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 ?
9251(12113^12113+3627)/2^2/5/19/1449629949451Makoto Morimoto07/2016
92525^70746-1601649450Enzo Doria02/2013
9253(2^164258+9)/1349446Lelio R Paula01/2012
92542^164255-11268749446Enzo Doria06/2014
9255(21*2^164222-1)/171749434Lelio R Paula01/2014
92562^164212+1270549433Lelio R Paula11/2011
92573*2^164205+749432Lelio R Paula02/2014
92582^164203+57729457549431Lelio R Paula02/2013
9259(12109^12109+2534)/3^2/23/24763/78102149430Makoto Morimoto07/2016
9260Pell-LucasQ(129127)/249427Eric W. Weisstein05/2006
92612^164187+769549426Lelio R Paula11/2011
92623^103585-2649423Lelio R Paula07/2012
9263(3*2^164194+1)/1425501749421Lelio R Paula07/2012
926410^49415+7683749416Patrick De Geest01/2016
926710^49415-6^49415-4^49415-149415Mike Oakes01/2010
926510^49415-3281349415Patrick De Geest01/2016
926612943^6574+6574^1294349415Hans Havermann02/2016
9268(6^63497-61)/2549409Lelio R Paula05/2014
926911376^12181+12181^1137649407Norbert Schneider12/2013
92702^164110-1749403Lelio R Paula08/2010
927112^45773+4149398Lelio R Paula10/2012
92722^164090+425749397Lelio R Paula04/2009
9273(12101^12101+1403)/2^4/193/349/160231/692768949389Makoto Morimoto07/2016
92742^164046+2549383Lelio R Paula01/2009
9275(24737*2^164045+1)/590658549381Lelio R Paula05/2014
9276(12097^12097+1922)/3/139/225340949380Makoto Morimoto07/2016
92785^70640-1829649376Enzo Doria02/2013
9277(9179*2^164010-1)/549376Lelio R Paula03/2015
9279(-lucasV(1,2,328052)+2)/10896149372Mike Oakes02/2017
92809*2^164002-749371Lelio R Paula02/2014
92815^70626-4449366Lelio R Paula06/2012
928211^47396-105049358Enzo Doria11/2012
9283(13*2^163956+1)/749356Lelio R Paula07/2012
92852^163934-13549350Lelio R Paula01/2011
92843^103431+2049350Lelio R Paula07/2012
92867192^12795-12795^719249349Norbert Schneider03/2017
928713^44300+2249348Lelio R Paula11/2012
9288(2^163904+3)/749340Lelio R Paula01/2012
92892^163872+1291549331Lelio R Paula11/2011
9290130^23332-12949323Norbert Schneider03/2015
92917^58357-3849318Lelio R Paula06/2012
92927760^12677-12677^776049312Norbert Schneider01/2017
929313^44265-249309Lelio R Paula11/2012
9295(19*2^163785+1)/204349303Lelio R Paula01/2012
92942^163781-174149303Yves Minet09/2012
92964*5^70529+349299Lelio R Paula09/2014
9297(2^163742-3)/13149290Lelio R Paula01/2012
92985^70514-1721649288Enzo Doria02/2013
92992^163727-174149287Yves Minet09/2012
9300Linear(0,1,1,-1,327433)49283Henri Lifchitz04/2007
93015^70498-1757649276Enzo Doria02/2013
9302(12073^12073+1070)/3/13/3106349274Makoto Morimoto07/2016
93032^163667+7211349269Enzo Doria04/2016
93045^70484-1769649267Enzo Doria02/2013
9305(12071^12071+4263)/2/101/1148949265Makoto Morimoto07/2016
93067^58293+6649264Lelio R Paula06/2012
9307(52*10^49261-1)/349263Robert Price02/2017
93082671^14376-11449262Enzo Doria06/2012
9309(15185*2^163636-1)/20949262Lelio R Paula03/2015
93102^163630+18349258Lelio R Paula01/2011
93112^163560+1549237Lelio R Paula08/2010
93133^103189+11049234Lelio R Paula07/2012
9312(41*10^49233+31)/949234Erik Branger05/2013
