PRP Records

Probable Primes Top 10000

(277054 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 ?
47512^336243-108777101220Enzo Doria03/2014
4752(31*2^336189-1)/19101204Lelio R Paula03/2014
475323535^19954+19954^23535101202Hans Havermann11/2018
4754(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
47552^336150-20393101192Enzo Doria06/2013
475623996^16473+16473^23996101186Hans Havermann11/2018
47572^336112-1865249101180Enzo Doria03/2016
47582^336103-109015101178Enzo Doria04/2014
4759(2^336095+2078)/2101175Stefano Morozzi09/2020
476013^90809-96101157Lelio R Paula10/2016
476126199^7258+7258^26199101150Hans Havermann11/2018
476219^79098-30101147Lelio R Paula10/2016
476319^79095+88101144Lelio R Paula10/2016
476415^85976+32101116Lelio R Paula10/2016
47652^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
4766(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
4767(4^167933+17)/3101106Robert Price02/2017
47692^335858+153101104Lelio R Paula10/2009
4768(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
4770(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
4771(2^335839+2114)/2101098Stefano Morozzi09/2020
4772(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
47736^129918-35101096Lelio R Paula10/2016
4774(2*10^101096-107)/3101096Robert Price11/2020
47753^211885-70101095Lelio R Paula09/2016
4777(29*2^335835-1)/550599101093Lelio R Paula03/2014
4776(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
47782^335818-20033101092Enzo Doria06/2013
47792^335813-110083101090Enzo Doria04/2014
47802^335804+2155101088Lelio R Paula09/2016
4781(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
47822^335784-16145101082Enzo Doria04/2013
478311^97051+62101069Lelio R Paula10/2016
47843*10^101065+11101066Robert Price07/2018
478527820^4293+4293^27820101064Hans Havermann10/2018
4786(2^335714+3750)/2101060Stefano Morozzi01/2021
4787(2^335690+1038)/2101053Stefano Morozzi09/2020
4788(2^335691-3)/26515101049Lelio R Paula12/2013
47892^335658-94395101044Lelio R Paula09/2016
479024514^13215+13215^24514101024Hans Havermann11/2018
47912^335586+169101022Lelio R Paula10/2009
4792(56^57787-1)/55101021Paul Bourdelais08/2017
4793(2^335562+1258)/2101014Stefano Morozzi09/2020
4794(19*10^100997+737)/9100998Robert Price07/2018
479547599!2+1024100991Robert Price02/2015
47962^335468-18629100986Enzo Doria05/2013
47972^335454-20961100982Enzo Doria06/2013
479810^100978+61100979Lelio R Paula09/2016
479910^100978-156437100978Patrick De Geest11/2016
4800(2^335422+3114)/2100972Stefano Morozzi09/2020
4801(15*2^335417+1)/481100970Lelio R Paula12/2013
48022^335403-1859167100967Enzo Doria03/2016
480323599^18976+18976^23599100962Hans Havermann10/2018
48046*10^100958+43100959Robert Price07/2020
48059*2^335364-5100956Lelio R Paula08/2014
48062^335349+72287100951Enzo Doria04/2016
48072^335329+16095100945Lelio R Paula09/2016
4808232823#+233663100937Makoto Morimoto10/2017
4809(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
48102^335237-20893100917Enzo Doria06/2013
48112^335222-19337100912Enzo Doria05/2013
48122^335222-109985100912Enzo Doria04/2014
48132^335182-17237100900Enzo Doria05/2013
4814(2^335107+1634)/2100877Stefano Morozzi09/2020
48162^335043-16737100858Enzo Doria05/2013
4815(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
48172^335038-20633100857Enzo Doria06/2013
48182^335031+1873373100855Enzo Doria06/2016
481923489^19650+19650^23489100847Hans Havermann10/2018
48203^211354-8816100842Enzo Doria05/2014
48212^334984-112757100841Enzo Doria06/2014
4822(746*10^100827+1)/9100829Robert Price03/2020
482329451^2648+2648^29451100809Hans Havermann09/2018
482425583^8716+8716^25583100806Hans Havermann08/2018
48262^334857+48527100803Lelio R Paula08/2011
482512^93406+29100803Lelio R Paula10/2016
482728780^3179+3179^28780100796Hans Havermann09/2018
4828(5*2^334825+1)/47100792Lelio R Paula12/2013
48292^334809-13100788Lelio R Paula04/2011
4830(82*10^100780-1)/9100781Robert Price12/2014
483131395^1622+1622^31395100780Hans Havermann09/2018
4832(2^334779+47)/5100778Lelio R Paula12/2013
48332^334751+2049100771Lelio R Paula09/2016
