991270Enzo Doria05/2014
663681539!4+3291267Robert Price09/2019
6637(2^303116+3570)/291247Stefano Morozzi09/2020
663910^91230+9^(91230+1)91231Robert Price08/2016
663810^91230+792191231Patrick De Geest11/2016
664110^91230-91114191230Patrick De Geest11/2016
664010^91229+34879391230Patrick De Geest07/2019
664210^91229-247191229Patrick De Geest01/2019
66432996^26241+26241^299691228Norbert Schneider01/2020
664510^91225+527191226Patrick De Geest01/2019
66442816^26445+26445^281691226Norbert Schneider02/2020
66476^117232-1742391225Enzo Doria02/2013
664610^91225-14721991225Patrick De Geest07/2019
66487*10^91215+391216Erik Branger11/2009
664910^91215+23061191216Patrick De Geest07/2019
665010^91215-453991215Patrick De Geest01/2019
6651(2^303007+606)/291214Stefano Morozzi09/2020
6652(2^302998+3102)/291212Stefano Morozzi09/2020
665310^91210+242191211Patrick De Geest01/2019
665410^91210-173791210Patrick De Geest01/2019
665597*10^91205-391207Robert Price01/2017
66562^302979-16118191206Enzo Doria04/2013
6657(166*10^91199-7)/391201Robert Price11/2020
66582^302949+8191197Henri Lifchitz02/2007
665910^91194+20036191195Patrick De Geest07/2019
66614*6^117192-591194Lelio R Paula10/2014
666010^91194-866391194Patrick De Geest01/2019
66622^302918+9991188Lelio R Paula11/2012
666310^91186+26811191187Patrick De Geest07/2019
666410^91186-776391186Patrick De Geest01/2019
666510^91181+55047191182Patrick De Geest07/2019
666610^91181-136791181Patrick De Geest01/2019
666710^91178+7188391179Patrick De Geest07/2019
666810^91178-471991178Patrick De Geest01/2019
666924686^4935+4935^2468691173Hans Havermann08/2020
667010^91165+304391166Patrick De Geest01/2019
667110^91165-39941391165Patrick De Geest07/2019
667210^91156+386191157Patrick De Geest01/2019
667310^91156-23149791156Patrick De Geest07/2019
66742^302797+186958791151Enzo Doria05/2016
6675265^37614+37614^26591148Norbert Schneider01/2015
66767^107852+8291146Lelio R Paula04/2016
6677(38*10^91144-11)/991145Robert Price05/2015
6678(55*10^91142+377)/991143Robert Price10/2017
667910^91128+996191129Patrick De Geest01/2019
6681249^38030+38030^24991128Norbert Schneider01/2015
668010^91128-18915391128Patrick De Geest07/2019
6682(2^302718+2814)/291127Stefano Morozzi02/2021
66836^117094-21104991117Mike Oakes05/2011
668421353^18472+18472^2135391103Hans Havermann05/2020
66862^302602-186718191093Enzo Doria03/2016
668510^91092+5612791093Patrick De Geest07/2019
668710^91092-910791092Patrick De Geest01/2019
6688(1017*2^302592-1)/5391091Lelio R Paula04/2015
668915^77445-1691083Lelio R Paula07/2016
669021656^16053+16053^2165691076Hans Havermann05/2020
66912^302505+8191064Henri Lifchitz02/2007
66922^302496-11234991061Enzo Doria06/2014
6693(2^302475+1790)/291054Stefano Morozzi01/2021
669417^73999-7291052Lelio R Paula07/2016
669510^91047+933191048Patrick De Geest01/2019
669610^91047-67116991047Patrick De Geest07/2019
669710^91044+207791045Patrick De Geest01/2019
669810^91044-13635991044Patrick De Geest07/2019
669910^91041+934991042Patrick De Geest01/2019
670010^91041-782391041Patrick De Geest01/2019
670110^91040+407791041Patrick De Geest01/2019
670210^91040-11942191040Patrick De Geest07/2019
670310^91037+276991038Patrick De Geest01/2019
670410^91037-2264991037Patrick De Geest07/2019
6705(16*10^91032+41)/391033Robert Price10/2017
670610^91023+5803991024Patrick De Geest07/2019
670710^91023-647191023Patrick De Geest01/2019
670810^91018+787391019Patrick De Geest01/2019
670910^91018-33317791018Patrick De Geest07/2019
671010^91017+6876791018Patrick De Geest07/2019
671110^91017-42832791017Patrick De Geest07/2019
671210^91016+7311191017Patrick De Geest07/2019
671310^91016-797391016Patrick De Geest01/2019
67141949^27666+27666^194991016Norbert Schneider04/2020
67152^302332+57729457591012Lelio R Paula08/2016
671610^91004+907391005Patrick De Geest01/2019
671710^91004-49151991004Patrick De Geest07/2019
671810^91003+7426991004Patrick De Geest07/2019
671910^91003-390391003Patrick De Geest01/2019
67202^302274+7420990994Enzo Doria04/2016
672110^90991+8114790992Patrick De Geest07/2019
672210^90991-627990991Patrick De Geest01/2019
672310^90983+139390984Patrick De Geest01/2019
672411*10^90982+990984Robert Price08/2020
672510^90983-56238390983Patrick De Geest07/2019
6726(311^36497-1)/31090976Eric Chen09/2017
6727(2^302210+1014)/290974Stefano Morozzi09/2020
6728(3^190668+2)/8990970Lelio R Paula04/2013
67292^302188+9019590968Lelio R Paula02/2016
6731(53*10^90965-71)/990966Robert Price09/2015
673010^90965+57398790966Patrick De Geest07/2019
673210^90965-683390965Patrick De Geest01/2019
673310^90964+4878990965Patrick De Geest07/2019
673410^90964-5210390964Patrick De Geest07/2019
673510^90963+19188990964Patrick De Geest07/2019
673610^90963-365990963Patrick De Geest01/2019
673710^90962+765790963Patrick De Geest01/2019
673810^90962-21563390962Patrick De Geest07/2019
673910^90961+6747190962Patrick De Geest07/2019
674010^90961-21104390961Patrick De Geest07/2019
674110^90960+107211790961Patrick De Geest07/2019
674210^90959+879190960Patrick De Geest01/2019
674310^90960-61065990960Patrick De Geest07/2019
674410^90959-27521390959Patrick De Geest07/2019
6745(2^302129+3110)/290950Stefano Morozzi09/2020
674710^90948+986790949Patrick De Geest01/2019
674621665^15774+15774^2166590949Hans Havermann04/2020
674810^90948-10923990948Patrick De Geest07/2019
67492^302113+7410590946Enzo Doria04/2016
67502^302102-655590942Lelio R Paula02/2016


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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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