9314(1023052^8192+1)/6553749229Syoichiro Yamada05/2008
93152*10^49216+9349217Robert Price07/2016
93162^163453+88549205Lelio R Paula10/2011
9317(67607*2^163432+1)/349203Lelio R Paula05/2014
931815^41835-4649202Lelio R Paula11/2012
931910^49190+4550749191Patrick De Geest01/2016
932110^49190-601865949190Marisa Kirisame02/2015
932010^49190-15443149190Patrick De Geest01/2016
93222^163385+9439549184Henri Lifchitz01/2005
93232^163382-202149183Yves Minet03/2013
9325(55*10^49169-1)/949170Ray Chandler02/2012
93242^163336-1517749170Enzo Doria04/2013
93268323^12542-12542^832349169Norbert Schneider11/2016
9327(10^49165-991)/949165Serge Batalov07/2010
93287^58169-6^(58169+1)49159Robert Price06/2016
9330(F(5)^70327-F(4)^70327)/F(3)49157Wayne Halsdorf01/2010
9329(5^70327-3^70327)/249157Robert Price08/2011
93312^163283+5461549154Lelio R Paula04/2009
933218388^471+471^1838849152Anatoly F. Selevich12/2006
9333(12043^12043+799)/2/15749142Makoto Morimoto07/2016
933414^42875+6949141Lelio R Paula11/2012
9335(2^163243+9)/1749140Lelio R Paula01/2012
9336(F(770)^307-F(769)^307)/F(768)49136Wayne Halsdorf02/2010
9337(12041^12041+467)/2^2/23/4749132Makoto Morimoto07/2016
93385^70290-1944649131Enzo Doria03/2013
9339(F(760)^311-F(759)^311)/F(758)49130Wayne Halsdorf02/2010
93405^70286-2004649128Enzo Doria03/2013
934112^45519-9149124Lelio R Paula10/2012
93427^58126+7249123Lelio R Paula06/2012
93437^58125+449122Lelio R Paula06/2012
9344(991537^8192+1)/249122Lelio R Paula12/2014
9345(14*10^49119-11)/349120Erik Branger05/2013
9346t(185595)49118Robert Price12/2013
9347(2*10^49117+457)/949117Robert Price01/2017
9348(988635^8192+1)/249112Lelio R Paula12/2014
9349(26*10^49106-23)/349107Robert Price08/2016
9350(986617^8192+1)/249104Lelio R Paula12/2014
935114313^2696+2696^1431349104Hans Havermann08/2015
9352(89*10^49101-53)/949102Erik Branger05/2013
93539*7^58099-449101Lelio R Paula09/2014
9354(-lucasV(1,2,326291)+2)/(5*83563*7935289)49100Mike Oakes02/2017
935523^36054-105049096Enzo Doria08/2012
9356(984325^8192+1)/13107449091Lelio R Paula12/2014
9357(3^51443-87)^2-8949090Jorge Menendez02/2017
9358928649*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9359592271*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9360580043*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9361555500*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9362512651*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9363143358*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9364107445*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9365117360*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
936628124*2*((10^49081-1)/9)+149085Danilo Nitsche01/2016
936718^39100-2949082Lelio R Paula11/2012
9368(10^49081-1)/949081Harvey Dubner09/1999
9369(978811^8192+1)/249076Lelio R Paula12/2014
937017200^713+713^1720049074Anatoly F. Selevich07/2006
93719*2^163006+549071Lelio R Paula02/2014
937211^47113-171049064Enzo Doria11/2012
937311^47106-141049056Enzo Doria11/2012
93742^162954-2349055Lelio R Paula08/2010
93752^162924-2863549046Lelio R Paula04/2009
