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 ?
40012^399111-28489120145Enzo Doria08/2015
4002(2^399014+1318)/2120115Stefano Morozzi02/2021
400330254^9333+9333^30254120110Hans Havermann02/2021
400430882^7745+7745^30882120101Hans Havermann02/2021
40052^398877+105120074Donovan Johnson01/2006
4006(101*10^120072-87)/7120074Hans Havermann02/2015
4007(88^61751+1)/89120072Paul Bourdelais09/2017
40082^398710+57120024Lelio R Paula04/2013
4009(2^398698+1138)/2120020Stefano Morozzi09/2020
40102^398691-115057120018Enzo Doria06/2015
4011L(574219)120005Renaud Lifchitz03/2004
40122^398571+60413119982Yves Minet03/2011
401328623^15538+15538^28623119971Hans Havermann02/2021
4014p(24179)#/2-64119949Robert Price04/2017
40152^398448+1872001119945Enzo Doria05/2016
4016(191*10^119941-17)/3119943Robert Price11/2021
4017634^42803+42803^634119938Norbert Schneider07/2019
401831083^7220+7220^31083119935Hans Havermann01/2021
4019(68*10^119931-11)/3119933Robert Price01/2020
40208*10^119930-3119931Ray Chandler04/2011
4021(2^398398+774)/2119930Stefano Morozzi09/2020
4022(10^119880+179)/9119880Serge Batalov12/2014
4023(9*2^398145+1)/73119853Lelio R Paula04/2014
4024(10^119836+77)/3119836Robert Price01/2018
402528179^17870+17870^28179119821Hans Havermann02/2021
40262^398029+1872527119819Enzo Doria05/2016
402733142^4119+4119^33142119802Hans Havermann01/2021
40282^397897-113541119779Enzo Doria08/2014
402928636^15171+15171^28636119728Hans Havermann02/2021
4030(2^397696+1042)/2119719Stefano Morozzi09/2020
4032(19*10^119716+101)/3119717Robert Price09/2019
403129563^11208+11208^29563119717Hans Havermann02/2021
40332^397655-933075119707Paul Bourdelais06/2021
4034(21*2^397661-1)/27593119705Lelio R Paula04/2014
403528243^17308+17308^28243119701Hans Havermann02/2021
403677*10^119688+3119690Robert Price06/2020
4037(2^397504+1698)/2119661Stefano Morozzi09/2020
4038(58^67853-1)/57119653Paul Bourdelais09/2017
40392^397426+73849119638Enzo Doria04/2016
40408*10^119509+29119510Robert Price11/2021
40412^396933-112723119489Enzo Doria06/2014
404211^114738-150119488Enzo Doria10/2012
4043(4*10^119474+149)/9119474Robert Price04/2018
40442^396790-21119446Lelio R Paula04/2013
404532061^5300+5300^32061119405Hans Havermann01/2021
4046(2^396633-7)/5119398Lelio R Paula04/2014
404727382^22913+22913^27382119388Hans Havermann03/2021
4048(2^396577+2522)/2119382Stefano Morozzi09/2020
4049(2^396492+2230)/2119356Stefano Morozzi01/2021
4050(47*10^119354+259)/9119355Robert Price03/2022
4052105^59050+104119352Norbert Schneider11/2016
4051126^56824-125119352Norbert Schneider12/2018
40532^396469+111546435119350Paul Bourdelais10/2021
4054139^55690-138119345Norbert Schneider04/2019
4055790^41179+41179^790119322Norbert Schneider04/2019
40562^396374+73729119321Enzo Doria04/2016
405788*10^119295+3119297Robert Price05/2020
40582^396258-459491119286Enzo Doria05/2015
4059(2^396248+3126)/2119283Stefano Morozzi09/2020
40602^396128-396128-1119247Karsten Bonath06/2018
4062(893*10^119228+7)/9119230Robert Price06/2021
4061(31*10^119229+257)/9119230Robert Price12/2021
4063(28*10^119206-67)/3119207Robert Price10/2020