483413^90443-98100749Lelio R Paula10/2016
4835(2^334674+3190)/2100747Stefano Morozzi09/2020
4836(2^334651+1050)/2100740Stefano Morozzi09/2020
4837(7*10^100737+71)/3100738Robert Price05/2018
4838(24737*2^334628+1)/3100737Lelio R Paula07/2014
483915^85639-28100720Lelio R Paula10/2016
484027068^5259+5259^27068100718Hans Havermann08/2018
48412^334562+577294575100711Lelio R Paula09/2016
48424*3^211077-5100710Lelio R Paula08/2014
48432^334524+145100702Lelio R Paula07/2009
4844(2^334451+714)/2100680Stefano Morozzi09/2020
484527648^4375+4375^27648100666Hans Havermann09/2018
4846(1017*2^334391-1)/3535100662Lelio R Paula05/2015
4847(2^334309+3122)/2100637Stefano Morozzi09/2020
48482^334294-113111100633Enzo Doria07/2014
484925581^8582+8582^25581100626Hans Havermann08/2018
48506^129308-17723100622Enzo Doria03/2013
48516^129305+95100619Lelio R Paula10/2016
48522^334244-1167100618Lelio R Paula09/2016
4853(2^334233+3066)/2100614Stefano Morozzi09/2020
4854(76*10^100611+77)/9100612Robert Price10/2019
48557*10^100606-93100607Robert Price08/2020
4856(26*10^100566+49)/3100567Robert Price08/2019
4857(21*2^334050+1)/935100558Lelio R Paula12/2013
485824885^10984+10984^24885100555Hans Havermann07/2018
4859(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
4860(35*10^100542+1)/9100543Serge Batalov11/2010
486123578^18367+18367^23578100538Hans Havermann07/2018
486213^90251+24100535Lelio R Paula10/2016
48632^333963+789100533Lelio R Paula08/2011
48642^333919-1840087100520Enzo Doria06/2015
4865(2^333916+1698)/2100519Stefano Morozzi09/2020
48662^333911+72623100518Enzo Doria04/2016
486724605^12168+12168^24605100517Hans Havermann08/2018
486866*10^100502+7100504Robert Price07/2020
486918^80064-67100503Lelio R Paula10/2016
48705^143742-48100472Lelio R Paula10/2016
487124095^14784+14784^24095100472Hans Havermann08/2018
48722^333757-112123100471Enzo Doria06/2014
48737*10^100457-57100458Robert Price06/2020
487427358^4693+4693^27358100444Hans Havermann07/2018
48758*10^100439-51100440Robert Price08/2019
48762^333603-108861100425Enzo Doria03/2014
48779*7^118818-2100414Lelio R Paula11/2014
48782^333546-17097100408Enzo Doria05/2013
487917^81597+72100401Lelio R Paula10/2016
4880p(20559)#/2+8100384Robert Price01/2017
488111^96390-24100380Lelio R Paula10/2016
4882(2^333385+2730)/2100359Stefano Morozzi09/2020
48844832563059*2^333333+30029100353Donovan Johnson01/2008
488323565^18136+18136^23565100353Hans Havermann07/2018
48852^333354+763100350Lelio R Paula08/2011
4886(25*10^100343-67)/3100344Robert Price06/2019
48872^333289-109483100330Enzo Doria04/2014
48882^333240-2790209100316Enzo Doria03/2016
488923601^17798+17798^23601100314Hans Havermann05/2018
4891(2^333227-2^166614+1)/510031111/2006
48902^333225+719100311Lelio R Paula08/2011
48922^333221-2785333100310Enzo Doria10/2015
489376^53332-75100308Norbert Schneider02/2015
48946^128892-17573100298Enzo Doria03/2013
4895(47*10^100283-119)/9100284Robert Price05/2019
48962^333105-113215100275Enzo Doria07/2014
4897(31*2^333102+1)/2375100272Lelio R Paula11/2013
48984*10^100257-83100258Robert Price10/2018
489917^81476-74100253Lelio R Paula10/2016
490023392^19207+19207^23392100199Hans Havermann06/2018
4901(2^332830+750)/2100192Stefano Morozzi09/2020
4902(206*10^100189-17)/9100191Robert Price01/2020
490317^81417-16100180Theodore Burton11/2005
4904(2^332773+590)/2100175Stefano Morozzi09/2020
49052^332739-113215100165Enzo Doria07/2014
49062^332730-1865621100162Enzo Doria03/2016
490791^51127-2100160Lelio R Paula09/2013
490815^85159-32100155Lelio R Paula10/2016
49096^128661+97100118Lelio R Paula10/2016
491019^78285+40100108Lelio R Paula07/2016
49116^128640+5100102Lelio R Paula11/2014
491222779^22970-22970^22779100093Norbert Schneider08/2020
4913(2^332468+3130)/2100083Stefano Morozzi09/2020
4914(14*10^100075+61)/3100076Robert Price12/2018
4915(2^332435+3098)/2100073Stefano Morozzi09/2020
491628562^3189+3189^28562100072Hans Havermann05/2018
49176^128565-127100044Lelio R Paula08/2016
4918(2^332317+2106)/2100038Stefano Morozzi09/2020
49192^332309-133100035Lelio R Paula02/2011
