PRP Records

Probable Primes Top 10000

(271023 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 ?
42512^338559-1858777101917Enzo Doria04/2016
4252(9*2^338520+1)/365101904Lelio R Paula12/2013
425324502^14419+14419^24502101903Hans Havermann01/2019
42542^338497-17041101898Enzo Doria05/2013
42552^338475+54615101892Lelio R Paula10/2016
42562^338426-19797101877Enzo Doria06/2013
42572^338368-20369101859Enzo Doria06/2013
42582^338366+74179101859Enzo Doria04/2016
425927088^5755+5755^27088101853Hans Havermann01/2019
42602^338280-19745101833Enzo Doria06/2013
4261(3*2^338236-1)/347101818Lelio R Paula03/2014
42626^130841+103101815Lelio R Paula10/2016
42632^338122-20117101785Enzo Doria06/2013
4264(2^338139+5)/905333101785Lelio R Paula12/2013
426535^65917-7092101781Enzo Doria03/2013
42662^338010-19833101752Enzo Doria06/2013
42673^213215-76101730Lelio R Paula09/2016
426823907^17998+17998^23907101730Hans Havermann01/2019
426910^101728+154953101729Patrick De Geest02/2020
42722^337930+63101728Lelio R Paula07/2011
427010^101728-987654321101728Robert Price12/2019
427110^101728-60741101728Patrick De Geest02/2020
42732^337920+1869661101725Enzo Doria05/2016
427424116^16509+16509^24116101715Hans Havermann01/2019
4275(2^337875+3174)/2101711Stefano Morozzi09/2020
42762^337859-19645101706Enzo Doria05/2013
42772^337754+1869169101675Enzo Doria05/2016
42783*10^101657-37101658Robert Price07/2018
4279(31*2^337677-1)/593101650Lelio R Paula03/2014
428011^97605-24101646Lelio R Paula10/2016
4281(2^337624+3606)/2101635Stefano Morozzi09/2020
42828^112539-112539101633Robert Price01/2014
428325694^9003+9003^25694101605Hans Havermann12/2018
42842^337515-19869101603Enzo Doria06/2013
42852^337473+719101590Lelio R Paula08/2011
4286(2^337485-509203)/656647157101585Lelio R Paula12/2013
42872^337452-108815101584Enzo Doria03/2014
42882^337453+1185101584Lelio R Paula09/2016
42892^337410-113561101571Enzo Doria08/2014
42902^337387+855101564Lelio R Paula09/2016
42912^337367-17295101558Lelio R Paula09/2016
42922^337342-109035101551Enzo Doria04/2014
429323703^19238+19238^23703101548Hans Havermann12/2018
4294(26*10^101537-167)/3101538Robert Price10/2019
42952^337267-19101528Lelio R Paula07/2011
4296(2^337259+1766)/2101525Stefano Morozzi09/2020
4297(2^337195+2646)/2101506Stefano Morozzi09/2020
42982^337183-19989101503Enzo Doria06/2013
42992^337149+72425101492Enzo Doria04/2016
430024041^16642+16642^24041101483Hans Havermann12/2018
430133982^969+969^33982101482Hans Havermann12/2018
43022^337101-20241101478Enzo Doria06/2013
43032^337035-20001101458Enzo Doria06/2013
4304(7*10^101456+89)/3101457Robert Price08/2020
43052^337017-16995101453Lelio R Paula09/2016
43062^336979-115315101441Enzo Doria06/2015
43072^336970-20885101439Enzo Doria06/2013
43082^336958+79101435Lelio R Paula10/2009
43092^336942+169101430Lelio R Paula10/2009
4310(15185*2^336894-1)/7939101416Lelio R Paula05/2015
43114*10^101415-89101416Robert Price11/2018
4312(14*10^101410-89)/3101411Robert Price05/2020
43132^336871+257463101409Tony Prest / Never Odd Or Even04/2016
43142^336871+318105101409Tony Prest / Never Odd Or Even04/2016
43152^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
43162^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
43172^336871+389273101409Tony Prest / Never Odd Or Even04/2016
43182^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
43192^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
43202^336871+586905101409Tony Prest / Never Odd Or Even04/2016
43212^336871+674571101409Tony Prest / Never Odd Or Even04/2016
43222^336871+707009101409Tony Prest / Never Odd Or Even04/2016
43232^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
43242^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
43252^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
43262^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
43272^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
43282^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
43292^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
43302^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
4331(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
