PRP Records

Probable Primes Top 10000

(292102 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 ?
77512^338020-87797101755Stefano Morozzi12/2022
77522^338018-102741101754Stefano Morozzi01/2022
77532^338018+29937101754Stefano Morozzi01/2022
77542^338017-29505101754Stefano Morozzi02/2022
77552^338018-30873101754Stefano Morozzi02/2022
77562^338018-157013101754Stefano Morozzi03/2022
77572^338019+168929101754Stefano Morozzi09/2022
77582^338017+172721101754Stefano Morozzi11/2022
77592^338018-136131101754Stefano Morozzi12/2022
77602^338016+50797101753Stefano Morozzi11/2021
77612^338016+26707101753Stefano Morozzi12/2021
77622^338014+104677101753Stefano Morozzi01/2022
77632^338013+145091101753Stefano Morozzi11/2022
77642^338016-16335101753Stefano Morozzi01/2023
77672^338010-19833101752Enzo Doria06/2013
77652^338011+28665101752Stefano Morozzi01/2022
77662^338010+89505101752Stefano Morozzi05/2022
77682^338007+58985101751Stefano Morozzi03/2022
77692^338008+109741101751Stefano Morozzi03/2022
77702^338009+9527101751Stefano Morozzi03/2022
77712^338007+14511101751Stefano Morozzi05/2022
77722^338008+67957101751Stefano Morozzi09/2022
77732^338009-11935101751Stefano Morozzi12/2022
77742^338007-14199101751Stefano Morozzi01/2023
77752^338005-75829101750Stefano Morozzi12/2021
77762^338006-125055101750Stefano Morozzi12/2021
77772^338006+5013101750Stefano Morozzi01/2022
77782^338003+40269101750Stefano Morozzi06/2022
77792^338006+166495101750Stefano Morozzi06/2022
77802^338003-188551101750Stefano Morozzi12/2022
77812^338006-118041101750Stefano Morozzi02/2023
77822^338000+25113101749Stefano Morozzi12/2021
77843^213215-76101730Lelio R Paula09/2016
778323907^17998+17998^23907101730Hans Havermann01/2019
778510^101728+154953101729Patrick De Geest02/2020
77882^337930+63101728Lelio R Paula07/2011
778610^101728-987654321101728Robert Price12/2019
778710^101728-60741101728Patrick De Geest02/2020
77892^337920+1869661101725Enzo Doria05/2016
77902^337922+100280245065101725Paul Bourdelais10/2021
779124116^16509+16509^24116101715Hans Havermann01/2019
7792(2^337875+3174)/2101711Stefano Morozzi09/2020
77932^337859-19645101706Enzo Doria05/2013
77942^337754+1869169101675Enzo Doria05/2016
77953*10^101657-37101658Robert Price07/2018
7796(31*2^337677-1)/593101650Lelio R Paula03/2014
779711^97605-24101646Lelio R Paula10/2016
7798(83*10^101636+133)/9101637Robert Price08/2021
7799(2^337624+3606)/2101635Stefano Morozzi09/2020
78008^112539-112539101633Robert Price01/2014
7801(2^337575+1818)/2101620Stefano Morozzi02/2021
7802(11*10^101613+61)/9101614Tyler Busby01/2023
780325694^9003+9003^25694101605Hans Havermann12/2018
78042^337515-19869101603Enzo Doria06/2013
78052^337473+719101590Lelio R Paula08/2011
7806(2^337485-509203)/656647157101585Lelio R Paula12/2013
78072^337452-108815101584Enzo Doria03/2014
78082^337453+1185101584Lelio R Paula09/2016
7809(41*10^101583+319)/9101584Robert Price06/2021
78102^337410-113561101571Enzo Doria08/2014
78112^337387+855101564Lelio R Paula09/2016
78122^337367-17295101558Lelio R Paula09/2016
78132^337342-109035101551Enzo Doria04/2014
781423703^19238+19238^23703101548Hans Havermann12/2018
7815(26*10^101537-167)/3101538Robert Price10/2019
78162^337267-19101528Lelio R Paula07/2011
7817(2^337259+1766)/2101525Stefano Morozzi09/2020
7818(2^337257+2306)/2101525Stefano Morozzi02/2021
78192^337222-340871101514Harrison Mesh06/2022
7820(2^337195+2646)/2101506Stefano Morozzi09/2020
78212^337183-19989101503Enzo Doria06/2013
78222^337149+72425101492Enzo Doria04/2016
782324041^16642+16642^24041101483Hans Havermann12/2018
782433982^969+969^33982101482Hans Havermann12/2018
78252^337101-20241101478Enzo Doria06/2013
78262^337035-20001101458Enzo Doria06/2013
7827(7*10^101456+89)/3101457Robert Price08/2020
78282^337017-16995101453Lelio R Paula09/2016
7829(8677^25759-1)/8676101445Serge Batalov06/2022
78302^336979-115315101441Enzo Doria06/2015
78312^336970-20885101439Enzo Doria06/2013
78322^336958+79101435Lelio R Paula10/2009
7833(1589^31687-1)/1588101431Serge Batalov06/2022
78342^336942+169101430Lelio R Paula10/2009
7835(15185*2^336894-1)/7939101416Lelio R Paula05/2015
78364*10^101415-89101416Robert Price11/2018
