PRP Records

Probable Primes Top 10000

(173006 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 ?
875110^51872-100000000151872Robert Price05/2016
875210^51872-10014951872Patrick De Geest06/2016
87532147092^8192+6351871Jens K. Andersen04/2009
875413^46564-2451870Lelio R Paula01/2013
875513981^5110+5110^1398151848Hans Havermann05/2016
87562^172228+7626151846Enzo Doria04/2016
875711^49772-126051833Enzo Doria11/2012
8758(11*2^172157-1)/35151823Lelio R Paula01/2014
8759(43*10^51816-403)/951817Robert Price04/2017
87609001^13102-11451810Enzo Doria07/2012
8761(80051^10567+1)/8005251809Faysal YAtim07/2007
87632^172101-6151808Lelio R Paula01/2011
8762(2^172125+3)/3112550551808Lelio R Paula02/2012
87649*7^61301+451807Lelio R Paula09/2014
8765(23*2^172090-1)/3650951802Lelio R Paula01/2014
87662^172074+145951800Lelio R Paula07/2008
87672^172063+16551797Lelio R Paula02/2011
8768(21181*2^172061+1)/1814751796Lelio R Paula05/2014
876928^35785-2751787Norbert Schneider01/2014
8770(65*10^51778+43)/951779Ray Chandler09/2010
8771(15185*2^171975-1)/351774Lelio R Paula03/2015
87722^171978-11329751771Enzo Doria07/2014
877311^49708+7851766Lelio R Paula01/2013
8774(26*10^51764-107)/951765Robert Price07/2016
877512^47956-9751754Lelio R Paula12/2012
87762^171907-351151750Yves Minet03/2017
8777(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
8778(3*2^171761+1)/2951705Lelio R Paula07/2012
8779t(195346)51699Robert Price07/2014
878013^46409+4651697Lelio R Paula01/2013
87812^171663+1155*17166351676Henri Lifchitz01/2005
878215^43937+2651674Lelio R Paula01/2013
8783(3^108312-7)/12452651673Lelio R Paula03/2012
8784(12601^12601+465)/2/13151667Makoto Morimoto07/2016
8785(79*10^51663-97)/9951663Ray Chandler11/2010
8787(10^51652-31)/351652Serge Batalov12/2014
87862^171583+7379351652Enzo Doria04/2016
878812^47861-3551651Lelio R Paula12/2012
87896^66369-2681351646Enzo Doria03/2013
8790Phi(83967,10)/227248288951639Maksym Voznyy01/2010
87912^171524+15351634Lelio R Paula02/2011
8792(2^171516-509203)/486951628Lelio R Paula05/2012
8793(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
87945*10^51608-8151609Robert Price04/2017
8795(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
879610171^12872-12872^1017151583Norbert Schneider04/2017
87972^171351-11267751582Enzo Doria06/2014
8798(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
8799(3^108091+7)/38251570Lelio R Paula03/2012
88012^171287-318751563Yves Minet04/2009
8800-lucasV(-1,2,342569)51563Mike Oakes02/2017
88022^171280-103070951561Paul Bourdelais11/2012
880313300^7527+7527^1330051560Hans Havermann05/2016
88042^171268+7371151557Enzo Doria04/2016
8805(17*2^171266+1)/696351554Lelio R Paula01/2012
8806(1964814^8192+1)/6553751551Lelio R Paula06/2013
88074*10^51530-6351531Robert Price12/2016
88083*6^66216-551527Lelio R Paula09/2014
880912569^12569+54051525Makoto Morimoto07/2016
88102^171152-245951522Yves Minet07/2014
8811(13*10^51511-1)/351512Robert Price12/2014
88125*10^51508+351509Dmitry Domanov11/2010
88133^107919-4651491Lelio R Paula07/2012
88144*10^51489+8751490Robert Price05/2016
8815(22699*2^171030+1)/302951487Lelio R Paula05/2014
88162^171028-323951485Yves Minet12/2014
88172^170992-95420951474Paul Bourdelais11/2012
881876^27367+7551473Norbert Schneider11/2012
88196007^13620-10251466Enzo Doria07/2012
8820gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
8821t(194442)51459Robert Price08/2014
8822(22*10^51457+161)/351458Robert Price02/2017
88239^53921+8^(53921+1)51454Robert Price06/2016
88252^170921-1699551453Lelio R Paula08/2011
88242^170922-213551453Yves Minet06/2013
88264357^14138-12051451Enzo Doria06/2012
8827153^23550+251450Lelio R Paula05/2013
8828(3^107833+2)/2551449Lelio R Paula03/2012
88297*10^51440-4751441Robert Price02/2017
8830(10^51431-3^51431)/751431Robert Price06/2011
8832U(250849)51425Michael Porter08/2007
8831(86*10^51424-41)/951425Robert Price11/2015
