PRP Records

Probable Primes Top 10000

(277034 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
4751(4^167933+17)/3101106Robert Price02/2017
47532^335858+153101104Lelio R Paula10/2009
4752(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
4754(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
4755(2^335839+2114)/2101098Stefano Morozzi09/2020
4756(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
47576^129918-35101096Lelio R Paula10/2016
4758(2*10^101096-107)/3101096Robert Price11/2020
47593^211885-70101095Lelio R Paula09/2016
4761(29*2^335835-1)/550599101093Lelio R Paula03/2014
4760(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
47622^335818-20033101092Enzo Doria06/2013
47632^335813-110083101090Enzo Doria04/2014
47642^335804+2155101088Lelio R Paula09/2016
4765(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
47662^335784-16145101082Enzo Doria04/2013
476711^97051+62101069Lelio R Paula10/2016
47683*10^101065+11101066Robert Price07/2018
476927820^4293+4293^27820101064Hans Havermann10/2018
4770(2^335714+3750)/2101060Stefano Morozzi01/2021
4771(2^335690+1038)/2101053Stefano Morozzi09/2020
4772(2^335691-3)/26515101049Lelio R Paula12/2013
47732^335658-94395101044Lelio R Paula09/2016
477424514^13215+13215^24514101024Hans Havermann11/2018
47752^335586+169101022Lelio R Paula10/2009
4776(56^57787-1)/55101021Paul Bourdelais08/2017
4777(2^335562+1258)/2101014Stefano Morozzi09/2020
4778(19*10^100997+737)/9100998Robert Price07/2018
477947599!2+1024100991Robert Price02/2015
47802^335468-18629100986Enzo Doria05/2013
47812^335454-20961100982Enzo Doria06/2013
478210^100978+61100979Lelio R Paula09/2016
478310^100978-156437100978Patrick De Geest11/2016
4784(2^335422+3114)/2100972Stefano Morozzi09/2020
4785(15*2^335417+1)/481100970Lelio R Paula12/2013
47862^335403-1859167100967Enzo Doria03/2016
478723599^18976+18976^23599100962Hans Havermann10/2018
47886*10^100958+43100959Robert Price07/2020
47899*2^335364-5100956Lelio R Paula08/2014
47902^335349+72287100951Enzo Doria04/2016
47912^335329+16095100945Lelio R Paula09/2016
4792232823#+233663100937Makoto Morimoto10/2017
4793(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
47942^335237-20893100917Enzo Doria06/2013
47952^335222-19337100912Enzo Doria05/2013
47962^335222-109985100912Enzo Doria04/2014
47972^335182-17237100900Enzo Doria05/2013
4798(2^335107+1634)/2100877Stefano Morozzi09/2020
48002^335043-16737100858Enzo Doria05/2013
4799(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
48012^335038-20633100857Enzo Doria06/2013
48022^335031+1873373100855Enzo Doria06/2016
480323489^19650+19650^23489100847Hans Havermann10/2018
48043^211354-8816100842Enzo Doria05/2014
48052^334984-112757100841Enzo Doria06/2014
4806(746*10^100827+1)/9100829Robert Price03/2020
480729451^2648+2648^29451100809Hans Havermann09/2018
480825583^8716+8716^25583100806Hans Havermann08/2018
48102^334857+48527100803Lelio R Paula08/2011
480912^93406+29100803Lelio R Paula10/2016
481128780^3179+3179^28780100796Hans Havermann09/2018
4812(5*2^334825+1)/47100792Lelio R Paula12/2013
48132^334809-13100788Lelio R Paula04/2011
4814(82*10^100780-1)/9100781Robert Price12/2014
481531395^1622+1622^31395100780Hans Havermann09/2018
4816(2^334779+47)/5100778Lelio R Paula12/2013
48172^334751+2049100771Lelio R Paula09/2016
481813^90443-98100749Lelio R Paula10/2016
4819(2^334674+3190)/2100747Stefano Morozzi09/2020
4820(2^334651+1050)/2100740Stefano Morozzi09/2020
4821(7*10^100737+71)/3100738Robert Price05/2018
4822(24737*2^334628+1)/3100737Lelio R Paula07/2014
482315^85639-28100720Lelio R Paula10/2016
482427068^5259+5259^27068100718Hans Havermann08/2018
48252^334562+577294575100711Lelio R Paula09/2016
48264*3^211077-5100710Lelio R Paula08/2014
48272^334524+145100702Lelio R Paula07/2009
4828(2^334451+714)/2100680Stefano Morozzi09/2020
482927648^4375+4375^27648100666Hans Havermann09/2018
4830(1017*2^334391-1)/3535100662Lelio R Paula05/2015
4831(2^334309+3122)/2100637Stefano Morozzi09/2020
48322^334294-113111100633Enzo Doria07/2014
