PRP Records

Probable Primes Top 10000

(259919 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 ?
37512^338796+93101988Donovan Johnson06/2008
3752lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
375325295^10744+10744^25295101969Hans Havermann01/2019
375425712^9243+9243^25712101969Hans Havermann01/2019
3755(71^55079-1)/70101964Paul Bourdelais08/2017
37562^338682-19865101954Enzo Doria06/2013
3757(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
375828594^3673+3673^28594101939Hans Havermann02/2019
37592^338568+37101920Lelio R Paula07/2011
37602^338559-1858777101917Enzo Doria04/2016
3761(9*2^338520+1)/365101904Lelio R Paula12/2013
376224502^14419+14419^24502101903Hans Havermann01/2019
37632^338497-17041101898Enzo Doria05/2013
37642^338475+54615101892Lelio R Paula10/2016
37652^338426-19797101877Enzo Doria06/2013
37662^338368-20369101859Enzo Doria06/2013
37672^338366+74179101859Enzo Doria04/2016
376827088^5755+5755^27088101853Hans Havermann01/2019
37692^338280-19745101833Enzo Doria06/2013
3770(3*2^338236-1)/347101818Lelio R Paula03/2014
37716^130841+103101815Lelio R Paula10/2016
37722^338122-20117101785Enzo Doria06/2013
3773(2^338139+5)/905333101785Lelio R Paula12/2013
377435^65917-7092101781Enzo Doria03/2013
37752^338010-19833101752Enzo Doria06/2013
37763^213215-76101730Lelio R Paula09/2016
377723907^17998+17998^23907101730Hans Havermann01/2019
377810^101728+154953101729Patrick De Geest02/2020
37812^337930+63101728Lelio R Paula07/2011
377910^101728-987654321101728Robert Price12/2019
378010^101728-60741101728Patrick De Geest02/2020
37822^337920+1869661101725Enzo Doria05/2016
378324116^16509+16509^24116101715Hans Havermann01/2019
37842^337859-19645101706Enzo Doria05/2013
37852^337754+1869169101675Enzo Doria05/2016
37863*10^101657-37101658Robert Price07/2018
3787(31*2^337677-1)/593101650Lelio R Paula03/2014
378811^97605-24101646Lelio R Paula10/2016
37898^112539-112539101633Robert Price01/2014
379025694^9003+9003^25694101605Hans Havermann12/2018
37912^337515-19869101603Enzo Doria06/2013
37922^337473+719101590Lelio R Paula08/2011
3793(2^337485-509203)/656647157101585Lelio R Paula12/2013
37942^337452-108815101584Enzo Doria03/2014
37952^337453+1185101584Lelio R Paula09/2016
37962^337410-113561101571Enzo Doria08/2014
37972^337387+855101564Lelio R Paula09/2016
37982^337367-17295101558Lelio R Paula09/2016
37992^337342-109035101551Enzo Doria04/2014
380023703^19238+19238^23703101548Hans Havermann12/2018
3801(26*10^101537-167)/3101538Robert Price10/2019
38022^337267-19101528Lelio R Paula07/2011
38032^337183-19989101503Enzo Doria06/2013
38042^337149+72425101492Enzo Doria04/2016
380524041^16642+16642^24041101483Hans Havermann12/2018
380633982^969+969^33982101482Hans Havermann12/2018
38072^337101-20241101478Enzo Doria06/2013
38082^337035-20001101458Enzo Doria06/2013
38092^337017-16995101453Lelio R Paula09/2016
38102^336979-115315101441Enzo Doria06/2015
38112^336970-20885101439Enzo Doria06/2013
38122^336958+79101435Lelio R Paula10/2009
38132^336942+169101430Lelio R Paula10/2009
3814(15185*2^336894-1)/7939101416Lelio R Paula05/2015
38154*10^101415-89101416Robert Price11/2018
38162^336871+257463101409Tony Prest / Never Odd Or Even04/2016
38172^336871+318105101409Tony Prest / Never Odd Or Even04/2016
38182^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
38192^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
38202^336871+389273101409Tony Prest / Never Odd Or Even04/2016
38212^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
38222^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
38232^336871+586905101409Tony Prest / Never Odd Or Even04/2016
38242^336871+674571101409Tony Prest / Never Odd Or Even04/2016
38252^336871+707009101409Tony Prest / Never Odd Or Even04/2016
38262^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
38272^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
38282^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
38292^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
38302^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
38312^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
