PRP Records

Probable Primes Top 10000

(183432 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 ?
9251(73*10^51162-1)/951163Robert Price01/2015
92522^169899+6351145Lelio R Paula05/2009
92532^169898+51351145Lelio R Paula05/2009
92543^107186-1238851141Enzo Doria02/2013
9255(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
92563*6^65715-751137Lelio R Paula09/2014
9257116^24768+11551133Norbert Schneider10/2013
925835^33113-402651129Enzo Doria03/2013
9259(13*2^169830-1)/8447751121Lelio R Paula01/2014
9260(46*10^51111-1)/951112Serge Batalov10/2014
926115^43452-3451104Lelio R Paula01/2013
92622^169750-13751100Lelio R Paula01/2011
92632^169739+9406551097Lelio R Paula10/2011
926515^43442-2651092Lelio R Paula01/2013
92665^73096-1700651092Enzo Doria02/2013
926410^51091+7160151092Patrick De Geest07/2017
926710^51091-70151091Robert Price06/2017
9268(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
92692^169706-27055151087Gary Barnes08/2009
9270(2^169696+5)/2151083Lelio R Paula01/2012
9271(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
927211^49051-876051082Enzo Doria02/2013
9273(24737*2^169672+1)/2751080Lelio R Paula05/2014
92742^169677+1609551078Lelio R Paula05/2009
92752^169659-13551073Lelio R Paula01/2011
92762^169638-11318351067Enzo Doria07/2014
9277(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9278(10^51054+17)/951054Robert Price10/2014
92798329^13022-13022^832951054Norbert Schneider07/2017
9280(24737*2^169577+1)/551052Lelio R Paula05/2014
928111^49021-7851051Lelio R Paula01/2013
928218^40669+6151051Lelio R Paula01/2013
928314038^4327+4327^1403851045Hans Havermann02/2016
92842^169555-15951042Lelio R Paula01/2011
928591^26054-251041Lelio R Paula08/2013
9286Phi(101775,10)/162840151034Makoto Kamada05/2015
928797*10^51027-351029Robert Price01/2017
92882^169499-264751025Yves Minet07/2014
92895*6^65567+751022Lelio R Paula09/2014
929014763^2858+2858^1476351022Hans Havermann08/2015
929124^36966-147751021Enzo Doria03/2013
9292(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9293(34*10^51008-43)/951009Ray Chandler09/2010
929410^51004+12842751005Patrick De Geest08/2009
929610^51004-11351004Milton L. Brown12/2008
929510^51003+1695151004Patrick De Geest08/2009
929710^51003-7960151003Milton L. Brown12/2008
929810^51003-8083151003Milton L. Brown12/2008
929910^51002+887751003Patrick De Geest08/2009
930110^51002-1054151002Milton L. Brown11/2008
930010^51001+5205151002Patrick De Geest08/2009
930210^51001-15868751001Milton L. Brown10/2008
93042*10^51000+9351001Robert Price07/2016
930310^51000+18825151001Patrick De Geest10/2017
930510^51000-3128951000Patrick De Geest10/2017
9306(2^169416+5)/350999Lelio R Paula01/2012
9307(49*10^50998+41)/950999Robert Price07/2015
930813292^6867+6867^1329250999Hans Havermann02/2016
9309(35*10^50997-71)/950998Robert Price05/2015
93106^65536+2*97878-150997Jiahao He05/2017
931129^34871-28^3487150996Robert Price09/2012
931276^27112-7550993Norbert Schneider11/2012
9313(70^27631-1)/6950981Richard Fischer08/2017
9314(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
931510736^12645-12645^1073650971Norbert Schneider12/2016
9317(1017*2^169315-1)/971550968Lelio R Paula03/2015
93167^60309-6^(60309+1)50968Robert Price06/2016
93192^169267+9950955Lelio R Paula07/2009
93185*2^169264+350955Lelio R Paula02/2014
9320t(192517)50950Robert Price08/2014
932110^50943+62445150944Robert Price03/2015
932210^50943+5440950944Patrick De Geest02/2016
932310^50943-10055950943Patrick De Geest03/2016
93242^169206-364550937Lelio R Paula05/2009
93252^169196-11257750934Enzo Doria06/2014
932620^39146-348350931Enzo Doria03/2013
932710^50929+1684950930Patrick De Geest01/2012
932910^50929-5150929Robert Price05/2011
93287^60264+4850929Lelio R Paula10/2012
93312^169167+129950925Lelio R Paula05/2009
933010103^12717-10050925Enzo Doria07/2012
93323^106721-13050919Lelio R Paula07/2012
933418225^622+622^1822550917Anatoly F. Selevich11/2006
9333(10223*2^169138+1)/111350917Lelio R Paula05/2014
