PRP Records

Probable Primes Top 10000

(172742 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 ?
87515^73524-1442651392Enzo Doria02/2013
87522^170712+24351390Lelio R Paula10/2011
8753(15*2^170713+1)/179351388Lelio R Paula07/2012
8754(2^170702+9)/126151384Lelio R Paula01/2012
8755283^20956+20956^28351380Norbert Schneider08/2014
87562^170665-3151376Lelio R Paula01/2011
875711^49330-1251372Lelio R Paula01/2013
8758(25*10^51366-73)/351367Robert Price09/2016
87595^73486-2^7348751365Mike Oakes10/2010
8760(10^51364+119)/351364Serge Batalov12/2014
876115^43672+6851363Lelio R Paula01/2013
87622^170609-11314351359Enzo Doria07/2014
8763760^17827-759^1782751357Jean-Louis Charton12/2010
8764(22699*2^170592+1)/443551355Lelio R Paula05/2014
87658*7^60767+351355Lelio R Paula09/2014
87665^73452-2064651341Enzo Doria03/2013
87672^170531-23040751335Gary Barnes08/2009
876835^33243-211251330Enzo Doria03/2013
8769(1845768^8192+1)/6553751328Lelio R Paula06/2013
877013^46072+4251322Lelio R Paula01/2013
877114^44778-9551322Lelio R Paula01/2013
877211008^12697+12697^1100851318Norbert Schneider01/2016
8773t(180039)51312Robert Price09/2014
87742^170444-44351309Yves Minet05/2013
8775(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
8776(2*10^51285-71)/351285Robert Price01/2017
8777(1819288^8192+1)/6553751277Lelio R Paula06/2013
87785^73350+2851270Lelio R Paula10/2012
87793^107450+251267Mike Oakes11/2009
87802^170296+253351265Henri Lifchitz07/2004
87812^170293+7648151264Enzo Doria05/2016
878211835^12584+12584^1183551257Norbert Schneider11/2015
8783(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
878512^47489+47489^1251250Serge Batalov02/2012
878414637^3172+3172^1463751250Hans Havermann04/2016
8786(2^170245+7)/951248Lelio R Paula02/2012
87875^73308-1992651241Enzo Doria03/2013
87883*2^170203+551237Lelio R Paula02/2014
87895^73300+4651235Lelio R Paula10/2012
87902^170167+7151226Lelio R Paula01/2011
87912^170140-1507751218Enzo Doria04/2013
879215^43542-4651210Lelio R Paula01/2013
87932^170111-101751209Lelio R Paula06/2008
87944*10^51208-8751209Robert Price03/2017
879514^44679+8351208Lelio R Paula01/2013
879610^51207+10014751208Patrick De Geest06/2016
879710^51207-80151207Robert Price04/2016
8799t(170300)51191Robert Price03/2015
879811966^12553-12553^1196651191Norbert Schneider11/2016
880014670^3083+3083^1467051184Hans Havermann04/2016
880199^25644-9851177Norbert Schneider07/2013
880213211^7468+7468^1321151169Hans Havermann04/2016
8803(2^169969-1017)/3551165Lelio R Paula01/2012
88045*10^51163-751164Dmitry Domanov11/2010
8805(73*10^51162-1)/951163Robert Price01/2015
88062^169899+6351145Lelio R Paula05/2009
88072^169898+51351145Lelio R Paula05/2009
88083^107186-1238851141Enzo Doria02/2013
8809(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
88103*6^65715-751137Lelio R Paula09/2014
8811116^24768+11551133Norbert Schneider10/2013
881235^33113-402651129Enzo Doria03/2013
8813(13*2^169830-1)/8447751121Lelio R Paula01/2014
8814(46*10^51111-1)/951112Serge Batalov10/2014
881515^43452-3451104Lelio R Paula01/2013
88162^169750-13751100Lelio R Paula01/2011
88172^169739+9406551097Lelio R Paula10/2011
881815^43442-2651092Lelio R Paula01/2013
88195^73096-1700651092Enzo Doria02/2013
8820(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
88212^169706-27055151087Gary Barnes08/2009
8822(2^169696+5)/2151083Lelio R Paula01/2012
8823(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
882411^49051-876051082Enzo Doria02/2013
8825(24737*2^169672+1)/2751080Lelio R Paula05/2014
88262^169677+1609551078Lelio R Paula05/2009
88272^169659-13551073Lelio R Paula01/2011
88282^169638-11318351067Enzo Doria07/2014
8829(29*2^169622-1)/234653118551054Lelio R Paula01/2014
8830(10^51054+17)/951054Robert Price10/2014
8831(24737*2^169577+1)/551052Lelio R Paula05/2014
883211^49021-7851051Lelio R Paula01/2013
883318^40669+6151051Lelio R Paula01/2013
883414038^4327+4327^1403851045Hans Havermann02/2016
