PRP Records

Probable Primes Top 10000

(224926 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 (> 30000) Who ? When ?
85017*10^58815-8358816Robert Price09/2017
85022^195357-430358809Yves Minet08/2018
8503(47*2^195254+1)/26882158774Lelio R Paula03/2015
85042^195207-1810958764Enzo Doria05/2013
85052^195199-156758761Yves Minet08/2012
85062^195190+7375958759Enzo Doria04/2016
85079*7^69525-458757Lelio R Paula09/2014
85082^195170-1804558753Enzo Doria05/2013
85092^195166-16558751Lelio R Paula04/2011
8510(754*10^58748-7)/958750Robert Price11/2017
8511(22699*2^195140+1)/17558746Lelio R Paula05/2014
85127*3^123109-258739Lelio R Paula04/2014
8513(8*10^58738-611)/958738Robert Price11/2017
851418^46790+7758735Lelio R Paula03/2013
85152^195095-33729758730Gary Barnes09/2009
8516(14*10^58729+31)/958730Robert Price02/2015
851799^29424+9858720Norbert Schneider07/2013
8518(15185*2^195039-1)/21958715Lelio R Paula04/2015
85192^195001-6958702Lelio R Paula04/2011
85202^194978-48781158695Gary Barnes09/2009
8521163^26530+26530^16358690Serge Batalov05/2014
85222^194940-194940+158683Robert Price10/2014
8523(76*10^58669+41)/958670Robert Price10/2015
852414^51186+8758666Lelio R Paula03/2013
85252^194878-9730558665Lelio R Paula09/2011
85265^83927-1813658663Enzo Doria05/2014
8527(24737*2^194865+1)/108558662Lelio R Paula06/2014
85287^69411+4058660Lelio R Paula10/2012
85296^75382-7958659Lelio R Paula10/2012
85302^194854+2758657Lelio R Paula04/2011
85312^194801+2983558641Lelio R Paula10/2012
85322^194752+19558627Lelio R Paula04/2011
85337^69371-6^6937158626Predrag Minovic08/2004
85342^194747-11251958625Enzo Doria06/2014
8535(15*2^194737+1)/5958622Lelio R Paula07/2012
8536(23*2^194700+1)/358612Lelio R Paula02/2012
853710^58608+5527358609Patrick De Geest07/2017
853810^58608-80000158608Robert Price06/2017
853910^58608-6011958608Patrick De Geest07/2017
85405^83836+7658599Lelio R Paula10/2012
854118^46664+3158577Lelio R Paula03/2013
8542(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
85432^194574+16558573Lelio R Paula04/2011
85462^194569-1221158572Enzo Doria06/2014
854410^58571+5^58571+2^5857158572Robert Price12/2016
854510^58571+20283758572Patrick De Geest02/2017
8547(10^58571+41)/358571Robert Price01/2017
854810^58571-34362958571Patrick De Geest02/2017
8549(43*10^58563-403)/958564Robert Price04/2017
855011^56235-795058563Enzo Doria02/2013
8551(14*10^58550+211)/958551Robert Price11/2017
85522^194479-11323958545Enzo Doria07/2014
85532^194455-11224958537Enzo Doria06/2014
85542^194405-11191958522Enzo Doria05/2014
8555(4*10^58521-19)/358522Robert Price06/2017
8556(7^69247-4^69247)/358521Robert Price06/2012
85575*7^69246+858521Lelio R Paula09/2014
85582^194358-116758508Lelio R Paula05/2011
8559(2^194366+7)/137358507Lelio R Paula02/2012
8560(493*10^58486-7)/958488Robert Price07/2016
85613^122579-34058486Lelio R Paula10/2012
8562(11*10^58458-149)/358459Robert Price01/2017
8563(47*10^58456+133)/958457Robert Price04/2017
85642^194186+8558456Lelio R Paula04/2011
85653^122506-2^(122506-1)58451Robert Price01/2016
8566(74^31267-1)/7358444Paul Bourdelais08/2017
8567177^25998-258443Lelio R Paula10/2017
856815^49690-2658440Lelio R Paula03/2013
856910^58437+11072158438Patrick De Geest12/2012
857010^58437-1158437Robert Price05/2011
85712^194095+6958429Lelio R Paula04/2011
8572(29*10^58417-77)/358418Robert Price01/2017
85732^194034+17758411Lelio R Paula04/2011
8574789^20158+20158^78958400Norbert Schneider06/2016
857514^50949+7558395Lelio R Paula03/2013
85762^193974-11476158392Enzo Doria05/2015
85772^193965+558390Henri Lifchitz12/2002
8578(5*10^58384-29)/358385Robert Price02/2017
85793^122360+8058381Lelio R Paula10/2012
858010103^14577-11458373Enzo Doria07/2012
8581(22699*2^193883+1)/2158368Lelio R Paula06/2014
8582(31*2^193886+1)/14076558362Lelio R Paula07/2012
