PRP Records

Probable Primes Top 10000

(291192 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 ?
4001p(24442)#/2-64121381Robert Price04/2017
400211^116555-720121380Enzo Doria11/2012
40032^403100-461267121346Enzo Doria07/2015
40042^403093-112213121344Enzo Doria06/2014
400529404^13385+13385^29404121340Hans Havermann02/2021
400628106^20745+20745^28106121332Hans Havermann02/2021
4007(316^48539+1)/317121330Eric Chen10/2017
4008(23*10^121320-71)/3121321Robert Price07/2020
40092^403004+1866361121317Enzo Doria03/2016
40102^402953+89121301Lelio R Paula10/2013
40112^402944-2788319121299Enzo Doria03/2016
4012(44*10^121297-719)/9121298Robert Price12/2018
4013(27*2^402865+1)/5121276Lelio R Paula04/2014
40142^402828-113183121264Enzo Doria07/2014
4015(17*10^121242+1)/9121243Serge Batalov05/2010
4016(15*2^402757+1)/101121242Lelio R Paula05/2014
40182^402715+1874223121230Enzo Doria06/2016
4017(35*10^121229-593)/9121230Robert Price07/2018
4019(91^61879+1)/92121222Paul Bourdelais09/2017
402028719^16568+16568^28719121174Hans Havermann02/2021
40217*10^121144+9121145Robert Price09/2015
402227490^25467+25467^27490121121Hans Havermann02/2021
402334575^3182+3182^34575121106Hans Havermann02/2021
40245*10^121100-37121101Robert Price11/2021
402529954^10935+10935^29954120979Hans Havermann02/2021
402633585^3992+3992^33585120946Hans Havermann02/2021
402740296^1003+1003^40296120941Hans Havermann02/2021
40282^401725-113251120932Enzo Doria07/2014
4029(15*2^401677-1)/19120917Lelio R Paula05/2014
40302^401652+73711120910Enzo Doria04/2016
4031(2^401632+3)/79120902Lelio R Paula04/2014
403240450^973+973^40450120870Hans Havermann01/2021
403310^120841+88417120842Patrick De Geest04/2020
403410^120841-123456789120841Robert Price02/2020
403510^120841-176853120841Patrick De Geest04/2020
40362^401406-2791331120836Enzo Doria03/2016
4037(28^83497+1)/29120832Robert Price07/2013
4038(22*10^120828+161)/3120829Robert Price05/2019
40392^401369+1867367120825Enzo Doria03/2016
4040(5*10^120821+43)/3120822Robert Price12/2021
4041(10^120782+29)/3120782Serge Batalov12/2014
40422^401215-1657120778Yves Minet07/2014
40432^401159+53120761Lelio R Paula10/2013
404427782^22179+22179^27782120739Hans Havermann01/2021
404532974^4585+4585^32974120730Hans Havermann02/2021
40462^401031-113047120723Enzo Doria07/2014
404730598^8813+8813^30598120713Hans Havermann02/2021
4048(71*10^120703-287)/9120704Robert Price09/2019
4049(29*2^400909-1)/303120685Lelio R Paula04/2014
405034793^2940+2940^34793120675Hans Havermann02/2021
4051(2^400846+538)/2120667Stefano Morozzi09/2020
4052(166*10^120654+11)/3120656Robert Price03/2021
405334066^3481+3481^34066120652Hans Havermann02/2021
40548*10^120637-27120638Robert Price10/2021
4055(2^400709+3546)/2120626Stefano Morozzi09/2020
4056(2^400700+3126)/2120623Stefano Morozzi09/2020
4057(2^400693+2634)/2120621Stefano Morozzi09/2020
40589*10^120617-61120618Robert Price06/2021
4059(29*10^120590-71)/3120591Robert Price07/2021
40602^400571-15120584Lelio R Paula10/2013
4061(10^120574+359)/9120574Serge Batalov12/2014
406227431^24810+24810^27431120550Hans Havermann02/2021
