PRP Records

Probable Primes Top 10000

(218736 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
97519818^12919-12919^981851573Norbert Schneider05/2017
9752(3^108091+7)/38251570Lelio R Paula03/2012
97542^171287-318751563Yves Minet04/2009
9753-lucasV(-1,2,342569)51563Mike Oakes02/2017
97552^171280-103070951561Paul Bourdelais11/2012
975613300^7527+7527^1330051560Hans Havermann05/2016
97572^171268+7371151557Enzo Doria04/2016
9758(17*2^171266+1)/696351554Lelio R Paula01/2012
9759(1964814^8192+1)/6553751551Lelio R Paula06/2013
9760(26*10^51537-503)/951538Robert Price12/2017
97614*10^51530-6351531Robert Price12/2016
97623*6^66216-551527Lelio R Paula09/2014
976312569^12569+54051525Makoto Morimoto07/2016
97642^171152-245951522Yves Minet07/2014
9765(13*10^51511-1)/351512Robert Price12/2014
97665*10^51508+351509Dmitry Domanov11/2010
97673^107919-4651491Lelio R Paula07/2012
97684*10^51489+8751490Robert Price05/2016
9769(22699*2^171030+1)/302951487Lelio R Paula05/2014
97702^171028-323951485Yves Minet12/2014
97712^170992-95420951474Paul Bourdelais11/2012
977276^27367+7551473Norbert Schneider11/2012
97736007^13620-10251466Enzo Doria07/2012
9774gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9775t(194442)51459Robert Price08/2014
97766470^13503-13503^647051459Norbert Schneider05/2018
9777(22*10^51457+161)/351458Robert Price02/2017
97789^53921+8^(53921+1)51454Robert Price06/2016
97802^170921-1699551453Lelio R Paula08/2011
97792^170922-213551453Yves Minet06/2013
97814357^14138-12051451Enzo Doria06/2012
9782153^23550+251450Lelio R Paula05/2013
9783(3^107833+2)/2551449Lelio R Paula03/2012
9784(159^23369+1)/16051443Eric Chen12/2017
97857*10^51440-4751441Robert Price02/2017
9786(10^51431-3^51431)/751431Robert Price06/2011
9788U(250849)51425Michael Porter08/2007
9787(86*10^51424-41)/951425Robert Price11/2015
979012^47649+751422Lelio R Paula12/2012
9789(25*10^51421+11)/951422Robert Price03/2015
97913^107768+266051419Lelio R Paula07/2012
97932^170784-655551412Lelio R Paula05/2009
9792(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
979551^30106+251409Lelio R Paula05/2013
97942^170777-415951409Yves Minet02/2018
97965^73546-1280651407Enzo Doria02/2013
9797(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9798(3^107735-4)/43151401Lelio R Paula03/2012
979920^39505-648351398Enzo Doria03/2013
98002^170736-1519751397Enzo Doria04/2013
98012^170737-382351397Yves Minet04/2017
9802(12541^12541+393)/2/56351395Makoto Morimoto07/2016
98039^53857-8^5385751393Jean-Louis Charton11/2004
98045^73524-1442651392Enzo Doria02/2013
98052^170712+24351390Lelio R Paula10/2011
9806(15*2^170713+1)/179351388Lelio R Paula07/2012
9807(2^170702+9)/126151384Lelio R Paula01/2012
9808283^20956+20956^28351380Norbert Schneider08/2014
98092^170665-3151376Lelio R Paula01/2011
981011^49330-1251372Lelio R Paula01/2013
9811(25*10^51366-73)/351367Robert Price09/2016
98125^73486-2^7348751365Mike Oakes10/2010
9813(10^51364+119)/351364Serge Batalov12/2014
981415^43672+6851363Lelio R Paula01/2013
98152^170609-11314351359Enzo Doria07/2014
9816760^17827-759^1782751357Jean-Louis Charton12/2010
9817(22699*2^170592+1)/443551355Lelio R Paula05/2014
98188*7^60767+351355Lelio R Paula09/2014
98197009^13352-13352^700951348Norbert Schneider03/2018
98205^73452-2064651341Enzo Doria03/2013
98212^170531-23040751335Gary Barnes08/2009
982235^33243-211251330Enzo Doria03/2013
9823(1845768^8192+1)/6553751328Lelio R Paula06/2013
982413^46072+4251322Lelio R Paula01/2013
982514^44778-9551322Lelio R Paula01/2013
982611008^12697+12697^1100851318Norbert Schneider01/2016
9827(11^49279+7^49279)/1851318Eric Chen05/2018
9828t(180039)51312Robert Price09/2014
98292^170444-44351309Yves Minet05/2013
9830(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9831(2*10^51285-71)/351285Robert Price01/2017
9832(23*10^51283-47)/351284Robert Price10/2017
9833(1819288^8192+1)/6553751277Lelio R Paula06/2013