858311^56041-156058361Enzo Doria11/2012
8584(2^193881+9)/1769958360Lelio R Paula02/2012
85853^122313+5858359Lelio R Paula10/2012
85866^74996-11958359Lelio R Paula10/2012
8587(11*2^193859+1)/1358358Lelio R Paula07/2012
85882^193861-11225558358Enzo Doria06/2014
8589(22699*2^193854+1)/492758357Lelio R Paula06/2014
859018^46487+3758354Lelio R Paula03/2013
859117^47419+5458347Lelio R Paula03/2013
8592(31*2^193791+1)/358338Lelio R Paula02/2012
8593(27*2^193805-1)/98224958337Lelio R Paula01/2014
85943^122219-2^12221958314Mike Oakes09/2003
8595(199*10^58306+11)/358308Robert Price05/2017
85962^193674-1882558302Lelio R Paula05/2011
85975*10^58275+358276Dmitry Domanov11/2010
85982^193578-11291358273Enzo Doria06/2014
85992^193541+129958262Lelio R Paula05/2011
860010^58250+9358251Robert Price01/2011
860110^58250-17560758250Patrick De Geest12/2012
8602(107^28703+1)/10858248Richard Fischer05/2018
86032^193492+841558247Lelio R Paula10/2012
86042^193444+15758233Lelio R Paula04/2011
8605Phi(28754,28754)58231Henri Lifchitz08/2013
86062^193430-11188158229Enzo Doria05/2014
860710^58225+12457958226Patrick De Geest12/2012
860810^58225-9358225Robert Price05/2011
86092^193375-29558212Yves Minet05/2013
86102^193345+7726758203Enzo Doria05/2016
861121^44017-20^4401758201Robert Price05/2012
8612(17*2^193329-1)/958199Lelio R Paula01/2014
861317^47291+2058190Lelio R Paula03/2013
8614p(12528)#/2-12858170Robert Price05/2017
86152^193214-13558164Lelio R Paula04/2011
861619^45483-8058162Lelio R Paula03/2013
8617(4*10^58155+83)/358156Robert Price01/2017
861914^50739-1358154Lelio R Paula03/2013
8618(1017*2^193184-1)/482358154Lelio R Paula04/2015
8620(2*10^58151+457)/958151Robert Price01/2017
8621(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8622(19*2^193114-1)/118675558129Lelio R Paula01/2014
86242^193091-123758127Yves Minet08/2012
86239*7^68780-258127Lelio R Paula09/2014
86252^193083-86968810558124Lelio R Paula10/2012
86262^193058-4558117Lelio R Paula04/2011
8627(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
862811^55795-4258105Lelio R Paula03/2013
86293^121779-1658104Lelio R Paula10/2012
8630(13*10^58103+191)/358104Robert Price08/2017
86312^192986+19558095Lelio R Paula04/2011
86327^68740+2*3^6874058093Mike Oakes07/2010
8633(85*10^58091-1)/358093Robert Price07/2017
8634(404*10^58087-53)/958089Robert Price11/2017
863512^53821+1158083Lelio R Paula02/2013
8636119^27979-11858072Norbert Schneider10/2013
8637(10223*2^192828+1)/24358049Lelio R Paula05/2014
86382^192808-112758041Yves Minet05/2013
8639(27*2^192803+1)/982758037Lelio R Paula07/2012
8641(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
86403*10^58032-2358033Robert Price11/2017
86422^192678+7294358002Enzo Doria04/2016
8643(13*10^57997-37)/357998Robert Price08/2017
86442^192657-318957996Yves Minet10/2014
86456^74525-14957992Lelio R Paula10/2012
864642^35723-4157988Norbert Schneider06/2014
8647(29*2^192625-1)/18357986Lelio R Paula01/2014
8648(3^121520-8)/384757977Lelio R Paula03/2012
8649(2^192596-5)/13957976Lelio R Paula02/2012
865010^57975+6783357976Patrick De Geest09/2013
865110^57975-4769357975Patrick De Geest09/2013
8652(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8653(29*10^57967+673)/957968Robert Price10/2017
8654(3^121492-5)/457966Lelio R Paula03/2012
86552^192549+3557964Lelio R Paula04/2011
865628799!2+257962Robert Price10/2012
8657(7*2^192534-1)/134757957Lelio R Paula01/2014
86587001^15069-10057943Enzo Doria07/2012
8659L(277273)/1109092157940Donovan Johnson11/2005
8660(2^192469-1017)/3557938Lelio R Paula02/2012
86612^192457-1155*19245757936Henri Lifchitz02/2005
86622^192443+138557932Lelio R Paula05/2011
8663132^27317-13157928Norbert Schneider03/2015
866441522!3-5904957912Robert Price12/2015
8665(3*2^192380-1)/16957911Lelio R Paula01/2014
86662^192339-251557900Yves Minet07/2014
86672^192303+769557889Lelio R Paula10/2012
