PRP Records

Probable Primes Top 10000

(180278 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(12113^12113+3627)/2^2/5/19/1449629949451Makoto Morimoto07/2016
95025^70746-1601649450Enzo Doria02/2013
9504(2^164258+9)/1349446Lelio R Paula01/2012
95032^164255-11268749446Enzo Doria06/2014
9505(21*2^164222-1)/171749434Lelio R Paula01/2014
95062^164212+1270549433Lelio R Paula11/2011
95073*2^164205+749432Lelio R Paula02/2014
95082^164203+57729457549431Lelio R Paula02/2013
9509(12109^12109+2534)/3^2/23/24763/78102149430Makoto Morimoto07/2016
9510Pell-LucasQ(129127)/249427Eric W. Weisstein05/2006
95112^164187+769549426Lelio R Paula11/2011
95123^103585-2649423Lelio R Paula07/2012
9513(3*2^164194+1)/1425501749421Lelio R Paula07/2012
951410^49415+7683749416Patrick De Geest01/2016
951710^49415-6^49415-4^49415-149415Mike Oakes01/2010
951510^49415-3281349415Patrick De Geest01/2016
951612943^6574+6574^1294349415Hans Havermann02/2016
9518(6^63497-61)/2549409Lelio R Paula05/2014
951911376^12181+12181^1137649407Norbert Schneider12/2013
95202^164110-1749403Lelio R Paula08/2010
952112^45773+4149398Lelio R Paula10/2012
95222^164090+425749397Lelio R Paula04/2009
9523(12101^12101+1403)/2^4/193/349/160231/692768949389Makoto Morimoto07/2016
95242^164061-388949388Yves Minet04/2017
95252^164046+2549383Lelio R Paula01/2009
9526(24737*2^164045+1)/590658549381Lelio R Paula05/2014
9527(12097^12097+1922)/3/139/225340949380Makoto Morimoto07/2016
95285^70640-1829649376Enzo Doria02/2013
9529(9179*2^164010-1)/549376Lelio R Paula03/2015
9530(-lucasV(1,2,328052)+2)/10896149372Mike Oakes02/2017
95319*2^164002-749371Lelio R Paula02/2014
95325^70626-4449366Lelio R Paula06/2012
953311^47396-105049358Enzo Doria11/2012
9534(13*2^163956+1)/749356Lelio R Paula07/2012
95362^163934-13549350Lelio R Paula01/2011
95353^103431+2049350Lelio R Paula07/2012
95377192^12795-12795^719249349Norbert Schneider03/2017
953813^44300+2249348Lelio R Paula11/2012
9539(2^163904+3)/749340Lelio R Paula01/2012
95402^163872+1291549331Lelio R Paula11/2011
9541130^23332-12949323Norbert Schneider03/2015
95427^58357-3849318Lelio R Paula06/2012
95437760^12677-12677^776049312Norbert Schneider01/2017
954413^44265-249309Lelio R Paula11/2012
9546(19*2^163785+1)/204349303Lelio R Paula01/2012
95452^163781-174149303Yves Minet09/2012
95474*5^70529+349299Lelio R Paula09/2014
9548(2^163742-3)/13149290Lelio R Paula01/2012
95495^70514-1721649288Enzo Doria02/2013
95502^163727-174149287Yves Minet09/2012
9551Linear(0,1,1,-1,327433)49283Henri Lifchitz04/2007
95525^70498-1757649276Enzo Doria02/2013
9553(12073^12073+1070)/3/13/3106349274Makoto Morimoto07/2016
95542^163667+7211349269Enzo Doria04/2016
95555^70484-1769649267Enzo Doria02/2013
9556(12071^12071+4263)/2/101/1148949265Makoto Morimoto07/2016
95577^58293+6649264Lelio R Paula06/2012
9558(52*10^49261-1)/349263Robert Price02/2017
95592671^14376-11449262Enzo Doria06/2012
9560(15185*2^163636-1)/20949262Lelio R Paula03/2015
95612^163630+18349258Lelio R Paula01/2011
95622^163560+1549237Lelio R Paula08/2010
95643^103189+11049234Lelio R Paula07/2012
9563(41*10^49233+31)/949234Erik Branger05/2013
9565(1023052^8192+1)/6553749229Syoichiro Yamada05/2008
95662*10^49216+9349217Robert Price07/2016
9567(107^24251-1)/10649213Richard Fischer07/2017
95682^163453+88549205Lelio R Paula10/2011
9569(67607*2^163432+1)/349203Lelio R Paula05/2014