483325581^8582+8582^25581100626Hans Havermann08/2018
48346^129308-17723100622Enzo Doria03/2013
48356^129305+95100619Lelio R Paula10/2016
48362^334244-1167100618Lelio R Paula09/2016
4837(2^334233+3066)/2100614Stefano Morozzi09/2020
4838(76*10^100611+77)/9100612Robert Price10/2019
48397*10^100606-93100607Robert Price08/2020
4840(26*10^100566+49)/3100567Robert Price08/2019
4841(21*2^334050+1)/935100558Lelio R Paula12/2013
484224885^10984+10984^24885100555Hans Havermann07/2018
4843(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
4844(35*10^100542+1)/9100543Serge Batalov11/2010
484523578^18367+18367^23578100538Hans Havermann07/2018
484613^90251+24100535Lelio R Paula10/2016
48472^333963+789100533Lelio R Paula08/2011
48482^333919-1840087100520Enzo Doria06/2015
4849(2^333916+1698)/2100519Stefano Morozzi09/2020
48502^333911+72623100518Enzo Doria04/2016
485124605^12168+12168^24605100517Hans Havermann08/2018
485266*10^100502+7100504Robert Price07/2020
485318^80064-67100503Lelio R Paula10/2016
48545^143742-48100472Lelio R Paula10/2016
485524095^14784+14784^24095100472Hans Havermann08/2018
48562^333757-112123100471Enzo Doria06/2014
48577*10^100457-57100458Robert Price06/2020
485827358^4693+4693^27358100444Hans Havermann07/2018
48598*10^100439-51100440Robert Price08/2019
48602^333603-108861100425Enzo Doria03/2014
48619*7^118818-2100414Lelio R Paula11/2014
48622^333546-17097100408Enzo Doria05/2013
486317^81597+72100401Lelio R Paula10/2016
4864p(20559)#/2+8100384Robert Price01/2017
486511^96390-24100380Lelio R Paula10/2016
4866(2^333385+2730)/2100359Stefano Morozzi09/2020
48684832563059*2^333333+30029100353Donovan Johnson01/2008
486723565^18136+18136^23565100353Hans Havermann07/2018
48692^333354+763100350Lelio R Paula08/2011
4870(25*10^100343-67)/3100344Robert Price06/2019
48712^333289-109483100330Enzo Doria04/2014
48722^333240-2790209100316Enzo Doria03/2016
487323601^17798+17798^23601100314Hans Havermann05/2018
4875(2^333227-2^166614+1)/510031111/2006
48742^333225+719100311Lelio R Paula08/2011
48762^333221-2785333100310Enzo Doria10/2015
487776^53332-75100308Norbert Schneider02/2015
48786^128892-17573100298Enzo Doria03/2013
4879(47*10^100283-119)/9100284Robert Price05/2019
48802^333105-113215100275Enzo Doria07/2014
4881(31*2^333102+1)/2375100272Lelio R Paula11/2013
48824*10^100257-83100258Robert Price10/2018
488317^81476-74100253Lelio R Paula10/2016
488423392^19207+19207^23392100199Hans Havermann06/2018
4885(2^332830+750)/2100192Stefano Morozzi09/2020
4886(206*10^100189-17)/9100191Robert Price01/2020
488717^81417-16100180Theodore Burton11/2005
4888(2^332773+590)/2100175Stefano Morozzi09/2020
48892^332739-113215100165Enzo Doria07/2014
48902^332730-1865621100162Enzo Doria03/2016
489191^51127-2100160Lelio R Paula09/2013
489215^85159-32100155Lelio R Paula10/2016
48936^128661+97100118Lelio R Paula10/2016
489419^78285+40100108Lelio R Paula07/2016
48956^128640+5100102Lelio R Paula11/2014
489622779^22970-22970^22779100093Norbert Schneider08/2020
4897(2^332468+3130)/2100083Stefano Morozzi09/2020
4898(14*10^100075+61)/3100076Robert Price12/2018
4899(2^332435+3098)/2100073Stefano Morozzi09/2020
490028562^3189+3189^28562100072Hans Havermann05/2018
49016^128565-127100044Lelio R Paula08/2016
4902(2^332317+2106)/2100038Stefano Morozzi09/2020
49032^332309-133100035Lelio R Paula02/2011
49042^332307+731100035Lelio R Paula07/2011
49052^332301+12927100033Lelio R Paula04/2013
490623406^18781+18781^23406100031Hans Havermann04/2018
49072^332277-4573100026Yves Minet03/2019
490812^92684-13100023Lelio R Paula07/2016
490978557*2^332193+55669100005Jorge Menendez04/2019
491078557*2^332192+72689100005Jorge Menendez04/2019
491110^100003+45799100004Stefano Morozzi04/2019
491210^100003+155461100004Stefano Morozzi04/2019
491310^100003+211389100004Stefano Morozzi04/2019
491410^100003+381027100004Stefano Morozzi04/2019
491510^100003+540703100004Stefano Morozzi04/2019
491610^100003+823977100004Stefano Morozzi04/2019
492810^100002+236023100003Stefano Morozzi05/2018
492910^100002+433741100003Stefano Morozzi05/2018