4332(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
4333(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
4334(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
433524097^16150+16150^24097101405Hans Havermann12/2018
43362^336842+94065101400Lelio R Paula09/2016
4337(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
4338(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
4339(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
4340(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
4341(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
4342(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
4343(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
434410^101369+203811101370Patrick De Geest11/2016
434510^101369-99101369Lelio R Paula09/2016
4346(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
43472^336701-113563101358Enzo Doria08/2014
434889717!4-512101351Robert Price11/2019
43492^336644-109023101340Enzo Doria04/2014
43502^336601-21081101327Enzo Doria06/2013
435120^77869+63101310Lelio R Paula09/2016
4352(13*2^336523-1)/19101304Lelio R Paula03/2014
43536^130179-137101299Lelio R Paula10/2016
4354(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
4355(24737*2^336485+1)/7285101293Lelio R Paula07/2014
4356(2^336448+9)/497405101276Lelio R Paula12/2013
43572^336369-19753101258Enzo Doria05/2013
435823842^17653+17653^23842101253Hans Havermann11/2018
43592^336350-344291101252Enzo Doria07/2015
4360(56*10^101222-47)/9101223Robert Price02/2019
43612^336243-108777101220Enzo Doria03/2014
4362(31*2^336189-1)/19101204Lelio R Paula03/2014
436323535^19954+19954^23535101202Hans Havermann11/2018
4364(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
43652^336150-20393101192Enzo Doria06/2013
436623996^16473+16473^23996101186Hans Havermann11/2018
43672^336112-1865249101180Enzo Doria03/2016
43682^336103-109015101178Enzo Doria04/2014
4369(2^336095+2078)/2101175Stefano Morozzi09/2020
437013^90809-96101157Lelio R Paula10/2016
437126199^7258+7258^26199101150Hans Havermann11/2018
437219^79098-30101147Lelio R Paula10/2016
437319^79095+88101144Lelio R Paula10/2016
437415^85976+32101116Lelio R Paula10/2016
43752^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
4376(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
4377(4^167933+17)/3101106Robert Price02/2017
43792^335858+153101104Lelio R Paula10/2009
4378(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
4380(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
4381(2^335839+2114)/2101098Stefano Morozzi09/2020
4382(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
43836^129918-35101096Lelio R Paula10/2016
43843^211885-70101095Lelio R Paula09/2016
4386(29*2^335835-1)/550599101093Lelio R Paula03/2014
4385(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
43872^335818-20033101092Enzo Doria06/2013
43882^335813-110083101090Enzo Doria04/2014
43892^335804+2155101088Lelio R Paula09/2016
4390(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
43912^335784-16145101082Enzo Doria04/2013
439211^97051+62101069Lelio R Paula10/2016
43933*10^101065+11101066Robert Price07/2018
439427820^4293+4293^27820101064Hans Havermann10/2018
4395(2^335690+1038)/2101053Stefano Morozzi09/2020
4396(2^335691-3)/26515101049Lelio R Paula12/2013
43972^335658-94395101044Lelio R Paula09/2016
439824514^13215+13215^24514101024Hans Havermann11/2018
43992^335586+169101022Lelio R Paula10/2009
4400(56^57787-1)/55101021Paul Bourdelais08/2017
4401(2^335562+1258)/2101014Stefano Morozzi09/2020
4402(19*10^100997+737)/9100998Robert Price07/2018
440347599!2+1024100991Robert Price02/2015
44042^335468-18629100986Enzo Doria05/2013
44052^335454-20961100982Enzo Doria06/2013
440610^100978+61100979Lelio R Paula09/2016
440710^100978-156437100978Patrick De Geest11/2016
4408(2^335422+3114)/2100972Stefano Morozzi09/2020
4409(15*2^335417+1)/481100970Lelio R Paula12/2013
44102^335403-1859167100967Enzo Doria03/2016
441123599^18976+18976^23599100962Hans Havermann10/2018
44126*10^100958+43100959Robert Price07/2020
44139*2^335364-5100956Lelio R Paula08/2014
44142^335349+72287100951Enzo Doria04/2016
44152^335329+16095100945Lelio R Paula09/2016
