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 ?
3751(23*10^121320-71)/3121321Robert Price07/2020
37522^403004+1866361121317Enzo Doria03/2016
37532^402953+89121301Lelio R Paula10/2013
37542^402944-2788319121299Enzo Doria03/2016
3755(44*10^121297-719)/9121298Robert Price12/2018
3756(27*2^402865+1)/5121276Lelio R Paula04/2014
37572^402828-113183121264Enzo Doria07/2014
3758(17*10^121242+1)/9121243Serge Batalov05/2010
3759(15*2^402757+1)/101121242Lelio R Paula05/2014
37612^402715+1874223121230Enzo Doria06/2016
3760(35*10^121229-593)/9121230Robert Price07/2018
3762(91^61879+1)/92121222Paul Bourdelais09/2017
376328719^16568+16568^28719121174Hans Havermann02/2021
37647*10^121144+9121145Robert Price09/2015
376527490^25467+25467^27490121121Hans Havermann02/2021
376634575^3182+3182^34575121106Hans Havermann02/2021
37675*10^121100-37121101Robert Price11/2021
376829954^10935+10935^29954120979Hans Havermann02/2021
376933585^3992+3992^33585120946Hans Havermann02/2021
377040296^1003+1003^40296120941Hans Havermann02/2021
37712^401725-113251120932Enzo Doria07/2014
3772(15*2^401677-1)/19120917Lelio R Paula05/2014
37732^401652+73711120910Enzo Doria04/2016
3774(2^401632+3)/79120902Lelio R Paula04/2014
377540450^973+973^40450120870Hans Havermann01/2021
377610^120841+88417120842Patrick De Geest04/2020
377710^120841-123456789120841Robert Price02/2020
377810^120841-176853120841Patrick De Geest04/2020
37792^401406-2791331120836Enzo Doria03/2016
3780(28^83497+1)/29120832Robert Price07/2013
3781(22*10^120828+161)/3120829Robert Price05/2019
37822^401369+1867367120825Enzo Doria03/2016
3783(5*10^120821+43)/3120822Robert Price12/2021
3784(10^120782+29)/3120782Serge Batalov12/2014
37852^401215-1657120778Yves Minet07/2014
37862^401159+53120761Lelio R Paula10/2013
378727782^22179+22179^27782120739Hans Havermann01/2021
378832974^4585+4585^32974120730Hans Havermann02/2021
37892^401031-113047120723Enzo Doria07/2014
379030598^8813+8813^30598120713Hans Havermann02/2021
3791(71*10^120703-287)/9120704Robert Price09/2019
3792(29*2^400909-1)/303120685Lelio R Paula04/2014
379334793^2940+2940^34793120675Hans Havermann02/2021
3794(2^400846+538)/2120667Stefano Morozzi09/2020
3795(166*10^120654+11)/3120656Robert Price03/2021
379634066^3481+3481^34066120652Hans Havermann02/2021
37978*10^120637-27120638Robert Price10/2021
3798(2^400709+3546)/2120626Stefano Morozzi09/2020
3799(2^400700+3126)/2120623Stefano Morozzi09/2020
3800(2^400693+2634)/2120621Stefano Morozzi09/2020
38019*10^120617-61120618Robert Price06/2021
3802(29*10^120590-71)/3120591Robert Price07/2021
38032^400571-15120584Lelio R Paula10/2013
3804(10^120574+359)/9120574Serge Batalov12/2014
380527431^24810+24810^27431120550Hans Havermann02/2021
38062^400424-216413120540Enzo Doria04/2013
380729090^13911+13911^29090120531Hans Havermann02/2021
3808(2^400346+1722)/2120516Stefano Morozzi09/2020
380927899^20868+20868^27899120510Hans Havermann02/2021
381033740^3729+3729^33740120506Hans Havermann02/2021
3811(17*2^400200-1)/587120471Lelio R Paula05/2014
38122^400166+1874899120462Enzo Doria06/2016
3813(2^400165+1602)/2120462Stefano Morozzi09/2020
