PRP Records

Probable Primes Top 10000

(205869 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 ?
9501(11*2^172157-1)/35151823Lelio R Paula01/2014
9502(43*10^51816-403)/951817Robert Price04/2017
95039001^13102-11451810Enzo Doria07/2012
9504(80051^10567+1)/8005251809Faysal YAtim07/2007
95062^172101-6151808Lelio R Paula01/2011
9505(2^172125+3)/3112550551808Lelio R Paula02/2012
95079*7^61301+451807Lelio R Paula09/2014
9508(23*2^172090-1)/3650951802Lelio R Paula01/2014
95092^172074+145951800Lelio R Paula07/2008
95102^172063+16551797Lelio R Paula02/2011
9511(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9512(56*10^51793+367)/951794Robert Price10/2017
951328^35785-2751787Norbert Schneider01/2014
9514(65*10^51778+43)/951779Ray Chandler09/2010
9515(15185*2^171975-1)/351774Lelio R Paula03/2015
95162^171978-11329751771Enzo Doria07/2014
951711^49708+7851766Lelio R Paula01/2013
9518(26*10^51764-107)/951765Robert Price07/2016
951912^47956-9751754Lelio R Paula12/2012
95202^171907-351151750Yves Minet03/2017
95218203^13220-13220^820351743Norbert Schneider12/2017
95227706^13307-13307^770651723Norbert Schneider02/2018
95238*10^51721+8751722Robert Price10/2017
952410306^12885-12885^1030651709Norbert Schneider05/2017
9525(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9526(3*2^171761+1)/2951705Lelio R Paula07/2012
9527t(195346)51699Robert Price07/2014
952813^46409+4651697Lelio R Paula01/2013
95292^171663+1155*17166351676Henri Lifchitz01/2005
953015^43937+2651674Lelio R Paula01/2013
9531(3^108312-7)/12452651673Lelio R Paula03/2012
9532(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9533(79*10^51663-97)/9951663Ray Chandler11/2010
953448589!4+102451656Robert Price08/2017
9536(10^51652-31)/351652Serge Batalov12/2014
95372^171583+7379351652Enzo Doria04/2016
9535(28*10^51651-31)/351652Robert Price10/2017
953812^47861-3551651Lelio R Paula12/2012
95396^66369-2681351646Enzo Doria03/2013
9540Phi(83967,10)/227248288951639Maksym Voznyy01/2010
95412^171524+15351634Lelio R Paula02/2011
9542(2^171516-509203)/486951628Lelio R Paula05/2012
9543(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
95445*10^51608-8151609Robert Price04/2017
9545(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9546(2*10^51597-23)/351597Robert Price09/2017
954710171^12872-12872^1017151583Norbert Schneider04/2017
95482^171351-11267751582Enzo Doria06/2014
9549(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
95509818^12919-12919^981851573Norbert Schneider05/2017
9551(3^108091+7)/38251570Lelio R Paula03/2012
95532^171287-318751563Yves Minet04/2009
9552-lucasV(-1,2,342569)51563Mike Oakes02/2017
95542^171280-103070951561Paul Bourdelais11/2012
955513300^7527+7527^1330051560Hans Havermann05/2016
95562^171268+7371151557Enzo Doria04/2016
9557(17*2^171266+1)/696351554Lelio R Paula01/2012
9558(1964814^8192+1)/6553751551Lelio R Paula06/2013
9559(26*10^51537-503)/951538Robert Price12/2017
95604*10^51530-6351531Robert Price12/2016
95613*6^66216-551527Lelio R Paula09/2014
956212569^12569+54051525Makoto Morimoto07/2016
95632^171152-245951522Yves Minet07/2014
9564(13*10^51511-1)/351512Robert Price12/2014
95655*10^51508+351509Dmitry Domanov11/2010
95663^107919-4651491Lelio R Paula07/2012
95674*10^51489+8751490Robert Price05/2016
9568(22699*2^171030+1)/302951487Lelio R Paula05/2014
95692^171028-323951485Yves Minet12/2014
95702^170992-95420951474Paul Bourdelais11/2012
957176^27367+7551473Norbert Schneider11/2012
95726007^13620-10251466Enzo Doria07/2012
9573gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9574t(194442)51459Robert Price08/2014
9575(22*10^51457+161)/351458Robert Price02/2017
95769^53921+8^(53921+1)51454Robert Price06/2016
95782^170921-1699551453Lelio R Paula08/2011
95772^170922-213551453Yves Minet06/2013
95794357^14138-12051451Enzo Doria06/2012
9580153^23550+251450Lelio R Paula05/2013
9581(3^107833+2)/2551449Lelio R Paula03/2012
9582(159^23369+1)/16051443Eric Chen12/2017