957015^41835-4649202Lelio R Paula11/2012
957110^49190+4550749191Patrick De Geest01/2016
957310^49190-601865949190Marisa Kirisame02/2015
957210^49190-15443149190Patrick De Geest01/2016
95742^163385+9439549184Henri Lifchitz01/2005
95752^163382-202149183Yves Minet03/2013
9577(55*10^49169-1)/949170Ray Chandler02/2012
95762^163336-1517749170Enzo Doria04/2013
95788323^12542-12542^832349169Norbert Schneider11/2016
9579(10^49165-991)/949165Serge Batalov07/2010
95807^58169-6^(58169+1)49159Robert Price06/2016
9581(F(5)^70327-F(4)^70327)/F(3)49157Wayne Halsdorf01/2010
9582(5^70327-3^70327)/249157Robert Price08/2011
95832^163283+5461549154Lelio R Paula04/2009
958418388^471+471^1838849152Anatoly F. Selevich12/2006
9585(782*10^49148-71)/949150Robert Price06/2017
9586(12043^12043+799)/2/15749142Makoto Morimoto07/2016
958714^42875+6949141Lelio R Paula11/2012
9588(2^163243+9)/1749140Lelio R Paula01/2012
9589(F(770)^307-F(769)^307)/F(768)49136Wayne Halsdorf02/2010
9590(12041^12041+467)/2^2/23/4749132Makoto Morimoto07/2016
95915^70290-1944649131Enzo Doria03/2013
9592(F(760)^311-F(759)^311)/F(758)49130Wayne Halsdorf02/2010
95935^70286-2004649128Enzo Doria03/2013
959412^45519-9149124Lelio R Paula10/2012
95957^58126+7249123Lelio R Paula06/2012
95967^58125+449122Lelio R Paula06/2012
9597(991537^8192+1)/249122Lelio R Paula12/2014
9598(14*10^49119-11)/349120Erik Branger05/2013
9599t(185595)49118Robert Price12/2013
9600(2*10^49117+457)/949117Robert Price01/2017
9601(988635^8192+1)/249112Lelio R Paula12/2014
9602(26*10^49106-23)/349107Robert Price08/2016
9603(986617^8192+1)/249104Lelio R Paula12/2014
960414313^2696+2696^1431349104Hans Havermann08/2015
9605(89*10^49101-53)/949102Erik Branger05/2013
96069*7^58099-449101Lelio R Paula09/2014
9607(-lucasV(1,2,326291)+2)/(5*83563*7935289)49100Mike Oakes02/2017
960823^36054-105049096Enzo Doria08/2012
9609(984325^8192+1)/13107449091Lelio R Paula12/2014
9610(3^51443-87)^2-8949090Jorge Menendez02/2017
9611928649*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9612592271*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9613580043*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9614555500*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9615512651*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9616143358*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9617107445*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9618117360*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
961928124*2*((10^49081-1)/9)+149085Danilo Nitsche01/2016
962018^39100-2949082Lelio R Paula11/2012
9621(10^49081-1)/949081Harvey Dubner09/1999
9622(978811^8192+1)/249076Lelio R Paula12/2014
962317200^713+713^1720049074Anatoly F. Selevich07/2006
96249*2^163006+549071Lelio R Paula02/2014
962511^47113-171049064Enzo Doria11/2012
962611^47106-141049056Enzo Doria11/2012
96272^162954-2349055Lelio R Paula08/2010
96282^162924-2863549046Lelio R Paula04/2009
962924771!2-849045Robert Price06/2015
9630(26*10^49039-77)/349040Robert Price02/2017
96315^70155-449037Theodore Burton11/2005
96323^102763-1449031Lelio R Paula06/2012
9633(21*2^162876+1)/2349031Lelio R Paula07/2012
96345^70146+5849030Lelio R Paula06/2012
96352^162864-74438949027Paul Bourdelais11/2012
96362^162860-11285949026Enzo Doria06/2014
9637(10^49025-1)/3-2*10^2451249025Patrick De Geest07/2005