88352^169555-15951042Lelio R Paula01/2011
883691^26054-251041Lelio R Paula08/2013
8837Phi(101775,10)/162840151034Makoto Kamada05/2015
883897*10^51027-351029Robert Price01/2017
88392^169499-264751025Yves Minet07/2014
88405*6^65567+751022Lelio R Paula09/2014
884114763^2858+2858^1476351022Hans Havermann08/2015
884224^36966-147751021Enzo Doria03/2013
8843(78557*2^169464+1)/16052751014Lelio R Paula06/2014
8844(34*10^51008-43)/951009Ray Chandler09/2010
884510^51004+12842751005Patrick De Geest08/2009
884710^51004-11351004Milton L. Brown12/2008
884610^51003+1695151004Patrick De Geest08/2009
884810^51003-7960151003Milton L. Brown12/2008
884910^51003-8083151003Milton L. Brown12/2008
885010^51002+887751003Patrick De Geest08/2009
885210^51002-1054151002Milton L. Brown11/2008
885110^51001+5205151002Patrick De Geest08/2009
885310^51001-15868751001Milton L. Brown10/2008
88542*10^51000+9351001Robert Price07/2016
8857(2^169416+5)/350999Lelio R Paula01/2012
8855(49*10^50998+41)/950999Robert Price07/2015
885613292^6867+6867^1329250999Hans Havermann02/2016
8858(35*10^50997-71)/950998Robert Price05/2015
885929^34871-28^3487150996Robert Price09/2012
886076^27112-7550993Norbert Schneider11/2012
8861(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
886210736^12645-12645^1073650971Norbert Schneider12/2016
8864(1017*2^169315-1)/971550968Lelio R Paula03/2015
88637^60309-6^(60309+1)50968Robert Price06/2016
88662^169267+9950955Lelio R Paula07/2009
88655*2^169264+350955Lelio R Paula02/2014
8867t(192517)50950Robert Price08/2014
886810^50943+62445150944Robert Price03/2015
886910^50943+5440950944Patrick De Geest02/2016
887010^50943-10055950943Patrick De Geest03/2016
88712^169206-364550937Lelio R Paula05/2009
88722^169196-11257750934Enzo Doria06/2014
887320^39146-348350931Enzo Doria03/2013
887410^50929+1684950930Patrick De Geest01/2012
887610^50929-5150929Robert Price05/2011
88757^60264+4850929Lelio R Paula10/2012
88782^169167+129950925Lelio R Paula05/2009
887710103^12717-10050925Enzo Doria07/2012
88793^106721-13050919Lelio R Paula07/2012
888118225^622+622^1822550917Anatoly F. Selevich11/2006
8880(10223*2^169138+1)/111350917Lelio R Paula05/2014
88827*2^169125+950913Lelio R Paula02/2014
8883(47*2^169123+1)/2950912Lelio R Paula03/2015
888420^39131+9350911Lelio R Paula01/2013
8885(21*27^35567-94921)/2650910Curtis Bright05/2015
8886(7*2^169124-1)/954950909Lelio R Paula01/2014
8887(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
888813693^5212+5212^1369350897Hans Havermann02/2016
88897*5^72813+650895Lelio R Paula09/2014
88905*10^50890-8150891Robert Price04/2017
88913^106656-1202850888Enzo Doria02/2013
8892(2^169028+3)/25950881Lelio R Paula01/2012
88932^169000-112750875Yves Minet05/2013
889419^39780+1650869Lelio R Paula01/2013
8895(19*2^168960+1)/550863Lelio R Paula07/2012
8896(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
889811^48840+4650862Lelio R Paula01/2013
8897(5*10^50861-107)/350862Robert Price01/2017
889920^39087-420350854Enzo Doria03/2013
8900(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
89012^168907-54444750847Paul Bourdelais11/2012
890219312^429+429^1931250839Anatoly F. Selevich12/2006
89035^72716-1322650827Enzo Doria02/2013
89042^168823+102550821Lelio R Paula01/2009
89057*10^50818-8950819Robert Price01/2017
89062^168811+15015*16881150818Henri Lifchitz02/2005
89072^168813-283350818Yves Minet09/2014
8908(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
89092^168795+538550813Lelio R Paula05/2009
89104*3^106483+550806Lelio R Paula03/2014
891113^45606+450803Lelio R Paula01/2013
891213^45606-3850803Lelio R Paula01/2013
89132^168746+5890550798Lelio R Paula05/2009
8914(16*10^50795-43)/950796Robert Price02/2015
8915gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
89167*10^50789-4750790Robert Price02/2017
89172^168717-72952350789Paul Bourdelais11/2012
8918(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
8919(21*2^168652-1)/21550769Lelio R Paula01/2014