937624771!2-849045Robert Price06/2015
9377(26*10^49039-77)/349040Robert Price02/2017
93785^70155-449037Theodore Burton11/2005
93793^102763-1449031Lelio R Paula06/2012
9380(21*2^162876+1)/2349031Lelio R Paula07/2012
93815^70146+5849030Lelio R Paula06/2012
93822^162864-74438949027Paul Bourdelais11/2012
93832^162860-11285949026Enzo Doria06/2014
9384(10^49025-1)/3-2*10^2451249025Patrick De Geest07/2005
93852^162856-22920949025Enzo Doria01/2013
9386(10^(2*24512+1)-6*10^24512-1)/349025Robert Price02/2016
9387(965897^8192+1)/32768249024Lelio R Paula12/2014
9388(5*2^162859-1)/5391949022Lelio R Paula01/2014
93896^62990+3149016Lelio R Paula06/2012
939046329!4+249014Robert Price03/2017
93912^162816-21920949013Enzo Doria11/2012
9392(127^23297-1)/12649011Alexander Zhirkov10/2010
9393(13^43997+12^43997)/2549009Robert Price04/2013
939410^49008+6666949009Patrick De Geest01/2016
939510^49008-503749008Robert Price09/2015
93965^70110+5249005Lelio R Paula06/2012
939710^49000+21303749001Patrick De Geest07/2012
939815^41664-9449001Lelio R Paula11/2012
93993^102699-34049000Lelio R Paula06/2012
940010^49000-62149000Patrick De Geest07/2012
940110^48999+26879149000Patrick De Geest07/2012
940210^48999-7463948999Patrick De Geest07/2012
9403(21181*2^162764+1)/6558370948994Lelio R Paula05/2014
94041033^16254+16254^103348992Serge Batalov05/2014
94058602^12451+12451^860248990Norbert Schneider07/2014
940612^45385+548979Lelio R Paula10/2012
9407(951919^8192+1)/248977Lelio R Paula12/2014
9408(12007^12007+2128)/37/1180148977Makoto Morimoto07/2016
94092^162669-179548969Lelio R Paula01/2009
94102^162668-11275748968Enzo Doria06/2014
941113527^4168+4168^1352748967Hans Havermann04/2016
9412(6883*2^162649-1)/548966Lelio R Paula03/2015
9413(944123^8192+1)/248948Lelio R Paula12/2014
9414(229*10^48944-1)/348946Robert Price12/2016
94152003^14821-10248935Enzo Doria06/2012
94167^57901+8248933Lelio R Paula06/2012
9417t(166683)48933Robert Price10/2014
941811^46985-1848930Lelio R Paula10/2012
94192^162521+9876533148924Jason Earls12/2008
9420V(380406)48914Serge Batalov03/2015
94212^162482+6583548912Lelio R Paula10/2011
942212^45317+748906Lelio R Paula10/2012
9423(4^81223+3^81223)/748901Jean-Louis Charton03/2011
9424(2^162474-5)/135309483148901Lelio R Paula01/2012
94253^102477+266048894Lelio R Paula07/2012
94262^162412+2983548891Lelio R Paula10/2011
94279*6^62820+748885Lelio R Paula09/2014
9428(169^21943+1)/17048885Richard Fischer11/2015
9429(11987^11987+3067)/2/3/5^2/11/13/285748884Makoto Morimoto07/2016
943013^43881-5048881Lelio R Paula11/2012
94318173^12492-12492^817348874Norbert Schneider05/2013
943220^37563-136348871Enzo Doria03/2013
9434(923522^8192+1)/11468948864Lelio R Paula11/2014
943313137^5242+5242^1313748864Hans Havermann04/2016
943515^41545+9248861Lelio R Paula11/2012
9436(11981^11981+632)/97/170948860Makoto Morimoto07/2016
9437(919695^8192+1)/13107448850Lelio R Paula12/2014
9438(917697^8192+1)/248847Lelio R Paula12/2014
9439(12^45259-5^45259)/748842Robert Price03/2013
94409*5^69862+848833Lelio R Paula09/2014