4064(2^395986+5)/76881119199Lelio R Paula04/2014
406511^114458+6119196Paul Bourdelais02/2021
4066(23*2^395942-1)/91119190Lelio R Paula04/2014
4067(2^395902+202)/2119179Stefano Morozzi09/2020
4068(2^395825+582)/2119155Stefano Morozzi09/2020
4069(2^395733+1130)/2119128Stefano Morozzi09/2020
407029548^10725+10725^29548119091Hans Havermann02/2021
4071(11*2^395548+1)/3119073Lelio R Paula04/2014
4072(30^80599+1)/31119054Robert Price07/2013
4073(232*10^119047+17)/3119049Robert Price04/2021
4074(43*10^119024-403)/9119025Robert Price01/2019
4075(4*10^119021+47)/3119022Robert Price01/2022
407626603^26888-26888^26603118978Norbert Schneider07/2021
40776*10^118964+43118965Robert Price07/2020
4078(8*10^118960+49)/3118961Robert Price05/2020
407931253^6402+6402^31253118959Hans Havermann02/2021
4080(194*10^118925-17)/3118927Robert Price09/2020
40812^395062-109121118926Enzo Doria04/2014
40822^395055-4627118924Yves Minet05/2019
4083(2^395054+702)/2118923Stefano Morozzi09/2020
40842^395018-224141118913Harrison Mesh06/2022
4085(2^395011+2526)/2118910Stefano Morozzi09/2020
4086(2^394918+78557)/3118882Lelio R Paula01/2015
4087(2^394858+1018)/2118864Stefano Morozzi09/2020
4088(77*10^118862-149)/9118863Robert Price03/2022
4089(16*10^118852+77)/3118853Robert Price03/2019
4090(2^394739+3)/1883118826Lelio R Paula04/2014
409110^118772+163599118773Patrick De Geest02/2021
409310^118772-40000000001118772Robert Price09/2020
409210^118772-207603118772Patrick De Geest02/2021
409426842^26577+26577^26842118763Hans Havermann02/2021
4095(2^394513+2034)/2118760Stefano Morozzi09/2020
4096(2^394473+2774)/2118748Stefano Morozzi02/2021
409727949^17710+17710^27949118734Hans Havermann02/2021
40982^394266+71389118686Enzo Doria04/2016
40992^394215-51261118671Tony Prest / Never Odd Or Even04/2018
4100(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
4101(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
4102(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
4103(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
4104(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
410529201^11568+11568^29201118652Hans Havermann02/2021
4106(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
4107(2^394131+2214)/2118645Stefano Morozzi09/2020
4108(17*10^118635+13)/3118636Robert Price01/2019
41095^169727+2118635Lelio R Paula08/2013
41102^394034-3118617M. Frind & P. Underwood09/2002
4111(7*10^118607+179)/3118608Robert Price09/2018
41123^248572-6242118599Enzo Doria05/2014
4113(3*2^393964-1)/181118594Lelio R Paula04/2014
4114(49*10^118576-319)/9118577Robert Price10/2021
41157^140303-6118570Robert Price11/2014
4116(2^393864+2686)/2118565Stefano Morozzi09/2020
4117(2^393862+3150)/2118564Stefano Morozzi09/2020
4118(2^393849+3762)/2118561Stefano Morozzi01/2021
4119(529*10^118554-7)/9118556Robert Price08/2021
412026712^26777-26777^26712118534Norbert Schneider07/2021
4121(2^393661+2666)/2118504Stefano Morozzi09/2020
4122(2^393650+1614)/2118501Stefano Morozzi09/2020
412327655^19264+19264^27655118495Hans Havermann02/2021
412410^118485+469413118486Patrick De Geest05/2021
412510^118485-50001118485Robert Price08/2020