883312^47649+751422Lelio R Paula12/2012
8834(25*10^51421+11)/951422Robert Price03/2015
88353^107768+266051419Lelio R Paula07/2012
88372^170784-655551412Lelio R Paula05/2009
8836(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
883851^30106+251409Lelio R Paula05/2013
88395^73546-1280651407Enzo Doria02/2013
8840(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
8841(3^107735-4)/43151401Lelio R Paula03/2012
884220^39505-648351398Enzo Doria03/2013
88432^170736-1519751397Enzo Doria04/2013
88442^170737-382351397Yves Minet04/2017
8845(12541^12541+393)/2/56351395Makoto Morimoto07/2016
88469^53857-8^5385751393Jean-Louis Charton11/2004
88475^73524-1442651392Enzo Doria02/2013
88482^170712+24351390Lelio R Paula10/2011
8849(15*2^170713+1)/179351388Lelio R Paula07/2012
8850(2^170702+9)/126151384Lelio R Paula01/2012
8851283^20956+20956^28351380Norbert Schneider08/2014
88522^170665-3151376Lelio R Paula01/2011
885311^49330-1251372Lelio R Paula01/2013
8854(25*10^51366-73)/351367Robert Price09/2016
88555^73486-2^7348751365Mike Oakes10/2010
8856(10^51364+119)/351364Serge Batalov12/2014
885715^43672+6851363Lelio R Paula01/2013
88582^170609-11314351359Enzo Doria07/2014
8859760^17827-759^1782751357Jean-Louis Charton12/2010
8860(22699*2^170592+1)/443551355Lelio R Paula05/2014
88618*7^60767+351355Lelio R Paula09/2014
88625^73452-2064651341Enzo Doria03/2013
88632^170531-23040751335Gary Barnes08/2009
886435^33243-211251330Enzo Doria03/2013
8865(1845768^8192+1)/6553751328Lelio R Paula06/2013
886613^46072+4251322Lelio R Paula01/2013
886714^44778-9551322Lelio R Paula01/2013
886811008^12697+12697^1100851318Norbert Schneider01/2016
8869t(180039)51312Robert Price09/2014
88702^170444-44351309Yves Minet05/2013
8871(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
8872(2*10^51285-71)/351285Robert Price01/2017
8873(1819288^8192+1)/6553751277Lelio R Paula06/2013
88745^73350+2851270Lelio R Paula10/2012
88753^107450+251267Mike Oakes11/2009
88762^170296+253351265Henri Lifchitz07/2004
88772^170293+7648151264Enzo Doria05/2016
887811835^12584+12584^1183551257Norbert Schneider11/2015
8879(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
888112^47489+47489^1251250Serge Batalov02/2012
888014637^3172+3172^1463751250Hans Havermann04/2016
8882(2^170245+7)/951248Lelio R Paula02/2012
88835^73308-1992651241Enzo Doria03/2013
88843*2^170203+551237Lelio R Paula02/2014
88855^73300+4651235Lelio R Paula10/2012
88862^170167+7151226Lelio R Paula01/2011
88872^170140-1507751218Enzo Doria04/2013
888815^43542-4651210Lelio R Paula01/2013
88902^170111-101751209Lelio R Paula06/2008
88894*10^51208-8751209Robert Price03/2017
889114^44679+8351208Lelio R Paula01/2013
889210^51207+10014751208Patrick De Geest06/2016
889310^51207-80151207Robert Price04/2016
8894t(170300)51191Robert Price03/2015
889511966^12553-12553^1196651191Norbert Schneider11/2016
889614670^3083+3083^1467051184Hans Havermann04/2016
889799^25644-9851177Norbert Schneider07/2013
889813211^7468+7468^1321151169Hans Havermann04/2016
8899(2^169969-1017)/3551165Lelio R Paula01/2012
89005*10^51163-751164Dmitry Domanov11/2010
8901(73*10^51162-1)/951163Robert Price01/2015
89022^169899+6351145Lelio R Paula05/2009
89032^169898+51351145Lelio R Paula05/2009
89043^107186-1238851141Enzo Doria02/2013
8905(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
89063*6^65715-751137Lelio R Paula09/2014
8907116^24768+11551133Norbert Schneider10/2013
890835^33113-402651129Enzo Doria03/2013
8909(13*2^169830-1)/8447751121Lelio R Paula01/2014
8910(46*10^51111-1)/951112Serge Batalov10/2014
891115^43452-3451104Lelio R Paula01/2013
89122^169750-13751100Lelio R Paula01/2011
89132^169739+9406551097Lelio R Paula10/2011
891415^43442-2651092Lelio R Paula01/2013
89155^73096-1700651092Enzo Doria02/2013
8916(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
89172^169706-27055151087Gary Barnes08/2009
8918(2^169696+5)/2151083Lelio R Paula01/2012