381437078^1771+1771^37078120438Hans Havermann02/2021
3815(2^400084+1638)/2120437Stefano Morozzi09/2020
3816(3*2^400045-1)/865120424Lelio R Paula04/2014
3817(2^399974+2790)/2120404Stefano Morozzi02/2021
38182^399966+73759120402Enzo Doria04/2016
3819(2^399961+2306)/2120400Stefano Morozzi02/2021
3820(112*10^120395-1)/3120397Serge Batalov12/2014
38212^399918-95120388Lelio R Paula04/2013
3822(28*10^120381-67)/3120382Robert Price10/2020
3823(49*10^120380-139)/9120381Robert Price03/2019
3824(2^399874+2194)/2120374Stefano Morozzi09/2020
38252^399792-1849259120350Enzo Doria08/2015
38269*10^120342-7120343Robert Price09/2015
3827(2^399751+786)/2120337Stefano Morozzi09/2020
3828(13*10^120306-37)/3120307Robert Price01/2019
3829(2^399604+3070)/2120293Stefano Morozzi09/2020
3830(2^399549+1062)/2120276Stefano Morozzi09/2020
38312^399526-1861721120270Enzo Doria11/2015
3832(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
383332016^5687+5687^32016120217Hans Havermann01/2021
3834(205*10^120212-1)/3120214Robert Price11/2021
38352^399322-2798111120208Enzo Doria04/2016
383630438^8867+8867^30438120163Hans Havermann02/2021
383872^64693-71^64693120157Robert Price03/2014
3837(17*10^120156-161)/9120157Robert Price02/2021
38392^399111-28489120145Enzo Doria08/2015
3840(2^399014+1318)/2120115Stefano Morozzi02/2021
384130254^9333+9333^30254120110Hans Havermann02/2021
384230882^7745+7745^30882120101Hans Havermann02/2021
38442^398877+105120074Donovan Johnson01/2006
3843(101*10^120072-87)/7120074Hans Havermann02/2015
3845(88^61751+1)/89120072Paul Bourdelais09/2017
38462^398710+57120024Lelio R Paula04/2013
3847(2^398698+1138)/2120020Stefano Morozzi09/2020
38482^398691-115057120018Enzo Doria06/2015
3849L(574219)120005Renaud Lifchitz03/2004
38502^398571+60413119982Yves Minet03/2011
385128623^15538+15538^28623119971Hans Havermann02/2021
3852p(24179)#/2-64119949Robert Price04/2017
38532^398448+1872001119945Enzo Doria05/2016
3854(191*10^119941-17)/3119943Robert Price11/2021
3855634^42803+42803^634119938Norbert Schneider07/2019
385631083^7220+7220^31083119935Hans Havermann01/2021
3857(68*10^119931-11)/3119933Robert Price01/2020
38588*10^119930-3119931Ray Chandler04/2011
3859(2^398398+774)/2119930Stefano Morozzi09/2020
3860(10^119880+179)/9119880Serge Batalov12/2014
3861(9*2^398145+1)/73119853Lelio R Paula04/2014
3862(10^119836+77)/3119836Robert Price01/2018
386328179^17870+17870^28179119821Hans Havermann02/2021
38642^398029+1872527119819Enzo Doria05/2016
386533142^4119+4119^33142119802Hans Havermann01/2021
38662^397897-113541119779Enzo Doria08/2014
386728636^15171+15171^28636119728Hans Havermann02/2021
3868(2^397696+1042)/2119719Stefano Morozzi09/2020
3870(19*10^119716+101)/3119717Robert Price09/2019
386929563^11208+11208^29563119717Hans Havermann02/2021
38712^397655-933075119707Paul Bourdelais06/2021
3872(21*2^397661-1)/27593119705Lelio R Paula04/2014
387328243^17308+17308^28243119701Hans Havermann02/2021
387477*10^119688+3119690Robert Price06/2020
3875(2^397504+1698)/2119661Stefano Morozzi09/2020
3876(58^67853-1)/57119653Paul Bourdelais09/2017
38772^397426+73849119638Enzo Doria04/2016