944112^45244-9548827Lelio R Paula10/2012
9442(29*2^162182-1)/548823Lelio R Paula01/2014
9443(2^162167-3)*6+10^48818*13803-748823Gilbert Mozzo11/2016
9444(2^162167-3)*6-748818Gilbert Mozzo03/2016
94457*10^48816-6948817Robert Price01/2017
9446(11971^11971+3180)/103/757748814Makoto Morimoto07/2016
94472^162143-5148810Lelio R Paula08/2010
94482^162136-28451948808Gary Barnes08/2009
94495^69828-1538648808Enzo Doria02/2013
94505^69826-3*4^6982648807Mike Oakes02/2010
94512^162123+7406348804Enzo Doria04/2016
945221001^11289-10448794Enzo Doria07/2012
94535^69802-3248790Lelio R Paula05/2012
9454(902939^8192+1)/248789Lelio R Paula12/2014
9455(2^162059+78557)/3548784Lelio R Paula05/2012
9456(900239^8192+1)/248778Lelio R Paula12/2014
9457138^22794-13748777Norbert Schneider10/2015
94582^162033+7675748777Enzo Doria05/2016
945918^38850-3748768Lelio R Paula11/2012
9460(898286^8192+1)/78643348765Lelio R Paula11/2014
946168^26610+6748764Norbert Schneider10/2012
94622^161987+1501548763Lelio R Paula10/2011
9463(11959^11959+6523)/2/558148762Makoto Morimoto07/2016
94643^102198-8648761Lelio R Paula06/2012
9465(13224!+1)/22149748755Donovan Johnson04/2006
946618^38838-1348753Lelio R Paula11/2012
9467161923*2^161923+161923+248749Robert Price05/2016
9468(892493^8192+1)/13107448743Lelio R Paula12/2014
9469(11953^11953+133)/2/4686148734Makoto Morimoto06/2016
94702^161881-1494148732Enzo Doria04/2013
9471(888215^8192+1)/248730Lelio R Paula12/2014
9472-lucasV(1,2,323749)-248730Mike Oakes02/2017
947310268^12147+12147^1026848728Norbert Schneider11/2013
9475(26*10^48726-11)/348727Erik Branger05/2013
94743*6^62618-748727Lelio R Paula09/2014
94772^161857-4548724Lelio R Paula08/2010
9476(889160^8192+1)/7328363315348724Lelio R Paula11/2014
94782^161837+46748718Lelio R Paula11/2007
94793^102102+1048716Lelio R Paula01/2007
94802^161806-829548709Lelio R Paula04/2009
9481(25*2^161811-1)/45748709Lelio R Paula01/2014
948213311^4558+4558^1331148702Hans Havermann05/2016
948324^35284-45748700Enzo Doria03/2013
94843^102058+868048695Lelio R Paula06/2012
948513537^3948+3948^1353748685Hans Havermann05/2016
9486(11941^11941+6414)/548684Makoto Morimoto07/2016
94872^161719-1509748683Enzo Doria04/2013
9488(41*10^48678+373)/948679Robert Price04/2017
94893*10^48668-7^4866848669Mike Oakes01/2010
949013201!+13201!2+13201#-248666Joe McLean10/2007
94922*3^101994-548664Lelio R Paula03/2014
9491(11939^11939+2801)/2^2/5/19/307/221047348664Makoto Morimoto07/2016
949311933^11933+131648648Makoto Morimoto07/2016
9494(-lucasV(1,2,323096)+2)/(3*193)48629Mike Oakes02/2017
9495(lucasV(1,2,323208)-2)/(3^3*5*7*11*37*1733*2011*16603*17957*80803)48622Mike Oakes02/2017
949695^24584+9448621Norbert Schneider05/2013
9497(11927^11927+2091)/2/2273/6268348613Makoto Morimoto07/2016
9498(10^48604-31)/348604Serge Batalov12/2014
9499Phi(11923,11925)48600Henri Lifchitz11/2003
9500(11923^11923+3199)/2/4264948598Makoto Morimoto07/2016


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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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