8920(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
891911^49051-876051082Enzo Doria02/2013
8921(24737*2^169672+1)/2751080Lelio R Paula05/2014
89222^169677+1609551078Lelio R Paula05/2009
89232^169659-13551073Lelio R Paula01/2011
89242^169638-11318351067Enzo Doria07/2014
8925(29*2^169622-1)/234653118551054Lelio R Paula01/2014
8926(10^51054+17)/951054Robert Price10/2014
8927(24737*2^169577+1)/551052Lelio R Paula05/2014
892811^49021-7851051Lelio R Paula01/2013
892918^40669+6151051Lelio R Paula01/2013
893014038^4327+4327^1403851045Hans Havermann02/2016
89312^169555-15951042Lelio R Paula01/2011
893291^26054-251041Lelio R Paula08/2013
8933Phi(101775,10)/162840151034Makoto Kamada05/2015
893497*10^51027-351029Robert Price01/2017
89352^169499-264751025Yves Minet07/2014
89365*6^65567+751022Lelio R Paula09/2014
893714763^2858+2858^1476351022Hans Havermann08/2015
893824^36966-147751021Enzo Doria03/2013
8939(78557*2^169464+1)/16052751014Lelio R Paula06/2014
8940(34*10^51008-43)/951009Ray Chandler09/2010
894110^51004+12842751005Patrick De Geest08/2009
894310^51004-11351004Milton L. Brown12/2008
894210^51003+1695151004Patrick De Geest08/2009
894410^51003-7960151003Milton L. Brown12/2008
894510^51003-8083151003Milton L. Brown12/2008
894610^51002+887751003Patrick De Geest08/2009
894810^51002-1054151002Milton L. Brown11/2008
894710^51001+5205151002Patrick De Geest08/2009
894910^51001-15868751001Milton L. Brown10/2008
89502*10^51000+9351001Robert Price07/2016
8952(2^169416+5)/350999Lelio R Paula01/2012
8951(49*10^50998+41)/950999Robert Price07/2015
895313292^6867+6867^1329250999Hans Havermann02/2016
8954(35*10^50997-71)/950998Robert Price05/2015
89556^65536+2*97878-150997Jiahao He05/2017
895629^34871-28^3487150996Robert Price09/2012
895776^27112-7550993Norbert Schneider11/2012
8958(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
895910736^12645-12645^1073650971Norbert Schneider12/2016
8960(1017*2^169315-1)/971550968Lelio R Paula03/2015
89617^60309-6^(60309+1)50968Robert Price06/2016
89622^169267+9950955Lelio R Paula07/2009
89635*2^169264+350955Lelio R Paula02/2014
8964t(192517)50950Robert Price08/2014
896510^50943+62445150944Robert Price03/2015
896610^50943+5440950944Patrick De Geest02/2016
896710^50943-10055950943Patrick De Geest03/2016
89682^169206-364550937Lelio R Paula05/2009
89692^169196-11257750934Enzo Doria06/2014
897020^39146-348350931Enzo Doria03/2013
897110^50929+1684950930Patrick De Geest01/2012
897310^50929-5150929Robert Price05/2011
89727^60264+4850929Lelio R Paula10/2012
89752^169167+129950925Lelio R Paula05/2009
897410103^12717-10050925Enzo Doria07/2012
89763^106721-13050919Lelio R Paula07/2012
897818225^622+622^1822550917Anatoly F. Selevich11/2006
8977(10223*2^169138+1)/111350917Lelio R Paula05/2014
89797*2^169125+950913Lelio R Paula02/2014
8980(47*2^169123+1)/2950912Lelio R Paula03/2015
898120^39131+9350911Lelio R Paula01/2013
8982(21*27^35567-94921)/2650910Curtis Bright05/2015
8983(7*2^169124-1)/954950909Lelio R Paula01/2014
8984(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
898513693^5212+5212^1369350897Hans Havermann02/2016
89867*5^72813+650895Lelio R Paula09/2014
89875*10^50890-8150891Robert Price04/2017
89883^106656-1202850888Enzo Doria02/2013
8989(2^169028+3)/25950881Lelio R Paula01/2012
89902^169000-112750875Yves Minet05/2013
899119^39780+1650869Lelio R Paula01/2013
8992(19*2^168960+1)/550863Lelio R Paula07/2012
8993(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
899511^48840+4650862Lelio R Paula01/2013
8994(5*10^50861-107)/350862Robert Price01/2017
899620^39087-420350854Enzo Doria03/2013
8997(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
89982^168907-54444750847Paul Bourdelais11/2012
899919312^429+429^1931250839Anatoly F. Selevich12/2006
90005^72716-1322650827Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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