38322^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
38332^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3834(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3835(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3836(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3837(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
383824097^16150+16150^24097101405Hans Havermann12/2018
38392^336842+94065101400Lelio R Paula09/2016
3840(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3841(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3842(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3843(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3844(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3845(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3846(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
384710^101369+203811101370Patrick De Geest11/2016
384810^101369-99101369Lelio R Paula09/2016
3849(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
38502^336701-113563101358Enzo Doria08/2014
385189717!4-512101351Robert Price11/2019
38522^336644-109023101340Enzo Doria04/2014
38532^336601-21081101327Enzo Doria06/2013
385420^77869+63101310Lelio R Paula09/2016
3855(13*2^336523-1)/19101304Lelio R Paula03/2014
38566^130179-137101299Lelio R Paula10/2016
3857(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3858(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3859(2^336448+9)/497405101276Lelio R Paula12/2013
38602^336369-19753101258Enzo Doria05/2013
386123842^17653+17653^23842101253Hans Havermann11/2018
38622^336350-344291101252Enzo Doria07/2015
3863(56*10^101222-47)/9101223Robert Price02/2019
38642^336243-108777101220Enzo Doria03/2014
3865(31*2^336189-1)/19101204Lelio R Paula03/2014
386623535^19954+19954^23535101202Hans Havermann11/2018
3867(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
38682^336150-20393101192Enzo Doria06/2013
386923996^16473+16473^23996101186Hans Havermann11/2018
38702^336112-1865249101180Enzo Doria03/2016
38712^336103-109015101178Enzo Doria04/2014
387213^90809-96101157Lelio R Paula10/2016
387326199^7258+7258^26199101150Hans Havermann11/2018
387419^79098-30101147Lelio R Paula10/2016
387519^79095+88101144Lelio R Paula10/2016
387615^85976+32101116Lelio R Paula10/2016
38772^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
3878(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3879(4^167933+17)/3101106Robert Price02/2017
38812^335858+153101104Lelio R Paula10/2009
3880(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
3882(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
3883(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
38846^129918-35101096Lelio R Paula10/2016
38853^211885-70101095Lelio R Paula09/2016
3887(29*2^335835-1)/550599101093Lelio R Paula03/2014
3886(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
38882^335818-20033101092Enzo Doria06/2013
38892^335813-110083101090Enzo Doria04/2014
38902^335804+2155101088Lelio R Paula09/2016
3891(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
38922^335784-16145101082Enzo Doria04/2013
389311^97051+62101069Lelio R Paula10/2016
38943*10^101065+11101066Robert Price07/2018
389527820^4293+4293^27820101064Hans Havermann10/2018
3896(2^335691-3)/26515101049Lelio R Paula12/2013
38972^335658-94395101044Lelio R Paula09/2016
389824514^13215+13215^24514101024Hans Havermann11/2018
38992^335586+169101022Lelio R Paula10/2009
3900(56^57787-1)/55101021Paul Bourdelais08/2017
3901(19*10^100997+737)/9100998Robert Price07/2018
390247599!2+1024100991Robert Price02/2015
39032^335468-18629100986Enzo Doria05/2013
39042^335454-20961100982Enzo Doria06/2013
390510^100978+61100979Lelio R Paula09/2016
390610^100978-156437100978Patrick De Geest11/2016
3907(15*2^335417+1)/481100970Lelio R Paula12/2013
39082^335403-1859167100967Enzo Doria03/2016
390923599^18976+18976^23599100962Hans Havermann10/2018
39109*2^335364-5100956Lelio R Paula08/2014
39112^335349+72287100951Enzo Doria04/2016
39122^335329+16095100945Lelio R Paula09/2016
3913232823#+233663100937Makoto Morimoto10/2017
3914(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