49202^332307+731100035Lelio R Paula07/2011
49212^332301+12927100033Lelio R Paula04/2013
492223406^18781+18781^23406100031Hans Havermann04/2018
49232^332277-4573100026Yves Minet03/2019
492412^92684-13100023Lelio R Paula07/2016
492578557*2^332193+55669100005Jorge Menendez04/2019
492678557*2^332192+72689100005Jorge Menendez04/2019
492710^100003+45799100004Stefano Morozzi04/2019
492810^100003+155461100004Stefano Morozzi04/2019
492910^100003+211389100004Stefano Morozzi04/2019
493010^100003+381027100004Stefano Morozzi04/2019
493110^100003+540703100004Stefano Morozzi04/2019
493210^100003+823977100004Stefano Morozzi04/2019
494410^100002+236023100003Stefano Morozzi05/2018
494510^100002+433741100003Stefano Morozzi05/2018
49332^332202+104659100003Stefano Morozzi04/2019
49342^332202+857539100003Stefano Morozzi04/2019
49352^332202+181773100003Stefano Morozzi04/2019
49362^332202+687543100003Stefano Morozzi04/2019
49372^332202+941595100003Stefano Morozzi04/2019
49382^332202+445813100003Stefano Morozzi04/2019
49392^332202+1599727100003Stefano Morozzi04/2019
49402^332202+1389567100003Stefano Morozzi04/2019
49412^332202+1206315100003Stefano Morozzi04/2019
49422^332202+1958647100003Stefano Morozzi04/2019
494310^100003-562857100003Patrick De Geest07/2019
4946(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
4947(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
494810^100002-249519100002Patrick De Geest07/2018
494910^100001+314199100002Patrick De Geest07/2018
498610^100000+3938473100001Robert Price05/2015
498710^100000+3979761100001Robert Price05/2015
498810^100000+4293973100001Robert Price09/2015
496610^100000+4858267100001Robert Price12/2015
496710^100000+5113299100001Robert Price02/2016
496810^100000+5169411100001Robert Price02/2016
498910^100000+7867333100001Robert Price12/2016
499010^100000+8743093100001Robert Price02/2017
499110^100000+8955391100001Robert Price03/2017
499210^100000+9180019100001Robert Price03/2017
499310^100000+9225987100001Robert Price04/2017
499410^100000+9265587100001Robert Price04/2017
499510^100000+9287049100001Robert Price04/2017
499610^100000+9425053100001Robert Price05/2017
499710^100000+9450769100001Robert Price05/2017
499810^100000+9528747100001Robert Smith05/2017
499910^100000+9548071100001Robert Price06/2017
500010^100000+10064287100001Robert Price08/2017
495010^100000+11187931100001Robert Price03/2018
495110^100000+11264721100001Robert Price04/2018
495210^100000+11477661100001Robert Price05/2018
495310^100000+11644653100001Robert Price07/2018
495410^100001-431439100001Patrick De Geest07/2018
495510^100000+11769399100001Robert Price08/2018
495610^100000+11848159100001Robert Price08/2018
495710^100000+11863467100001Robert Price08/2018
49582^332196+1+2*17152100001Matt Stath12/2018
495910^100000+12778033100001Robert Price02/2019
496010^100000+13581679100001Robert Price05/2019
496110^100000+13613199100001Robert Price05/2019
496210^100000+13752327100001Robert Price05/2019
496310^100000+14139243100001Robert Price06/2019
496410^100000+14151057100001Robert Price06/2019
496510^100000+14218923100001Robert Price06/2019
496910^100000+19956229100001Robert Price09/2020
497010^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
497110^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
497210^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
497310^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
497410^100000+20234607100001Robert Price10/2020
497510^100000+20752303100001Robert Price11/2020
497610^100000+20774041100001Robert Price11/2020
497710^100000+20854741100001Robert Price11/2020
497810^100000+20908917100001Robert Price11/2020
497910^100000+20994793100001Robert Price11/2020
498010^100000+21354249100001Robert Price12/2020
498110^100000+21455559100001Robert Price12/2020
498210^100000+21538873100001Robert Price12/2020
498310^100000+21830901100001Robert Price01/2021
498410^100000+21842629100001Robert Price01/2021
498510^100000+21930861100001Robert Price01/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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