4126(2^393528+1030)/2118464Stefano Morozzi09/2020
41272^393427+75683118434Enzo Doria04/2016
41282^393376-114749118418Enzo Doria04/2015
4129(65*10^118417+493)/9118418Robert Price08/2021
413030960^6671+6671^30960118397Hans Havermann02/2021
4131(2^393234+2010)/2118375Stefano Morozzi09/2020
4132(2^393205+3030)/2118367Stefano Morozzi09/2020
4133(2^393191+2174)/2118362Stefano Morozzi09/2020
41342^393180+73118359Lelio R Paula04/2013
413527546^19771+19771^27546118339Hans Havermann02/2021
4136p(23881)#/2+256118328Robert Price05/2017
4137(10^118324+359)/9118324Serge Batalov12/2014
4138(2^393048+570)/2118319Stefano Morozzi09/2020
4139p(23879)#/2+64118317Robert Price03/2017
41408*10^118308+59118309Robert Price11/2021
41419*10^118282+29118283Robert Price03/2022
4142(238*10^118265-1)/3118267Robert Price04/2020
4144(53*10^118216+1)/9118217Serge Batalov11/2010
4143(2^392707+1710)/2118217Stefano Morozzi09/2020
4145(7*2^392697+1)/15118214Renaud Lifchitz03/2011
4146(157^53819-1)/156118179Alexander Zhirkov06/2016
4147(2^392567+2750)/2118175Stefano Morozzi01/2021
4148(19*2^392551+1)/3118171Lelio R Paula04/2014
414927185^22222+22222^27185118168Hans Havermann01/2021
41502^392516-29219118160Enzo Doria07/2015
415166*10^118155+7118157Robert Price07/2020
4152Phi(177231,10)118152Maksym Voznyy09/2015
41532^392413-112123118129Enzo Doria06/2014
415427491^19798+19798^27491118119Hans Havermann02/2021
4155(49*10^118109-319)/9118110Robert Price10/2021
4156(2^392342+5)/27118106Lelio R Paula04/2014
4157(2^392333+1782)/2118104Stefano Morozzi01/2021
41582^392300-1841429118095Enzo Doria06/2015
41592^392220+75241118070Enzo Doria04/2016
416027836^17409+17409^27836118047Hans Havermann02/2021
416110^118009+664447118010Patrick De Geest07/2018
416210^118009-20001118009Robert Price01/2018
4163(14*10^117991+61)/3117992Robert Price12/2018
41642^391933+5897117984Yves Minet02/2011
41652^391912-1849259117978Enzo Doria08/2015
416628357^14440+14440^28357117953Hans Havermann02/2021
4167(2^391812+5)/14181117944Lelio R Paula04/2014
4168(7*10^117930-79)/9117930Robert Price01/2021
416927531^19168+19168^27531117904Hans Havermann02/2021
4170(46*10^117902+683)/9117903Robert Price03/2019
417127670^18189+18189^27670117869Hans Havermann02/2021
4172(7*2^391521+1)/285117858Lelio R Paula04/2014
4173(56*10^117856+583)/9117857Robert Price08/2021
417432169^4606+4606^32169117846Hans Havermann02/2021
4175(71*10^117803-143)/9117804Robert Price10/2021
41762^391324+90901117801Yves Minet02/2011
41772^391301-1859923117794Enzo Doria03/2016
41782^391261-4131117782Yves Minet02/2018
4179(2^391211+554)/2117766Stefano Morozzi09/2020
418038434^1157+1157^38434117737Hans Havermann01/2021
4181(2^391115-7)/11791117734Lelio R Paula04/2014
4182(85*10^117719+473)/9117720Robert Price01/2020
4183(2^391049+582)/2117718Stefano Morozzi09/2020
418431083^6122+6122^31083117709Hans Havermann02/2021
41852^390960+1880881117691Enzo Doria11/2016
4186(71*10^117685+91)/9117686Robert Price04/2022
41872^390897-1860553117672Enzo Doria11/2015
41882^390889-115003117670Enzo Doria06/2015
41892^390779-30337117637Paul Bourdelais02/2012
4190(2^390735+378)/2117623Stefano Morozzi02/2021