98348907^12982-12982^890751276Norbert Schneider06/2017
98355^73350+2851270Lelio R Paula10/2012
98363^107450+251267Mike Oakes11/2009
98372^170296+253351265Henri Lifchitz07/2004
98382^170293+7648151264Enzo Doria05/2016
983911835^12584+12584^1183551257Norbert Schneider11/2015
9840(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
984212^47489+47489^1251250Serge Batalov02/2012
984114637^3172+3172^1463751250Hans Havermann04/2016
9843(2^170245+7)/951248Lelio R Paula02/2012
98445^73308-1992651241Enzo Doria03/2013
98458966^12963-12963^896651238Norbert Schneider06/2017
98463*2^170203+551237Lelio R Paula02/2014
98475^73300+4651235Lelio R Paula10/2012
98482^170167+7151226Lelio R Paula01/2011
98492^170140-1507751218Enzo Doria04/2013
985015^43542-4651210Lelio R Paula01/2013
98522^170111-101751209Lelio R Paula06/2008
98514*10^51208-8751209Robert Price03/2017
985314^44679+8351208Lelio R Paula01/2013
985410^51207+10014751208Patrick De Geest06/2016
985510^51207-80151207Robert Price04/2016
9857t(170300)51191Robert Price03/2015
985611966^12553-12553^1196651191Norbert Schneider11/2016
985814670^3083+3083^1467051184Hans Havermann04/2016
985999^25644-9851177Norbert Schneider07/2013
986013211^7468+7468^1321151169Hans Havermann04/2016
9861(2^169969-1017)/3551165Lelio R Paula01/2012
98625*10^51163-751164Dmitry Domanov11/2010
9863(73*10^51162-1)/951163Robert Price01/2015
9864L(244779)+P(244779)51156Robert Price12/2017
9865(22*10^51154+383)/951155Robert Price11/2017
98662^169899+6351145Lelio R Paula05/2009
98672^169898+51351145Lelio R Paula05/2009
98693^107186-1238851141Enzo Doria02/2013
9868(299*10^51139+1)/351141Robert Price11/2017
9870(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
98713*6^65715-751137Lelio R Paula09/2014
9872116^24768+11551133Norbert Schneider10/2013
987335^33113-402651129Enzo Doria03/2013
9874(13*2^169830-1)/8447751121Lelio R Paula01/2014
9875(46*10^51111-1)/951112Serge Batalov10/2014
987615^43452-3451104Lelio R Paula01/2013
98772^169750-13751100Lelio R Paula01/2011
98782^169739+9406551097Lelio R Paula10/2011
987915^43442-2651092Lelio R Paula01/2013
98805^73096-1700651092Enzo Doria02/2013
988110^51091+7160151092Patrick De Geest07/2017
988210^51091-70151091Robert Price06/2017
9883(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
98842^169706-27055151087Gary Barnes08/2009
9885(2^169696+5)/2151083Lelio R Paula01/2012
9886(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
988711^49051-876051082Enzo Doria02/2013
9888(24737*2^169672+1)/2751080Lelio R Paula05/2014
9889(14*10^51079+229)/951080Robert Price11/2017
98902^169677+1609551078Lelio R Paula05/2009
98912^169659-13551073Lelio R Paula01/2011
98922^169638-11318351067Enzo Doria07/2014
9893(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9894(10^51054+17)/951054Robert Price10/2014
98958329^13022-13022^832951054Norbert Schneider07/2017
9896(24737*2^169577+1)/551052Lelio R Paula05/2014
989711^49021-7851051Lelio R Paula01/2013
989818^40669+6151051Lelio R Paula01/2013
989914038^4327+4327^1403851045Hans Havermann02/2016
99002^169555-15951042Lelio R Paula01/2011
990191^26054-251041Lelio R Paula08/2013
9902Phi(101775,10)/162840151034Makoto Kamada05/2015
99037559^13158-13158^755951033Norbert Schneider11/2017
990497*10^51027-351029Robert Price01/2017
99052^169499-264751025Yves Minet07/2014
99065*6^65567+751022Lelio R Paula09/2014
990714763^2858+2858^1476351022Hans Havermann08/2015
990824^36966-147751021Enzo Doria03/2013
9909(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9910(34*10^51008-43)/951009Ray Chandler09/2010
991110^51004+12842751005Patrick De Geest08/2009
991310^51004-11351004Milton L. Brown12/2008
991210^51003+1695151004Patrick De Geest08/2009
991410^51003-7960151003Milton L. Brown12/2008
991510^51003-8083151003Milton L. Brown12/2008
991610^51002+887751003Patrick De Geest08/2009
991810^51002-1054151002Milton L. Brown11/2008
991710^51001+5205151002Patrick De Geest08/2009