49172^332202+104659100003Stefano Morozzi04/2019
49182^332202+857539100003Stefano Morozzi04/2019
49192^332202+181773100003Stefano Morozzi04/2019
49202^332202+687543100003Stefano Morozzi04/2019
49212^332202+941595100003Stefano Morozzi04/2019
49222^332202+445813100003Stefano Morozzi04/2019
49232^332202+1599727100003Stefano Morozzi04/2019
49242^332202+1389567100003Stefano Morozzi04/2019
49252^332202+1206315100003Stefano Morozzi04/2019
49262^332202+1958647100003Stefano Morozzi04/2019
492710^100003-562857100003Patrick De Geest07/2019
4930(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
4931(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
493210^100002-249519100002Patrick De Geest07/2018
493310^100001+314199100002Patrick De Geest07/2018
497310^100000+3938473100001Robert Price05/2015
497410^100000+3979761100001Robert Price05/2015
497510^100000+4293973100001Robert Price09/2015
495010^100000+4858267100001Robert Price12/2015
495110^100000+5113299100001Robert Price02/2016
495210^100000+5169411100001Robert Price02/2016
497610^100000+5354043100001Robert Price05/2016
497710^100000+5717979100001Robert Price05/2016
497810^100000+6080631100001Robert Price07/2016
497910^100000+6308469100001Robert Price07/2016
498010^100000+6512023100001Robert Price08/2016
498110^100000+6596557100001Robert Price08/2016
498210^100000+7115409100001Robert Price10/2016
498310^100000+7235803100001Robert Price10/2016
493410^100000+11187931100001Robert Price03/2018
493510^100000+11264721100001Robert Price04/2018
493610^100000+11477661100001Robert Price05/2018
493710^100000+11644653100001Robert Price07/2018
493810^100001-431439100001Patrick De Geest07/2018
493910^100000+11769399100001Robert Price08/2018
494010^100000+11848159100001Robert Price08/2018
494110^100000+11863467100001Robert Price08/2018
497010^100000+11992051100001Robert Price09/2018
49712^332196-1-2*29696100001Matt Stath11/2018
497210^100000+12363957100001Robert Price11/2018
49422^332196+1+2*17152100001Matt Stath12/2018
494310^100000+12778033100001Robert Price02/2019
494410^100000+13581679100001Robert Price05/2019
494510^100000+13613199100001Robert Price05/2019
494610^100000+13752327100001Robert Price05/2019
494710^100000+14139243100001Robert Price06/2019
494810^100000+14151057100001Robert Price06/2019
494910^100000+14218923100001Robert Price06/2019
498410^100000+15136771100001Robert Price09/2019
498510^100000+15219873100001Robert Price10/2019
498610^100000+15274039100001Robert Price10/2019
498710^100000+15394069100001Robert Price10/2019
498810^100000+15547119100001Robert Price10/2019
498910^100000+15932923100001Robert Price11/2019
499010^100000+16345467100001Robert Price12/2019
499110^100000+16672143100001Robert Price01/2020
499210^100000+16731939100001Robert Price02/2020
499310^100000+16907049100001Robert Price03/2020
499410^100000+17652523100001Robert Price05/2020
499510^100000+18047167100001Robert Price05/2020
499610^100000+18471819100001Robert Price06/2020
499710^100000+18494793100001Robert Price07/2020
499810^100000+18762609100001Robert Price07/2020
499910^100000+19204141100001Robert Price08/2020
500010^100000+19349793100001Robert Price08/2020
495310^100000+19956229100001Robert Price09/2020
495410^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
495510^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
495610^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
495710^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
495810^100000+20234607100001Robert Price10/2020
495910^100000+20752303100001Robert Price11/2020
496010^100000+20774041100001Robert Price11/2020
496110^100000+20854741100001Robert Price11/2020
496210^100000+20908917100001Robert Price11/2020
496310^100000+20994793100001Robert Price11/2020
496410^100000+21354249100001Robert Price12/2020
496510^100000+21455559100001Robert Price12/2020
496610^100000+21538873100001Robert Price12/2020
496710^100000+21830901100001Robert Price01/2021
496810^100000+21842629100001Robert Price01/2021
496910^100000+21930861100001Robert Price01/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!