95837*10^51440-4751441Robert Price02/2017
9584(10^51431-3^51431)/751431Robert Price06/2011
9586U(250849)51425Michael Porter08/2007
9585(86*10^51424-41)/951425Robert Price11/2015
958812^47649+751422Lelio R Paula12/2012
9587(25*10^51421+11)/951422Robert Price03/2015
95893^107768+266051419Lelio R Paula07/2012
95912^170784-655551412Lelio R Paula05/2009
9590(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
959351^30106+251409Lelio R Paula05/2013
95922^170777-415951409Yves Minet02/2018
95945^73546-1280651407Enzo Doria02/2013
9595(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9596(3^107735-4)/43151401Lelio R Paula03/2012
959720^39505-648351398Enzo Doria03/2013
95982^170736-1519751397Enzo Doria04/2013
95992^170737-382351397Yves Minet04/2017
9600(12541^12541+393)/2/56351395Makoto Morimoto07/2016
96019^53857-8^5385751393Jean-Louis Charton11/2004
96025^73524-1442651392Enzo Doria02/2013
96032^170712+24351390Lelio R Paula10/2011
9604(15*2^170713+1)/179351388Lelio R Paula07/2012
9605(2^170702+9)/126151384Lelio R Paula01/2012
9606283^20956+20956^28351380Norbert Schneider08/2014
96072^170665-3151376Lelio R Paula01/2011
960811^49330-1251372Lelio R Paula01/2013
9609(25*10^51366-73)/351367Robert Price09/2016
96105^73486-2^7348751365Mike Oakes10/2010
9611(10^51364+119)/351364Serge Batalov12/2014
961215^43672+6851363Lelio R Paula01/2013
96132^170609-11314351359Enzo Doria07/2014
9614760^17827-759^1782751357Jean-Louis Charton12/2010
9615(22699*2^170592+1)/443551355Lelio R Paula05/2014
96168*7^60767+351355Lelio R Paula09/2014
96177009^13352-13352^700951348Norbert Schneider03/2018
96185^73452-2064651341Enzo Doria03/2013
96192^170531-23040751335Gary Barnes08/2009
962035^33243-211251330Enzo Doria03/2013
9621(1845768^8192+1)/6553751328Lelio R Paula06/2013
962213^46072+4251322Lelio R Paula01/2013
962314^44778-9551322Lelio R Paula01/2013
962411008^12697+12697^1100851318Norbert Schneider01/2016
9625t(180039)51312Robert Price09/2014
96262^170444-44351309Yves Minet05/2013
9627(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9628(2*10^51285-71)/351285Robert Price01/2017
9629(23*10^51283-47)/351284Robert Price10/2017
9630(1819288^8192+1)/6553751277Lelio R Paula06/2013
96318907^12982-12982^890751276Norbert Schneider06/2017
96325^73350+2851270Lelio R Paula10/2012
96333^107450+251267Mike Oakes11/2009
96342^170296+253351265Henri Lifchitz07/2004
96352^170293+7648151264Enzo Doria05/2016
963611835^12584+12584^1183551257Norbert Schneider11/2015
9637(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
963912^47489+47489^1251250Serge Batalov02/2012
963814637^3172+3172^1463751250Hans Havermann04/2016
9640(2^170245+7)/951248Lelio R Paula02/2012
96415^73308-1992651241Enzo Doria03/2013
96428966^12963-12963^896651238Norbert Schneider06/2017
96433*2^170203+551237Lelio R Paula02/2014
96445^73300+4651235Lelio R Paula10/2012
96452^170167+7151226Lelio R Paula01/2011
96462^170140-1507751218Enzo Doria04/2013
964715^43542-4651210Lelio R Paula01/2013
96492^170111-101751209Lelio R Paula06/2008
96484*10^51208-8751209Robert Price03/2017
965014^44679+8351208Lelio R Paula01/2013
965110^51207+10014751208Patrick De Geest06/2016
965210^51207-80151207Robert Price04/2016
9654t(170300)51191Robert Price03/2015
965311966^12553-12553^1196651191Norbert Schneider11/2016
965514670^3083+3083^1467051184Hans Havermann04/2016
965699^25644-9851177Norbert Schneider07/2013
965713211^7468+7468^1321151169Hans Havermann04/2016
9658(2^169969-1017)/3551165Lelio R Paula01/2012
96595*10^51163-751164Dmitry Domanov11/2010
9660(73*10^51162-1)/951163Robert Price01/2015
9661L(244779)+P(244779)51156Robert Price12/2017
9662(22*10^51154+383)/951155Robert Price11/2017
96632^169899+6351145Lelio R Paula05/2009
96642^169898+51351145Lelio R Paula05/2009
96663^107186-1238851141Enzo Doria02/2013
9665(299*10^51139+1)/351141Robert Price11/2017
9667(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