93357*2^169125+950913Lelio R Paula02/2014
9336(47*2^169123+1)/2950912Lelio R Paula03/2015
933720^39131+9350911Lelio R Paula01/2013
9338(21*27^35567-94921)/2650910Curtis Bright05/2015
9339(7*2^169124-1)/954950909Lelio R Paula01/2014
9340(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
934113693^5212+5212^1369350897Hans Havermann02/2016
93427*5^72813+650895Lelio R Paula09/2014
93435*10^50890-8150891Robert Price04/2017
93443^106656-1202850888Enzo Doria02/2013
9345(2^169028+3)/25950881Lelio R Paula01/2012
93462^169000-112750875Yves Minet05/2013
934719^39780+1650869Lelio R Paula01/2013
9348(19*2^168960+1)/550863Lelio R Paula07/2012
9349(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
935111^48840+4650862Lelio R Paula01/2013
9350(5*10^50861-107)/350862Robert Price01/2017
935220^39087-420350854Enzo Doria03/2013
9353(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
93542^168907-54444750847Paul Bourdelais11/2012
935519312^429+429^1931250839Anatoly F. Selevich12/2006
93565^72716-1322650827Enzo Doria02/2013
93572^168823+102550821Lelio R Paula01/2009
93587*10^50818-8950819Robert Price01/2017
93602^168811+15015*16881150818Henri Lifchitz02/2005
93592^168813-283350818Yves Minet09/2014
9361(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
93622^168795+538550813Lelio R Paula05/2009
93637670^13079-13079^767050810Norbert Schneider09/2017
93644*3^106483+550806Lelio R Paula03/2014
936513^45606+450803Lelio R Paula01/2013
936613^45606-3850803Lelio R Paula01/2013
93672^168746+5890550798Lelio R Paula05/2009
9368(16*10^50795-43)/950796Robert Price02/2015
9369gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
93707*10^50789-4750790Robert Price02/2017
93712^168717-72952350789Paul Bourdelais11/2012
9372(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9373(21*2^168652-1)/21550769Lelio R Paula01/2014
93742^168629+1290950763Lelio R Paula01/2011
93759328^12787+12787^932850762Norbert Schneider01/2016
93762^168627+7311350762Enzo Doria04/2016
93772^168623+4733350761Yves Minet02/2010
9378(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9379(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
93808544^12901-12901^854450723Norbert Schneider05/2017
9381(17^41221+1)/1850720Paul Bourdelais03/2010
938210^50711+750712Jason Earls12/2007
938310^50711-31796950711Patrick De Geest04/2009
9385(17^41213+3^41213)/2050710Robert Price08/2013
9384(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
938647779!4+102450708Robert Price08/2017
93882^168431-15950703Lelio R Paula01/2011
9387(7*10^50702-1)/350703Erik Branger03/2014
9389117216#-p(117216)50700Henri Lifchitz03/2007
9390(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9391(13*2^168352-1)/47750678Lelio R Paula01/2014
93928*10^50675+3950676Robert Price01/2017
9393(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
939414415^3274+3274^1441550670Hans Havermann05/2016
9395(12379^12379+282)/1750663Makoto Morimoto07/2016
93975^72480-1712650662Enzo Doria02/2013
9396(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
93983^106143+250644Mike Oakes11/2009
93999178^12777-12777^917850633Norbert Schneider02/2017
9400(2*10^50603-41)/350603Robert Price01/2017
9401(12^46889-1)/1150601Paul Bourdelais09/2008
94022^168068-189350594Yves Minet09/2012
94032^168057+841550591Lelio R Paula11/2011
94044*10^50579+950580Robert Price05/2015
94052^168019-9439550579Lelio R Paula07/2011
94062^168019+7421350579Enzo Doria04/2016
94073^106002+7050576Lelio R Paula07/2012
94085*2^167970-950565Lelio R Paula02/2014
9409(58*10^50558-13)/950559Robert Price09/2015
941088*10^50547+750549Robert Price11/2016
94112^167910-11262550546Enzo Doria06/2014
9412(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
94132^167866+1171550533Lelio R Paula05/2009
9414gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
94152^167847-13550527Lelio R Paula01/2011
9416-lucasV(-1,2,335684)50526Mike Oakes01/2017
9417(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9418(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