40632^400424-216413120540Enzo Doria04/2013
406429090^13911+13911^29090120531Hans Havermann02/2021
4065(2^400346+1722)/2120516Stefano Morozzi09/2020
406627899^20868+20868^27899120510Hans Havermann02/2021
406733740^3729+3729^33740120506Hans Havermann02/2021
4068(17*2^400200-1)/587120471Lelio R Paula05/2014
40692^400166+1874899120462Enzo Doria06/2016
4070(2^400165+1602)/2120462Stefano Morozzi09/2020
407137078^1771+1771^37078120438Hans Havermann02/2021
4072(2^400084+1638)/2120437Stefano Morozzi09/2020
4073(3*2^400045-1)/865120424Lelio R Paula04/2014
4074(2^399974+2790)/2120404Stefano Morozzi02/2021
40752^399966+73759120402Enzo Doria04/2016
4076(2^399961+2306)/2120400Stefano Morozzi02/2021
4077(112*10^120395-1)/3120397Serge Batalov12/2014
40782^399918-95120388Lelio R Paula04/2013
4079(28*10^120381-67)/3120382Robert Price10/2020
4080(49*10^120380-139)/9120381Robert Price03/2019
4081(2^399874+2194)/2120374Stefano Morozzi09/2020
40822^399792-1849259120350Enzo Doria08/2015
40839*10^120342-7120343Robert Price09/2015
4084(2^399751+786)/2120337Stefano Morozzi09/2020
4085(331*10^120332-7)/9120334Robert Price04/2022
4086(13*10^120306-37)/3120307Robert Price01/2019
4087(23*10^120299+37)/3120300Robert Price02/2022
4088(2^399604+3070)/2120293Stefano Morozzi09/2020
4089(2^399549+1062)/2120276Stefano Morozzi09/2020
40902^399526-1861721120270Enzo Doria11/2015
4091(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
409232016^5687+5687^32016120217Hans Havermann01/2021
4093(205*10^120212-1)/3120214Robert Price11/2021
40942^399322-2798111120208Enzo Doria04/2016
409530438^8867+8867^30438120163Hans Havermann02/2021
409772^64693-71^64693120157Robert Price03/2014
4096(17*10^120156-161)/9120157Robert Price02/2021
40982^399111-28489120145Enzo Doria08/2015
4099(2^399014+1318)/2120115Stefano Morozzi02/2021
410030254^9333+9333^30254120110Hans Havermann02/2021
410130882^7745+7745^30882120101Hans Havermann02/2021
41022^398877+105120074Donovan Johnson01/2006
4103(101*10^120072-87)/7120074Hans Havermann02/2015
4104(88^61751+1)/89120072Paul Bourdelais09/2017
41052^398710+57120024Lelio R Paula04/2013
4106(2^398698+1138)/2120020Stefano Morozzi09/2020
41072^398691-115057120018Enzo Doria06/2015
4108L(574219)120005Renaud Lifchitz03/2004
41092^398571+60413119982Yves Minet03/2011
411028623^15538+15538^28623119971Hans Havermann02/2021
4111p(24179)#/2-64119949Robert Price04/2017
41122^398448+1872001119945Enzo Doria05/2016
4113(191*10^119941-17)/3119943Robert Price11/2021
4114634^42803+42803^634119938Norbert Schneider07/2019
411531083^7220+7220^31083119935Hans Havermann01/2021
4116(68*10^119931-11)/3119933Robert Price01/2020
41178*10^119930-3119931Ray Chandler04/2011
4118(2^398398+774)/2119930Stefano Morozzi09/2020
4119(10^119880+179)/9119880Serge Batalov12/2014
4120(9*2^398145+1)/73119853Lelio R Paula04/2014
4121(10^119836+77)/3119836Robert Price01/2018
412228179^17870+17870^28179119821Hans Havermann02/2021
41232^398029+1872527119819Enzo Doria05/2016
412433142^4119+4119^33142119802Hans Havermann01/2021
41252^397897-113541119779Enzo Doria08/2014
412628636^15171+15171^28636119728Hans Havermann02/2021