991910^51001-15868751001Milton L. Brown10/2008
99202*10^51000+9351001Robert Price07/2016
992110^51000+18825151001Patrick De Geest10/2017
992210^51000-3128951000Patrick De Geest10/2017
9924(2^169416+5)/350999Lelio R Paula01/2012
9923(49*10^50998+41)/950999Robert Price07/2015
992513292^6867+6867^1329250999Hans Havermann02/2016
9926(35*10^50997-71)/950998Robert Price05/2015
99276^65536+2*97878-150997Jiahao He05/2017
992829^34871-28^3487150996Robert Price09/2012
992976^27112-7550993Norbert Schneider11/2012
9930(70^27631-1)/6950981Richard Fischer08/2017
9931(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
993210736^12645-12645^1073650971Norbert Schneider12/2016
9933(1017*2^169315-1)/971550968Lelio R Paula03/2015
99347^60309-6^(60309+1)50968Robert Price06/2016
99362^169267+9950955Lelio R Paula07/2009
99355*2^169264+350955Lelio R Paula02/2014
9937t(192517)50950Robert Price08/2014
993810^50943+62445150944Robert Price03/2015
993910^50943+5440950944Patrick De Geest02/2016
994010^50943-10055950943Patrick De Geest03/2016
99412^169206-364550937Lelio R Paula05/2009
99422^169196-11257750934Enzo Doria06/2014
994320^39146-348350931Enzo Doria03/2013
994410^50929+1684950930Patrick De Geest01/2012
994610^50929-5150929Robert Price05/2011
99457^60264+4850929Lelio R Paula10/2012
99482^169167+129950925Lelio R Paula05/2009
994710103^12717-10050925Enzo Doria07/2012
99493^106721-13050919Lelio R Paula07/2012
995218225^622+622^1822550917Anatoly F. Selevich11/2006
9951(10223*2^169138+1)/111350917Lelio R Paula05/2014
99506057^13462-13462^605750917Norbert Schneider04/2018
99537*2^169125+950913Lelio R Paula02/2014
9954(47*2^169123+1)/2950912Lelio R Paula03/2015
995520^39131+9350911Lelio R Paula01/2013
9956(21*27^35567-94921)/2650910Curtis Bright05/2015
9957(7*2^169124-1)/954950909Lelio R Paula01/2014
9958(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
995913693^5212+5212^1369350897Hans Havermann02/2016
99607*5^72813+650895Lelio R Paula09/2014
99615*10^50890-8150891Robert Price04/2017
99623^106656-1202850888Enzo Doria02/2013
9963(2^169028+3)/25950881Lelio R Paula01/2012
99642^169000-112750875Yves Minet05/2013
996519^39780+1650869Lelio R Paula01/2013
9966(19*2^168960+1)/550863Lelio R Paula07/2012
9967(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
996911^48840+4650862Lelio R Paula01/2013
9968(5*10^50861-107)/350862Robert Price01/2017
997020^39087-420350854Enzo Doria03/2013
9971(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
99722^168907-54444750847Paul Bourdelais11/2012
997319312^429+429^1931250839Anatoly F. Selevich12/2006
99745^72716-1322650827Enzo Doria02/2013
99752^168823+102550821Lelio R Paula01/2009
99767*10^50818-8950819Robert Price01/2017
99782^168811+15015*16881150818Henri Lifchitz02/2005
99772^168813-283350818Yves Minet09/2014
9979(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
99807022^13211-13211^702250816Norbert Schneider12/2017
99812^168795+538550813Lelio R Paula05/2009
99827670^13079-13079^767050810Norbert Schneider09/2017
99834*3^106483+550806Lelio R Paula03/2014
998413^45606+450803Lelio R Paula01/2013
998513^45606-3850803Lelio R Paula01/2013
99862^168746+5890550798Lelio R Paula05/2009
9987(16*10^50795-43)/950796Robert Price02/2015
9988gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
99897*10^50789-4750790Robert Price02/2017
99902^168717-72952350789Paul Bourdelais11/2012
9991(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9992(21*2^168652-1)/21550769Lelio R Paula01/2014
99932^168629+1290950763Lelio R Paula01/2011
99949328^12787+12787^932850762Norbert Schneider01/2016
99952^168627+7311350762Enzo Doria04/2016
99962^168623+4733350761Yves Minet02/2010
9997(8*10^50750-101)/350751Robert Price10/2017
9998(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9999(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
100003*10^50727-3150728Robert Price10/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!