89202^168629+1290950763Lelio R Paula01/2011
89219328^12787+12787^932850762Norbert Schneider01/2016
89222^168627+7311350762Enzo Doria04/2016
89232^168623+4733350761Yves Minet02/2010
8924(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
8925(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
8926(17^41221+1)/1850720Paul Bourdelais03/2010
892710^50711+750712Jason Earls12/2007
892810^50711-31796950711Patrick De Geest04/2009
8930(17^41213+3^41213)/2050710Robert Price08/2013
8929(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
89312^168431-15950703Lelio R Paula01/2011
8932(7*10^50702-1)/350703Erik Branger03/2014
8933117216#-p(117216)50700Henri Lifchitz03/2007
8934(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
8935(13*2^168352-1)/47750678Lelio R Paula01/2014
89368*10^50675+3950676Robert Price01/2017
8937(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
893814415^3274+3274^1441550670Hans Havermann05/2016
8939(12379^12379+282)/1750663Makoto Morimoto07/2016
89415^72480-1712650662Enzo Doria02/2013
8940(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
89423^106143+250644Mike Oakes11/2009
89439178^12777-12777^917850633Norbert Schneider02/2017
8944(2*10^50603-41)/350603Robert Price01/2017
8945(12^46889-1)/1150601Paul Bourdelais09/2008
89462^168068-189350594Yves Minet09/2012
89472^168057+841550591Lelio R Paula11/2011
89484*10^50579+950580Robert Price05/2015
89492^168019-9439550579Lelio R Paula07/2011
89502^168019+7421350579Enzo Doria04/2016
89513^106002+7050576Lelio R Paula07/2012
89525*2^167970-950565Lelio R Paula02/2014
8953(58*10^50558-13)/950559Robert Price09/2015
895488*10^50547+750549Robert Price11/2016
89552^167910-11262550546Enzo Doria06/2014
8956(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
89572^167866+1171550533Lelio R Paula05/2009
8958gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
89592^167847-13550527Lelio R Paula01/2011
8960-lucasV(-1,2,335684)50526Mike Oakes01/2017
8961(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
8962(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
89642^167807+7550515Lelio R Paula08/2010
89632^167805+7627750515Enzo Doria04/2016
89658335^12882+12882^833550510Norbert Schneider03/2016
89667*2^167777+950507Lelio R Paula02/2014
896714162^3681+3681^1416250502Hans Havermann05/2016
8968(17*10^50495-11)/350496Robert Price07/2015
89692^167682+8550478Lelio R Paula08/2010
89702^167667-92742750473Paul Bourdelais11/2012
89719737^12654+12654^973750470Norbert Schneider01/2016
8972(9179*2^167644-1)/1750469Lelio R Paula03/2015
897313386^5891+5891^1338650468Hans Havermann05/2016
8974(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
89755003^13637-15650447Enzo Doria07/2012
89766^64826-2672350445Enzo Doria03/2013
8977(3^105718+7)/3250439Lelio R Paula03/2012
8978(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
897917^40989+5650435Lelio R Paula01/2013
8980(12329^12329+1652)/42150435Makoto Morimoto07/2016
89812*5^72153+750434Lelio R Paula09/2014
8982(3126^14431-1)/312550433Richard Fischer03/2015
898339^31694+3850428Norbert Schneider05/2014
89842^167460+218750411Lelio R Paula11/2011
8985(12323^12323+2709)/2^450409Makoto Morimoto07/2016
898611^48400-771050404Enzo Doria02/2013
89872^167432+5461550403Lelio R Paula05/2009
8988(23*2^167430-1)/416950400Lelio R Paula01/2014
898919^39404+2250389Lelio R Paula01/2013
899035^32629-783450382Enzo Doria03/2013
89916^64744+16350381Lelio R Paula06/2012
8992116447#+17465950381Nicolas PALAU09/2016
89942^167353+12950379Lelio R Paula05/2009
899320^38722-113350379Enzo Doria03/2013
89963^105567-1650369Lelio R Paula07/2012
89952^167321-11284950369Enzo Doria06/2014
8997(28*10^50362-43)/350363Robert Price04/2016
899811421^12410-12410^1142150357Norbert Schneider08/2013
89992^167278-206350356Yves Minet03/2013
9000181^22300+22300^18150347Serge Batalov05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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