38788*10^119509+29119510Robert Price11/2021
38792^396933-112723119489Enzo Doria06/2014
388011^114738-150119488Enzo Doria10/2012
3881(4*10^119474+149)/9119474Robert Price04/2018
38822^396790-21119446Lelio R Paula04/2013
388332061^5300+5300^32061119405Hans Havermann01/2021
3884(2^396633-7)/5119398Lelio R Paula04/2014
388527382^22913+22913^27382119388Hans Havermann03/2021
3886(2^396577+2522)/2119382Stefano Morozzi09/2020
3887(2^396492+2230)/2119356Stefano Morozzi01/2021
3889105^59050+104119352Norbert Schneider11/2016
3888126^56824-125119352Norbert Schneider12/2018
38902^396469+111546435119350Paul Bourdelais10/2021
3891139^55690-138119345Norbert Schneider04/2019
3892790^41179+41179^790119322Norbert Schneider04/2019
38932^396374+73729119321Enzo Doria04/2016
389488*10^119295+3119297Robert Price05/2020
38952^396258-459491119286Enzo Doria05/2015
3896(2^396248+3126)/2119283Stefano Morozzi09/2020
38972^396128-396128-1119247Karsten Bonath06/2018
3899(893*10^119228+7)/9119230Robert Price06/2021
3898(31*10^119229+257)/9119230Robert Price12/2021
3900(28*10^119206-67)/3119207Robert Price10/2020
3901(2^395986+5)/76881119199Lelio R Paula04/2014
390211^114458+6119196Paul Bourdelais02/2021
3903(23*2^395942-1)/91119190Lelio R Paula04/2014
3904(2^395902+202)/2119179Stefano Morozzi09/2020
3905(2^395825+582)/2119155Stefano Morozzi09/2020
3906(2^395733+1130)/2119128Stefano Morozzi09/2020
390729548^10725+10725^29548119091Hans Havermann02/2021
3908(11*2^395548+1)/3119073Lelio R Paula04/2014
3909(30^80599+1)/31119054Robert Price07/2013
3910(232*10^119047+17)/3119049Robert Price04/2021
3911(43*10^119024-403)/9119025Robert Price01/2019
391226603^26888-26888^26603118978Norbert Schneider07/2021
39136*10^118964+43118965Robert Price07/2020
3914(8*10^118960+49)/3118961Robert Price05/2020
391531253^6402+6402^31253118959Hans Havermann02/2021
3916(194*10^118925-17)/3118927Robert Price09/2020
39172^395062-109121118926Enzo Doria04/2014
39182^395055-4627118924Yves Minet05/2019
3919(2^395054+702)/2118923Stefano Morozzi09/2020
3920(2^395011+2526)/2118910Stefano Morozzi09/2020
3921(2^394918+78557)/3118882Lelio R Paula01/2015
3922(2^394858+1018)/2118864Stefano Morozzi09/2020
3923(16*10^118852+77)/3118853Robert Price03/2019
3924(2^394739+3)/1883118826Lelio R Paula04/2014
392510^118772+163599118773Patrick De Geest02/2021
392710^118772-40000000001118772Robert Price09/2020
392610^118772-207603118772Patrick De Geest02/2021
392826842^26577+26577^26842118763Hans Havermann02/2021
3929(2^394513+2034)/2118760Stefano Morozzi09/2020
3930(2^394473+2774)/2118748Stefano Morozzi02/2021
393127949^17710+17710^27949118734Hans Havermann02/2021
39322^394266+71389118686Enzo Doria04/2016
39332^394215-51261118671Tony Prest / Never Odd Or Even04/2018
3934(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
3935(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
3936(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
3937(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
3938(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
393929201^11568+11568^29201118652Hans Havermann02/2021