39152^335237-20893100917Enzo Doria06/2013
39162^335222-19337100912Enzo Doria05/2013
39172^335222-109985100912Enzo Doria04/2014
39182^335182-17237100900Enzo Doria05/2013
39192^335043-16737100858Enzo Doria05/2013
3920(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
39212^335038-20633100857Enzo Doria06/2013
39222^335031+1873373100855Enzo Doria06/2016
392323489^19650+19650^23489100847Hans Havermann10/2018
39243^211354-8816100842Enzo Doria05/2014
39252^334984-112757100841Enzo Doria06/2014
3926(746*10^100827+1)/9100829Robert Price03/2020
392729451^2648+2648^29451100809Hans Havermann09/2018
392825583^8716+8716^25583100806Hans Havermann08/2018
39302^334857+48527100803Lelio R Paula08/2011
392912^93406+29100803Lelio R Paula10/2016
393128780^3179+3179^28780100796Hans Havermann09/2018
3932(5*2^334825+1)/47100792Lelio R Paula12/2013
39332^334809-13100788Lelio R Paula04/2011
3934(82*10^100780-1)/9100781Robert Price12/2014
393531395^1622+1622^31395100780Hans Havermann09/2018
3936(2^334779+47)/5100778Lelio R Paula12/2013
39372^334751+2049100771Lelio R Paula09/2016
393813^90443-98100749Lelio R Paula10/2016
3939(7*10^100737+71)/3100738Robert Price05/2018
3940(24737*2^334628+1)/3100737Lelio R Paula07/2014
394115^85639-28100720Lelio R Paula10/2016
394227068^5259+5259^27068100718Hans Havermann08/2018
39432^334562+577294575100711Lelio R Paula09/2016
39444*3^211077-5100710Lelio R Paula08/2014
39452^334524+145100702Lelio R Paula07/2009
394627648^4375+4375^27648100666Hans Havermann09/2018
3947(1017*2^334391-1)/3535100662Lelio R Paula05/2015
39482^334294-113111100633Enzo Doria07/2014
394925581^8582+8582^25581100626Hans Havermann08/2018
39506^129308-17723100622Enzo Doria03/2013
39516^129305+95100619Lelio R Paula10/2016
39522^334244-1167100618Lelio R Paula09/2016
3953(76*10^100611+77)/9100612Robert Price10/2019
3954(26*10^100566+49)/3100567Robert Price08/2019
3955(21*2^334050+1)/935100558Lelio R Paula12/2013
395624885^10984+10984^24885100555Hans Havermann07/2018
3957(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3958(35*10^100542+1)/9100543Serge Batalov11/2010
395923578^18367+18367^23578100538Hans Havermann07/2018
396013^90251+24100535Lelio R Paula10/2016
39612^333963+789100533Lelio R Paula08/2011
39622^333919-1840087100520Enzo Doria06/2015
39632^333911+72623100518Enzo Doria04/2016
396424605^12168+12168^24605100517Hans Havermann08/2018
396518^80064-67100503Lelio R Paula10/2016
39665^143742-48100472Lelio R Paula10/2016
396724095^14784+14784^24095100472Hans Havermann08/2018
39682^333757-112123100471Enzo Doria06/2014
396927358^4693+4693^27358100444Hans Havermann07/2018
39708*10^100439-51100440Robert Price08/2019
39712^333603-108861100425Enzo Doria03/2014
39729*7^118818-2100414Lelio R Paula11/2014
39732^333546-17097100408Enzo Doria05/2013
397417^81597+72100401Lelio R Paula10/2016
3975p(20559)#/2+8100384Robert Price01/2017
397611^96390-24100380Lelio R Paula10/2016
39784832563059*2^333333+30029100353Donovan Johnson01/2008
397723565^18136+18136^23565100353Hans Havermann07/2018
39792^333354+763100350Lelio R Paula08/2011
3980(25*10^100343-67)/3100344Robert Price06/2019
39812^333289-109483100330Enzo Doria04/2014
39822^333240-2790209100316Enzo Doria03/2016
398323601^17798+17798^23601100314Hans Havermann05/2018
3985(2^333227-2^166614+1)/510031111/2006
39842^333225+719100311Lelio R Paula08/2011
39862^333221-2785333100310Enzo Doria10/2015
398776^53332-75100308Norbert Schneider02/2015
39886^128892-17573100298Enzo Doria03/2013
3989(47*10^100283-119)/9100284Robert Price05/2019
39902^333105-113215100275Enzo Doria07/2014
3991(31*2^333102+1)/2375100272Lelio R Paula11/2013
39924*10^100257-83100258Robert Price10/2018
399317^81476-74100253Lelio R Paula10/2016
399423392^19207+19207^23392100199Hans Havermann06/2018
3995(206*10^100189-17)/9100191Robert Price01/2020
399617^81417-16100180Theodore Burton11/2005
39972^332739-113215100165Enzo Doria07/2014
39982^332730-1865621100162Enzo Doria03/2016
399991^51127-2100160Lelio R Paula09/2013
400015^85159-32100155Lelio R Paula10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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