4416232823#+233663100937Makoto Morimoto10/2017
4417(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
44182^335237-20893100917Enzo Doria06/2013
44192^335222-19337100912Enzo Doria05/2013
44202^335222-109985100912Enzo Doria04/2014
44212^335182-17237100900Enzo Doria05/2013
4422(2^335107+1634)/2100877Stefano Morozzi09/2020
44242^335043-16737100858Enzo Doria05/2013
4423(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
44252^335038-20633100857Enzo Doria06/2013
44262^335031+1873373100855Enzo Doria06/2016
442723489^19650+19650^23489100847Hans Havermann10/2018
44283^211354-8816100842Enzo Doria05/2014
44292^334984-112757100841Enzo Doria06/2014
4430(746*10^100827+1)/9100829Robert Price03/2020
443129451^2648+2648^29451100809Hans Havermann09/2018
443225583^8716+8716^25583100806Hans Havermann08/2018
44342^334857+48527100803Lelio R Paula08/2011
443312^93406+29100803Lelio R Paula10/2016
443528780^3179+3179^28780100796Hans Havermann09/2018
4436(5*2^334825+1)/47100792Lelio R Paula12/2013
44372^334809-13100788Lelio R Paula04/2011
4438(82*10^100780-1)/9100781Robert Price12/2014
443931395^1622+1622^31395100780Hans Havermann09/2018
4440(2^334779+47)/5100778Lelio R Paula12/2013
44412^334751+2049100771Lelio R Paula09/2016
444213^90443-98100749Lelio R Paula10/2016
4443(2^334674+3190)/2100747Stefano Morozzi09/2020
4444(2^334651+1050)/2100740Stefano Morozzi09/2020
4445(7*10^100737+71)/3100738Robert Price05/2018
4446(24737*2^334628+1)/3100737Lelio R Paula07/2014
444715^85639-28100720Lelio R Paula10/2016
444827068^5259+5259^27068100718Hans Havermann08/2018
44492^334562+577294575100711Lelio R Paula09/2016
44504*3^211077-5100710Lelio R Paula08/2014
44512^334524+145100702Lelio R Paula07/2009
4452(2^334451+714)/2100680Stefano Morozzi09/2020
445327648^4375+4375^27648100666Hans Havermann09/2018
4454(1017*2^334391-1)/3535100662Lelio R Paula05/2015
4455(2^334309+3122)/2100637Stefano Morozzi09/2020
44562^334294-113111100633Enzo Doria07/2014
445725581^8582+8582^25581100626Hans Havermann08/2018
44586^129308-17723100622Enzo Doria03/2013
44596^129305+95100619Lelio R Paula10/2016
44602^334244-1167100618Lelio R Paula09/2016
4461(2^334233+3066)/2100614Stefano Morozzi09/2020
4462(76*10^100611+77)/9100612Robert Price10/2019
44637*10^100606-93100607Robert Price08/2020
4464(26*10^100566+49)/3100567Robert Price08/2019
4465(21*2^334050+1)/935100558Lelio R Paula12/2013
446624885^10984+10984^24885100555Hans Havermann07/2018
4467(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
4468(35*10^100542+1)/9100543Serge Batalov11/2010
446923578^18367+18367^23578100538Hans Havermann07/2018
447013^90251+24100535Lelio R Paula10/2016
44712^333963+789100533Lelio R Paula08/2011
44722^333919-1840087100520Enzo Doria06/2015
4473(2^333916+1698)/2100519Stefano Morozzi09/2020
44742^333911+72623100518Enzo Doria04/2016
447524605^12168+12168^24605100517Hans Havermann08/2018
447666*10^100502+7100504Robert Price07/2020
447718^80064-67100503Lelio R Paula10/2016
44785^143742-48100472Lelio R Paula10/2016
447924095^14784+14784^24095100472Hans Havermann08/2018
44802^333757-112123100471Enzo Doria06/2014
44817*10^100457-57100458Robert Price06/2020
448227358^4693+4693^27358100444Hans Havermann07/2018
44838*10^100439-51100440Robert Price08/2019
44842^333603-108861100425Enzo Doria03/2014
44859*7^118818-2100414Lelio R Paula11/2014
44862^333546-17097100408Enzo Doria05/2013
448717^81597+72100401Lelio R Paula10/2016
4488p(20559)#/2+8100384Robert Price01/2017
448911^96390-24100380Lelio R Paula10/2016
4490(2^333385+2730)/2100359Stefano Morozzi09/2020
44924832563059*2^333333+30029100353Donovan Johnson01/2008
449123565^18136+18136^23565100353Hans Havermann07/2018
44932^333354+763100350Lelio R Paula08/2011
4494(25*10^100343-67)/3100344Robert Price06/2019
44952^333289-109483100330Enzo Doria04/2014
44962^333240-2790209100316Enzo Doria03/2016
449723601^17798+17798^23601100314Hans Havermann05/2018
4499(2^333227-2^166614+1)/510031111/2006
44982^333225+719100311Lelio R Paula08/2011
45002^333221-2785333100310Enzo Doria10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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