7837(14*10^101410-89)/3101411Robert Price05/2020
78382^336871+257463101409Tony Prest / Never Odd Or Even04/2016
78392^336871+318105101409Tony Prest / Never Odd Or Even04/2016
78402^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
78412^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
78422^336871+389273101409Tony Prest / Never Odd Or Even04/2016
78432^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
78442^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
78452^336871+586905101409Tony Prest / Never Odd Or Even04/2016
78462^336871+674571101409Tony Prest / Never Odd Or Even04/2016
78472^336871+707009101409Tony Prest / Never Odd Or Even04/2016
78482^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
78492^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
78502^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
78512^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
78522^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
78532^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
78542^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
78552^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
7856(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
7857(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
7858(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
7859(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
786024097^16150+16150^24097101405Hans Havermann12/2018
78612^336842+94065101400Lelio R Paula09/2016
7862(7*10^101395-1)/3101396Robert Price08/2022
7863(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
7864(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
7865(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
7866(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
7867(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
7868(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
7869(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
787010^101369+203811101370Patrick De Geest11/2016
787110^101369-99101369Lelio R Paula09/2016
7872(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
78732^336701-113563101358Enzo Doria08/2014
787489717!4-512101351Robert Price11/2019
78752^336644-109023101340Enzo Doria04/2014
78762^336601-21081101327Enzo Doria06/2013
7877(4*34^66153+227)/33101312Eric Chen03/2023
787820^77869+63101310Lelio R Paula09/2016
7879(13*2^336523-1)/19101304Lelio R Paula03/2014
78816^130179-137101299Lelio R Paula10/2016
7880(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
7882(24737*2^336485+1)/7285101293Lelio R Paula07/2014
7883(2^336448+9)/497405101276Lelio R Paula12/2013
78842^336369-19753101258Enzo Doria05/2013
788523842^17653+17653^23842101253Hans Havermann11/2018
78862^336350-344291101252Enzo Doria07/2015
7887(17*10^101251-161)/9101252Robert Price02/2021
7888(56*10^101222-47)/9101223Robert Price02/2019
78892^336243-108777101220Enzo Doria03/2014
7890(31*2^336189-1)/19101204Lelio R Paula03/2014
789123535^19954+19954^23535101202Hans Havermann11/2018
7892(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
78932^336150-20393101192Enzo Doria06/2013
789423996^16473+16473^23996101186Hans Havermann11/2018
78952^336112-1865249101180Enzo Doria03/2016
78962^336103-109015101178Enzo Doria04/2014
7897(2^336095+2078)/2101175Stefano Morozzi09/2020
789813^90809-96101157Lelio R Paula10/2016
789926199^7258+7258^26199101150Hans Havermann11/2018
790019^79098-30101147Lelio R Paula10/2016
790119^79095+88101144Lelio R Paula10/2016
7902(30826*34^66040-59)/11101143Eric Chen03/2023
790312401^24702-24702^12401101117Norbert Schneider07/2022
790415^85976+32101116Lelio R Paula10/2016
79052^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
7906(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
7907(4^167933+17)/3101106Robert Price02/2017
79092^335858+153101104Lelio R Paula10/2009
7908(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
7910(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
7911(2^335839+2114)/2101098Stefano Morozzi09/2020
7912(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
79146^129918-35101096Lelio R Paula10/2016
7913(2*10^101096-107)/3101096Robert Price11/2020
79153^211885-70101095Lelio R Paula09/2016