94202^167807+7550515Lelio R Paula08/2010
94192^167805+7627750515Enzo Doria04/2016
94218335^12882+12882^833550510Norbert Schneider03/2016
94227*2^167777+950507Lelio R Paula02/2014
942314162^3681+3681^1416250502Hans Havermann05/2016
9424(17*10^50495-11)/350496Robert Price07/2015
94252^167682+8550478Lelio R Paula08/2010
94262^167667-92742750473Paul Bourdelais11/2012
94279737^12654+12654^973750470Norbert Schneider01/2016
9428(9179*2^167644-1)/1750469Lelio R Paula03/2015
942913386^5891+5891^1338650468Hans Havermann05/2016
9430(10^50467-97)/350467Robert Kinser10/2017
9431(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
94325003^13637-15650447Enzo Doria07/2012
94336^64826-2672350445Enzo Doria03/2013
9434(3^105718+7)/3250439Lelio R Paula03/2012
9435(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
943617^40989+5650435Lelio R Paula01/2013
9437(12329^12329+1652)/42150435Makoto Morimoto07/2016
94382*5^72153+750434Lelio R Paula09/2014
9439(3126^14431-1)/312550433Richard Fischer03/2015
94408078^12907-12907^807850432Norbert Schneider05/2017
944139^31694+3850428Norbert Schneider05/2014
9442(7*10^50414-151)/950414Robert Price09/2017
94432^167460+218750411Lelio R Paula11/2011
9444(12323^12323+2709)/2^450409Makoto Morimoto07/2016
944511^48400-771050404Enzo Doria02/2013
94462^167432+5461550403Lelio R Paula05/2009
9447(23*2^167430-1)/416950400Lelio R Paula01/2014
944868677!6-250395Robert Price07/2017
944919^39404+2250389Lelio R Paula01/2013
9450(102^25087-1)/10150388Richard Fischer08/2017
945135^32629-783450382Enzo Doria03/2013
94536^64744+16350381Lelio R Paula06/2012
9452116447#+17465950381Nicolas PALAU09/2016
94542^167353+12950379Lelio R Paula05/2009
945520^38722-113350379Enzo Doria03/2013
94563^105567-1650369Lelio R Paula07/2012
94572^167321-11284950369Enzo Doria06/2014
9458(28*10^50362-43)/350363Robert Price04/2016
945911421^12410-12410^1142150357Norbert Schneider08/2013
94602^167278-206350356Yves Minet03/2013
9461181^22300+22300^18150347Serge Batalov05/2014
94629932^12595-12595^993250343Norbert Schneider12/2016
94638993^12732-12732^899350342Norbert Schneider02/2017
94643*5^72018-450339Lelio R Paula09/2014
94652^167207-11268750335Enzo Doria06/2014
94666^64674-3750327Lelio R Paula06/2012
94672^167177+7480150326Enzo Doria04/2016
946813739^4600+4600^1373950323Hans Havermann10/2015
946911508^12391+12391^1150850320Norbert Schneider06/2014
94702^167132-216350312Yves Minet08/2013
94717^59527-6250307Lelio R Paula06/2012
9473(310027^9161+1)/31002850302Faysal YAtim04/2008
9472(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
94742^167083-11251950297Enzo Doria06/2014
9475272^20659-20659^27250296Norbert Schneider09/2015
947625337!!-1650290Robert Price06/2015
94779722^12611-12611^972250290Norbert Schneider12/2016
9478(15*2^167013+1)/64950275Lelio R Paula07/2012
947919^39315-1250275Lelio R Paula01/2013
94805^71925-3650274Lelio R Paula06/2012
94812^167002+279913950273Enzo Doria04/2016
948210957^12444-12444^1095750270Norbert Schneider07/2013
94838*10^50253-9950254Robert Price02/2017
94855^71894-5450252Lelio R Paula06/2012
9484(127^23887+1)/12850252Richard Fischer04/2017
948618^40028-550247Lelio R Paula01/2013
9487(3*2^166904+1)/127950241Lelio R Paula07/2012
948824^36397+2350236Norbert Schneider12/2013
94897984*29^34345+2150230Curtis Bright05/2015
94903^105248-1352850217Enzo Doria02/2013
94916^64532-6550216Lelio R Paula06/2012
94925^71834-2061650210Enzo Doria03/2013
9493(31*2^166778-1)/365150204Lelio R Paula01/2014
94942^166752-11239750198Enzo Doria06/2014
9495(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
949611^48199-93050195Enzo Doria11/2012
94973*10^50194-750195Erik Branger11/2013
94989992^12549+12549^999250192Norbert Schneider10/2015
94992^166708+15750185Lelio R Paula01/2011
9500(1338272^8192+1)/6553750184Syoichiro Yamada06/2008


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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