4127(2^397696+1042)/2119719Stefano Morozzi09/2020
4128(19*10^119716+101)/3119717Robert Price09/2019
412929563^11208+11208^29563119717Hans Havermann02/2021
41302^397655-933075119707Paul Bourdelais06/2021
4131(21*2^397661-1)/27593119705Lelio R Paula04/2014
413228243^17308+17308^28243119701Hans Havermann02/2021
413377*10^119688+3119690Robert Price06/2020
4134(2^397504+1698)/2119661Stefano Morozzi09/2020
4135(58^67853-1)/57119653Paul Bourdelais09/2017
41362^397426+73849119638Enzo Doria04/2016
41378*10^119509+29119510Robert Price11/2021
41382^396933-112723119489Enzo Doria06/2014
413911^114738-150119488Enzo Doria10/2012
4140(4*10^119474+149)/9119474Robert Price04/2018
41412^396790-21119446Lelio R Paula04/2013
414232061^5300+5300^32061119405Hans Havermann01/2021
4143(2^396633-7)/5119398Lelio R Paula04/2014
414427382^22913+22913^27382119388Hans Havermann03/2021
4145(2^396577+2522)/2119382Stefano Morozzi09/2020
4146(2^396492+2230)/2119356Stefano Morozzi01/2021
4147(47*10^119354+259)/9119355Robert Price03/2022
4149105^59050+104119352Norbert Schneider11/2016
4148126^56824-125119352Norbert Schneider12/2018
41502^396469+111546435119350Paul Bourdelais10/2021
4151139^55690-138119345Norbert Schneider04/2019
4152790^41179+41179^790119322Norbert Schneider04/2019
41532^396374+73729119321Enzo Doria04/2016
415488*10^119295+3119297Robert Price05/2020
41552^396258-459491119286Enzo Doria05/2015
4156(2^396248+3126)/2119283Stefano Morozzi09/2020
41572^396128-396128-1119247Karsten Bonath06/2018
4158(893*10^119228+7)/9119230Robert Price06/2021
4159(31*10^119229+257)/9119230Robert Price12/2021
4160(28*10^119206-67)/3119207Robert Price10/2020
4161(2^395986+5)/76881119199Lelio R Paula04/2014
416211^114458+6119196Paul Bourdelais02/2021
4163(23*2^395942-1)/91119190Lelio R Paula04/2014
4164(2^395902+202)/2119179Stefano Morozzi09/2020
4165(2^395825+582)/2119155Stefano Morozzi09/2020
4166(2^395733+1130)/2119128Stefano Morozzi09/2020
416729548^10725+10725^29548119091Hans Havermann02/2021
4168(11*2^395548+1)/3119073Lelio R Paula04/2014
4169(30^80599+1)/31119054Robert Price07/2013
4170(232*10^119047+17)/3119049Robert Price04/2021
4171(43*10^119024-403)/9119025Robert Price01/2019
4172(4*10^119021+47)/3119022Robert Price01/2022
417326603^26888-26888^26603118978Norbert Schneider07/2021
41746*10^118964+43118965Robert Price07/2020
4175(8*10^118960+49)/3118961Robert Price05/2020
417631253^6402+6402^31253118959Hans Havermann02/2021
4177(194*10^118925-17)/3118927Robert Price09/2020
41782^395062-109121118926Enzo Doria04/2014
41792^395055-4627118924Yves Minet05/2019
4180(2^395054+702)/2118923Stefano Morozzi09/2020
41812^395018-224141118913Harrison Mesh06/2022
4182(2^395011+2526)/2118910Stefano Morozzi09/2020
4183(2^394918+78557)/3118882Lelio R Paula01/2015
4184(2^394858+1018)/2118864Stefano Morozzi09/2020
4185(77*10^118862-149)/9118863Robert Price03/2022
4186(16*10^118852+77)/3118853Robert Price03/2019
4187(2^394739+3)/1883118826Lelio R Paula04/2014
418810^118772+163599118773Patrick De Geest02/2021
419010^118772-40000000001118772Robert Price09/2020
418910^118772-207603118772Patrick De Geest02/2021