3940(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
3941(2^394131+2214)/2118645Stefano Morozzi09/2020
3942(17*10^118635+13)/3118636Robert Price01/2019
39435^169727+2118635Lelio R Paula08/2013
39442^394034-3118617M. Frind & P. Underwood09/2002
3945(7*10^118607+179)/3118608Robert Price09/2018
39463^248572-6242118599Enzo Doria05/2014
3947(3*2^393964-1)/181118594Lelio R Paula04/2014
3948(49*10^118576-319)/9118577Robert Price10/2021
39497^140303-6118570Robert Price11/2014
3950(2^393864+2686)/2118565Stefano Morozzi09/2020
3951(2^393862+3150)/2118564Stefano Morozzi09/2020
3952(2^393849+3762)/2118561Stefano Morozzi01/2021
3953(529*10^118554-7)/9118556Robert Price08/2021
395426712^26777-26777^26712118534Norbert Schneider07/2021
3955(2^393661+2666)/2118504Stefano Morozzi09/2020
3956(2^393650+1614)/2118501Stefano Morozzi09/2020
395727655^19264+19264^27655118495Hans Havermann02/2021
395810^118485+469413118486Patrick De Geest05/2021
395910^118485-50001118485Robert Price08/2020
3960(2^393528+1030)/2118464Stefano Morozzi09/2020
39612^393427+75683118434Enzo Doria04/2016
39622^393376-114749118418Enzo Doria04/2015
3963(65*10^118417+493)/9118418Robert Price08/2021
396430960^6671+6671^30960118397Hans Havermann02/2021
3965(2^393234+2010)/2118375Stefano Morozzi09/2020
3966(2^393205+3030)/2118367Stefano Morozzi09/2020
3967(2^393191+2174)/2118362Stefano Morozzi09/2020
39682^393180+73118359Lelio R Paula04/2013
396927546^19771+19771^27546118339Hans Havermann02/2021
3970p(23881)#/2+256118328Robert Price05/2017
3971(10^118324+359)/9118324Serge Batalov12/2014
3972(2^393048+570)/2118319Stefano Morozzi09/2020
3973p(23879)#/2+64118317Robert Price03/2017
39748*10^118308+59118309Robert Price11/2021
3975(238*10^118265-1)/3118267Robert Price04/2020
3977(53*10^118216+1)/9118217Serge Batalov11/2010
3976(2^392707+1710)/2118217Stefano Morozzi09/2020
3978(7*2^392697+1)/15118214Renaud Lifchitz03/2011
3979(157^53819-1)/156118179Alexander Zhirkov06/2016
3980(2^392567+2750)/2118175Stefano Morozzi01/2021
3981(19*2^392551+1)/3118171Lelio R Paula04/2014
398227185^22222+22222^27185118168Hans Havermann01/2021
39832^392516-29219118160Enzo Doria07/2015
398466*10^118155+7118157Robert Price07/2020
3985Phi(177231,10)118152Maksym Voznyy09/2015
39862^392413-112123118129Enzo Doria06/2014
398727491^19798+19798^27491118119Hans Havermann02/2021
3988(49*10^118109-319)/9118110Robert Price10/2021
3989(2^392342+5)/27118106Lelio R Paula04/2014
3990(2^392333+1782)/2118104Stefano Morozzi01/2021
39912^392300-1841429118095Enzo Doria06/2015
39922^392220+75241118070Enzo Doria04/2016
399327836^17409+17409^27836118047Hans Havermann02/2021
399410^118009+664447118010Patrick De Geest07/2018
399510^118009-20001118009Robert Price01/2018
3996(14*10^117991+61)/3117992Robert Price12/2018
39972^391933+5897117984Yves Minet02/2011
39982^391912-1849259117978Enzo Doria08/2015
399928357^14440+14440^28357117953Hans Havermann02/2021
4000(2^391812+5)/14181117944Lelio R Paula04/2014


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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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