86682^192273-595557880Lelio R Paula05/2011
86692^192257+1609557876Lelio R Paula05/2011
8670109^28401-257865Lelio R Paula10/2017
86712^192218-11186157864Enzo Doria05/2014
86722^192214-394157863Yves Minet04/2017
8673(2^192212+3)/25957860Lelio R Paula02/2012
8674(3^121270+8)/15593975357853Lelio R Paula03/2012
867580^30393-7957841Norbert Schneider03/2015
867620^44455-312357838Enzo Doria03/2013
86772^192122-19557835Lelio R Paula04/2011
8678(29*10^57834+91)/357835Robert Price03/2016
86798*6^74306+557823Lelio R Paula09/2014
8680(39^36341-1)/3857820Robert Price04/2012
86812^192037-11180557809Enzo Doria05/2014
86822^192023-192023^257805Henri Lifchitz05/2005
868321^43717+257804Ray Chandler08/2011
86848*5^82687+757797Lelio R Paula09/2014
86855^82680-2457791Lelio R Paula10/2012
8686(2^191915+47)/9557771Lelio R Paula02/2012
8687(74*10^57763+133)/957764Robert Price10/2017
86886^74227-9557760Lelio R Paula10/2012
86892^191861+2983557756Lelio R Paula10/2012
86901908^17605+17605^190857755Serge Batalov05/2014
86915*10^57754+5957755Robert Price09/2016
8692(5*2^191821-1)/892406757738Lelio R Paula01/2014
86933*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
869441399!3-656157723Robert Price11/2015
8695(44*10^57721-233)/957722Robert Price10/2017
86962^191745+1757721Lelio R Paula04/2011
86972^191730-76157717Yves Minet01/2012
8698(2^191733-3)/225157715Lelio R Paula02/2012
86992^191698-11157707Lelio R Paula04/2011
8700(13*10^57691+23)/957692Robert Price02/2015
870120^44340-542357688Enzo Doria03/2013
8702(27*2^191629+1)/12557686Lelio R Paula07/2012
87034*10^57684+3*7^5768457685Mike Oakes11/2010
87042*3^120898+557684Lelio R Paula04/2014
8705(6883*2^191610-1)/734757681Lelio R Paula04/2015
87066^74117-4957675Lelio R Paula10/2012
87072^191586-11320157674Enzo Doria07/2014
87082^191580+19357672Lelio R Paula04/2011
8709(103*29^39433+10401)/457669Curtis Bright05/2015
87102^191560+25525557666Lelio R Paula05/2011
87112^191515-8557652Lelio R Paula04/2011
87122^191502-112757648Yves Minet05/2013
87132*5^82473-3^8247357647Mike Oakes08/2010
8714(13*10^57634-61)/357635Robert Price08/2017
871585^29868-29868^8557628Norbert Schneider11/2017
87162^191430+10357627Lelio R Paula04/2011
87173*2^191408+557621Lelio R Paula03/2014
87182^191382-185893157612Enzo Doria04/2016
87196*7^68163+557606Lelio R Paula09/2014
872091^29403-257602Lelio R Paula08/2013
872111^55308-795057598Enzo Doria02/2013
87222^191329+6557596Lelio R Paula04/2011
872311^55302-24057592Enzo Doria07/2012
87242^191299-103146757587Paul Bourdelais11/2012
87252^191295-11199157586Enzo Doria05/2014
87262^191279-129757581Yves Minet08/2012
87273*6^73961+557554Lelio R Paula09/2014
8728(3^120623+5)/5214457548Lelio R Paula04/2012
8729(17*10^57543-29)/357544Robert Price09/2017
873042^35445-4157537Norbert Schneider06/2014
8731(71^31079-1)/7057534Paul Bourdelais08/2017
87322^191069-72340357518Paul Bourdelais11/2012
87334*10^57506-357507Serge Batalov11/2010
873410^57501+6735957502Patrick De Geest06/2016
873510^57501-100000000157501Robert Price05/2016
873610^57501-24986157501Patrick De Geest06/2016
8737(9^60251+4^60251)/1357493Robert Price02/2013
873820^44184-600357485Enzo Doria03/2013
87392^190948+1270557482Lelio R Paula10/2012
87402^190945+2957481Henri Lifchitz06/2005
87412^190922-40157474Yves Minet01/2012
874215^48860+4657464Lelio R Paula02/2013
87433^120434+2057462Lelio R Paula10/2012
87447^67964-3857437Lelio R Paula10/2012
87452^190799-11306557437Enzo Doria07/2014
87469*5^82159+257428Lelio R Paula09/2014
8747(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8750lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8749(103*10^57414-1)/357416Serge Batalov12/2014
8748(1654*30^38869-1)/2957416Karsten Bonath05/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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