419111^112916-780117590Enzo Doria12/2012
419227641^17916+17916^27641117564Hans Havermann02/2021
419327906^16321+16321^27906117561Hans Havermann02/2021
419427294^20275+20275^27294117555Hans Havermann02/2021
4195(2^390473+1002)/2117544Stefano Morozzi09/2020
419635912^1875+1875^35912117541Hans Havermann02/2021
4197(16^97613-5^97613)/11117537Robert Price07/2013
4198(2^390438+1774)/2117534Stefano Morozzi01/2021
4199(2^390418+1722)/2117528Stefano Morozzi09/2020
4200(2^390403+654)/2117523Stefano Morozzi09/2020
4201(2^390343+2246)/2117505Stefano Morozzi01/2021
420228043^15478+15478^28043117493Hans Havermann02/2021
4203(17*2^390272+1)/1983117482Lelio R Paula04/2014
420437077^1474+1474^37077117479Hans Havermann01/2021
420531^78759-30117459Theodore Burton02/2007
4206(2^390176+1222)/2117455Stefano Morozzi09/2020
4207(2^390133+1242)/2117442Stefano Morozzi09/2020
4208(2^390013+2634)/2117406Stefano Morozzi09/2020
42093*10^117402+61117403Robert Price09/2020
42102^389998+37117402Lelio R Paula03/2013
4211(2^389977+314)/2117395Stefano Morozzi09/2020
4212(2^389921+342)/2117378Stefano Morozzi01/2021
421371830^43+43^71830117333Hans Havermann01/2021
4214(2^389768+1582)/2117332Stefano Morozzi09/2020
421533802^2951+2951^33802117292Hans Havermann02/2021
421626789^23866+23866^26789117277Hans Havermann02/2021
421729^80192-1*80192^29117273Dylan Delgado12/2019
4218(101*10^117260+7)/9117262Robert Price02/2022
4219(13*10^117249+161)/3117250Robert Price11/2018
42202^389478+43117245Lelio R Paula03/2013
4221(298*10^117229-7)/3117231Robert Price06/2020
4222(2^389416+342)/2117226Stefano Morozzi01/2021
4223(29*2^389351-1)/9117207Lelio R Paula04/2014
42245*10^117205+23117206Robert Price03/2019
4225(2^389341-7)/3865117200Lelio R Paula03/2014
422627272^19827+19827^27272117195Hans Havermann01/2021
4227(2^389276+2650)/2117184Stefano Morozzi09/2020
4228(844*10^117175-7)/9117177Robert Price05/2021
422910^117142+209223117143Patrick De Geest04/2018
423110^117142-1000000001117142Robert Price03/2018
423010^117142-966057117142Patrick De Geest04/2018
423210^117135+360577117136Patrick De Geest07/2018
423310^117135-401117135Robert Price01/2018
423426415^26488-26488^26415117126Norbert Schneider05/2021
42354*10^117123+79117124Robert Price08/2018
42362^389033-12797413117111Enzo Doria04/2016
4237(2^388987+2634)/2117097Stefano Morozzi09/2020
42382^388960-109505117089Enzo Doria04/2014
42397*10^117082-57117083Robert Price06/2020
4240(2^388928-5)/569117077Lelio R Paula03/2014
42412^388888-1529117067Yves Minet01/2013
424210^117059+28879117060Patrick De Geest05/2016
4243(10^117059-71)/1117059Serge Batalov12/2014
4244(2^388854+3630)/2117057Stefano Morozzi09/2020
4245(2^388842+2098)/2117053Stefano Morozzi09/2020
4246(2^388789+3150)/2117037Stefano Morozzi09/2020
4247(2^388748+378)/2117025Stefano Morozzi02/2021
4248(693^41189-1)/692117005Michael Stocker05/2020
4249(26*10^116999-503)/9117000Robert Price07/2018
4250(2^388609+1554)/2116983Stefano Morozzi09/2020


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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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