7916(29*2^335835-1)/550599101093Lelio R Paula03/2014
7917(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
79182^335818-20033101092Enzo Doria06/2013
79192^335813-110083101090Enzo Doria04/2014
79202^335804+2155101088Lelio R Paula09/2016
7921(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
79222^335784-16145101082Enzo Doria04/2013
792311^97051+62101069Lelio R Paula10/2016
79243*10^101065+11101066Robert Price07/2018
792527820^4293+4293^27820101064Hans Havermann10/2018
7926(2^335714+3750)/2101060Stefano Morozzi01/2021
7927(2^335690+1038)/2101053Stefano Morozzi09/2020
7928(2^335691-3)/26515101049Lelio R Paula12/2013
79292^335658-94395101044Lelio R Paula09/2016
793024514^13215+13215^24514101024Hans Havermann11/2018
79312^335586+169101022Lelio R Paula10/2009
7932(56^57787-1)/55101021Paul Bourdelais08/2017
7933(2^335562+1258)/2101014Stefano Morozzi09/2020
79342^335541+4849845101008Paul Bourdelais04/2022
7935(38*10^100999+169)/9101000Robert Price11/2021
7936(19*10^100997+737)/9100998Robert Price07/2018
793747599!2+1024100991Robert Price02/2015
79382^335468-18629100986Enzo Doria05/2013
79392^335454-20961100982Enzo Doria06/2013
7940(2^335454+3258)/2100982Stefano Morozzi02/2021
794110^100978+61100979Lelio R Paula09/2016
794210^100978-156437100978Patrick De Geest11/2016
7943(2^335422+3114)/2100972Stefano Morozzi09/2020
7944(35*10^100970-89)/9100971Robert Price02/2022
7945(15*2^335417+1)/481100970Lelio R Paula12/2013
79462^335403-1859167100967Enzo Doria03/2016
794723599^18976+18976^23599100962Hans Havermann10/2018
79486*10^100958+43100959Robert Price07/2020
79499*2^335364-5100956Lelio R Paula08/2014
7950(7998^25867-1)/7997100955Serge Batalov06/2022
79512^335349+72287100951Enzo Doria04/2016
79522^335329+16095100945Lelio R Paula09/2016
7953232823#+233663100937Makoto Morimoto10/2017
7954(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
79552^335237-20893100917Enzo Doria06/2013
79562^335222-19337100912Enzo Doria05/2013
79572^335222-109985100912Enzo Doria04/2014
79582^335182-17237100900Enzo Doria05/2013
7959(2^335107+1634)/2100877Stefano Morozzi09/2020
79602^335043-16737100858Enzo Doria05/2013
7961(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
79622^335038-20633100857Enzo Doria06/2013
79632^335031+1873373100855Enzo Doria06/2016
796423489^19650+19650^23489100847Hans Havermann10/2018
79653^211354-8816100842Enzo Doria05/2014
79662^334984-112757100841Enzo Doria06/2014
7967(746*10^100827+1)/9100829Robert Price03/2020
796829451^2648+2648^29451100809Hans Havermann09/2018
796925583^8716+8716^25583100806Hans Havermann08/2018
79712^334857+48527100803Lelio R Paula08/2011
797012^93406+29100803Lelio R Paula10/2016
797228780^3179+3179^28780100796Hans Havermann09/2018
7973(5*2^334825+1)/47100792Lelio R Paula12/2013
7974(328^40063-1)/327100791Serge Batalov06/2022
79752^334809-13100788Lelio R Paula04/2011
7976(3552^28387-1)/3551100784Serge Batalov06/2022
7977(82*10^100780-1)/9100781Robert Price12/2014
797831395^1622+1622^31395100780Hans Havermann09/2018
7979(2^334779+47)/5100778Lelio R Paula12/2013
79802^334751+2049100771Lelio R Paula09/2016
798113^90443-98100749Lelio R Paula10/2016
7982(2^334674+3190)/2100747Stefano Morozzi09/2020
7983(2^334651+1050)/2100740Stefano Morozzi09/2020
7984(7*10^100737+71)/3100738Robert Price05/2018
7985(24737*2^334628+1)/3100737Lelio R Paula07/2014
798615^85639-28100720Lelio R Paula10/2016
798727068^5259+5259^27068100718Hans Havermann08/2018
79882^334562+577294575100711Lelio R Paula09/2016
79894*3^211077-5100710Lelio R Paula08/2014
79902^334524+145100702Lelio R Paula07/2009
7991(2^334451+714)/2100680Stefano Morozzi09/2020
799227648^4375+4375^27648100666Hans Havermann09/2018
7993(1017*2^334391-1)/3535100662Lelio R Paula05/2015
7994(2^334309+3122)/2100637Stefano Morozzi09/2020
79952^334294-113111100633Enzo Doria07/2014
799625581^8582+8582^25581100626Hans Havermann08/2018
79986^129308-17723100622Enzo Doria03/2013
7997(19*10^100627+287)/9/292157100622Alfred Reich11/2022
79996^129305+95100619Lelio R Paula10/2016
80002^334244-1167100618Lelio R Paula09/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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