419126842^26577+26577^26842118763Hans Havermann02/2021
4192(2^394513+2034)/2118760Stefano Morozzi09/2020
4193(2^394473+2774)/2118748Stefano Morozzi02/2021
419427949^17710+17710^27949118734Hans Havermann02/2021
41952^394266+71389118686Enzo Doria04/2016
41962^394215-51261118671Tony Prest / Never Odd Or Even04/2018
4197(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
4198(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
4199(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
4200(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
4201(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
420229201^11568+11568^29201118652Hans Havermann02/2021
4203(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
4204(2^394131+2214)/2118645Stefano Morozzi09/2020
4205(17*10^118635+13)/3118636Robert Price01/2019
42065^169727+2118635Lelio R Paula08/2013
42072^394034-3118617M. Frind & P. Underwood09/2002
4208(7*10^118607+179)/3118608Robert Price09/2018
42093^248572-6242118599Enzo Doria05/2014
4210(3*2^393964-1)/181118594Lelio R Paula04/2014
4211(49*10^118576-319)/9118577Robert Price10/2021
42127^140303-6118570Robert Price11/2014
4213(2^393864+2686)/2118565Stefano Morozzi09/2020
4214(2^393862+3150)/2118564Stefano Morozzi09/2020
4215(2^393849+3762)/2118561Stefano Morozzi01/2021
4216(529*10^118554-7)/9118556Robert Price08/2021
421726712^26777-26777^26712118534Norbert Schneider07/2021
4218(2^393661+2666)/2118504Stefano Morozzi09/2020
4219(2^393650+1614)/2118501Stefano Morozzi09/2020
422027655^19264+19264^27655118495Hans Havermann02/2021
422110^118485+469413118486Patrick De Geest05/2021
422210^118485-50001118485Robert Price08/2020
4223(2^393528+1030)/2118464Stefano Morozzi09/2020
42242^393427+75683118434Enzo Doria04/2016
42252^393376-114749118418Enzo Doria04/2015
4226(65*10^118417+493)/9118418Robert Price08/2021
422730960^6671+6671^30960118397Hans Havermann02/2021
4228(2^393234+2010)/2118375Stefano Morozzi09/2020
4229(2^393205+3030)/2118367Stefano Morozzi09/2020
4230(2^393191+2174)/2118362Stefano Morozzi09/2020
42312^393180+73118359Lelio R Paula04/2013
423227546^19771+19771^27546118339Hans Havermann02/2021
4233p(23881)#/2+256118328Robert Price05/2017
4234(10^118324+359)/9118324Serge Batalov12/2014
4235(2^393048+570)/2118319Stefano Morozzi09/2020
4236p(23879)#/2+64118317Robert Price03/2017
42378*10^118308+59118309Robert Price11/2021
42389*10^118282+29118283Robert Price03/2022
4239(238*10^118265-1)/3118267Robert Price04/2020
4241(53*10^118216+1)/9118217Serge Batalov11/2010
4240(2^392707+1710)/2118217Stefano Morozzi09/2020
4242(7*2^392697+1)/15118214Renaud Lifchitz03/2011
4243(157^53819-1)/156118179Alexander Zhirkov06/2016
4244(2^392567+2750)/2118175Stefano Morozzi01/2021
424555*10^118172+3118174Robert Price07/2022
4246(19*2^392551+1)/3118171Lelio R Paula04/2014
424727185^22222+22222^27185118168Hans Havermann01/2021
42482^392516-29219118160Enzo Doria07/2015
424966*10^118155+7118157Robert Price07/2020
4250Phi(177231,10)118152Maksym Voznyy09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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