96683*6^65715-751137Lelio R Paula09/2014
9669116^24768+11551133Norbert Schneider10/2013
967035^33113-402651129Enzo Doria03/2013
9671(13*2^169830-1)/8447751121Lelio R Paula01/2014
9672(46*10^51111-1)/951112Serge Batalov10/2014
967315^43452-3451104Lelio R Paula01/2013
96742^169750-13751100Lelio R Paula01/2011
96752^169739+9406551097Lelio R Paula10/2011
967615^43442-2651092Lelio R Paula01/2013
96775^73096-1700651092Enzo Doria02/2013
967810^51091+7160151092Patrick De Geest07/2017
967910^51091-70151091Robert Price06/2017
9680(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
96812^169706-27055151087Gary Barnes08/2009
9682(2^169696+5)/2151083Lelio R Paula01/2012
9684(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
968311^49051-876051082Enzo Doria02/2013
9685(24737*2^169672+1)/2751080Lelio R Paula05/2014
9686(14*10^51079+229)/951080Robert Price11/2017
96872^169677+1609551078Lelio R Paula05/2009
96882^169659-13551073Lelio R Paula01/2011
96892^169638-11318351067Enzo Doria07/2014
9690(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9691(10^51054+17)/951054Robert Price10/2014
96928329^13022-13022^832951054Norbert Schneider07/2017
9693(24737*2^169577+1)/551052Lelio R Paula05/2014
969411^49021-7851051Lelio R Paula01/2013
969518^40669+6151051Lelio R Paula01/2013
969614038^4327+4327^1403851045Hans Havermann02/2016
96972^169555-15951042Lelio R Paula01/2011
969891^26054-251041Lelio R Paula08/2013
9699Phi(101775,10)/162840151034Makoto Kamada05/2015
97007559^13158-13158^755951033Norbert Schneider11/2017
970197*10^51027-351029Robert Price01/2017
97022^169499-264751025Yves Minet07/2014
97035*6^65567+751022Lelio R Paula09/2014
970414763^2858+2858^1476351022Hans Havermann08/2015
970524^36966-147751021Enzo Doria03/2013
9706(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9707(34*10^51008-43)/951009Ray Chandler09/2010
970810^51004+12842751005Patrick De Geest08/2009
971010^51004-11351004Milton L. Brown12/2008
970910^51003+1695151004Patrick De Geest08/2009
971110^51003-7960151003Milton L. Brown12/2008
971210^51003-8083151003Milton L. Brown12/2008
971310^51002+887751003Patrick De Geest08/2009
971510^51002-1054151002Milton L. Brown11/2008
971410^51001+5205151002Patrick De Geest08/2009
971610^51001-15868751001Milton L. Brown10/2008
97182*10^51000+9351001Robert Price07/2016
971710^51000+18825151001Patrick De Geest10/2017
971910^51000-3128951000Patrick De Geest10/2017
9720(2^169416+5)/350999Lelio R Paula01/2012
9722(49*10^50998+41)/950999Robert Price07/2015
972113292^6867+6867^1329250999Hans Havermann02/2016
9723(35*10^50997-71)/950998Robert Price05/2015
97246^65536+2*97878-150997Jiahao He05/2017
972529^34871-28^3487150996Robert Price09/2012
972676^27112-7550993Norbert Schneider11/2012
9727(70^27631-1)/6950981Richard Fischer08/2017
9728(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
972910736^12645-12645^1073650971Norbert Schneider12/2016
9730(1017*2^169315-1)/971550968Lelio R Paula03/2015
97317^60309-6^(60309+1)50968Robert Price06/2016
97322^169267+9950955Lelio R Paula07/2009
97335*2^169264+350955Lelio R Paula02/2014
9734t(192517)50950Robert Price08/2014
973510^50943+62445150944Robert Price03/2015
973610^50943+5440950944Patrick De Geest02/2016
973710^50943-10055950943Patrick De Geest03/2016
97382^169206-364550937Lelio R Paula05/2009
97392^169196-11257750934Enzo Doria06/2014
974020^39146-348350931Enzo Doria03/2013
974110^50929+1684950930Patrick De Geest01/2012
974310^50929-5150929Robert Price05/2011
97427^60264+4850929Lelio R Paula10/2012
97452^169167+129950925Lelio R Paula05/2009
974410103^12717-10050925Enzo Doria07/2012
97463^106721-13050919Lelio R Paula07/2012
974818225^622+622^1822550917Anatoly F. Selevich11/2006
9747(10223*2^169138+1)/111350917Lelio R Paula05/2014
97497*2^169125+950913Lelio R Paula02/2014
9750(47*2^169123+1)/2950912Lelio R Paula03/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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