96382^162856-22920949025Enzo Doria01/2013
9639(10^(2*24512+1)-6*10^24512-1)/349025Robert Price02/2016
9640(965897^8192+1)/32768249024Lelio R Paula12/2014
9641(5*2^162859-1)/5391949022Lelio R Paula01/2014
96426^62990+3149016Lelio R Paula06/2012
964346329!4+249014Robert Price03/2017
96442^162816-21920949013Enzo Doria11/2012
9645(127^23297-1)/12649011Alexander Zhirkov10/2010
9646(13^43997+12^43997)/2549009Robert Price04/2013
964710^49008+6666949009Patrick De Geest01/2016
964810^49008-503749008Robert Price09/2015
96495^70110+5249005Lelio R Paula06/2012
965010^49000+21303749001Patrick De Geest07/2012
965115^41664-9449001Lelio R Paula11/2012
96523^102699-34049000Lelio R Paula06/2012
965310^49000-62149000Patrick De Geest07/2012
965410^48999+26879149000Patrick De Geest07/2012
965510^48999-7463948999Patrick De Geest07/2012
9656(21181*2^162764+1)/6558370948994Lelio R Paula05/2014
96571033^16254+16254^103348992Serge Batalov05/2014
96588602^12451+12451^860248990Norbert Schneider07/2014
965912^45385+548979Lelio R Paula10/2012
9660(951919^8192+1)/248977Lelio R Paula12/2014
9661(12007^12007+2128)/37/1180148977Makoto Morimoto07/2016
96622^162669-179548969Lelio R Paula01/2009
96632^162668-11275748968Enzo Doria06/2014
966413527^4168+4168^1352748967Hans Havermann04/2016
9665(6883*2^162649-1)/548966Lelio R Paula03/2015
9666(944123^8192+1)/248948Lelio R Paula12/2014
9667(229*10^48944-1)/348946Robert Price12/2016
96682003^14821-10248935Enzo Doria06/2012
96697^57901+8248933Lelio R Paula06/2012
9670t(166683)48933Robert Price10/2014
967111^46985-1848930Lelio R Paula10/2012
96722^162521+9876533148924Jason Earls12/2008
9673V(380406)48914Serge Batalov03/2015
96742^162482+6583548912Lelio R Paula10/2011
967512^45317+748906Lelio R Paula10/2012
9676(4^81223+3^81223)/748901Jean-Louis Charton03/2011
9677(2^162474-5)/135309483148901Lelio R Paula01/2012
96783^102477+266048894Lelio R Paula07/2012
96792^162412+2983548891Lelio R Paula10/2011
96809*6^62820+748885Lelio R Paula09/2014
9681(169^21943+1)/17048885Richard Fischer11/2015
9682(11987^11987+3067)/2/3/5^2/11/13/285748884Makoto Morimoto07/2016
968313^43881-5048881Lelio R Paula11/2012
96848173^12492-12492^817348874Norbert Schneider05/2013
968520^37563-136348871Enzo Doria03/2013
9686(923522^8192+1)/11468948864Lelio R Paula11/2014
968713137^5242+5242^1313748864Hans Havermann04/2016
968815^41545+9248861Lelio R Paula11/2012
9689(11981^11981+632)/97/170948860Makoto Morimoto07/2016
9690(919695^8192+1)/13107448850Lelio R Paula12/2014
9691(917697^8192+1)/248847Lelio R Paula12/2014
9692(12^45259-5^45259)/748842Robert Price03/2013
96939*5^69862+848833Lelio R Paula09/2014
969412^45244-9548827Lelio R Paula10/2012
9695(29*2^162182-1)/548823Lelio R Paula01/2014
9696(2^162167-3)*6+10^48818*13803-748823Gilbert Mozzo11/2016
9697(2^162167-3)*6-748818Gilbert Mozzo03/2016
96987*10^48816-6948817Robert Price01/2017
9699(11971^11971+3180)/103/757748814Makoto Morimoto07/2016
97002^162143-5148810Lelio R Paula08/2010
97022^162136-28451948808Gary Barnes08/2009
97015^69828-1538648808Enzo Doria02/2013
97035^69826-3*4^6982648807Mike Oakes02/2010
97042^162123+7406348804Enzo Doria04/2016
970521001^11289-10448794Enzo Doria07/2012
97065^69802-3248790Lelio R Paula05/2012
9707(902939^8192+1)/248789Lelio R Paula12/2014
9708(2^162059+78557)/3548784Lelio R Paula05/2012
9709(900239^8192+1)/248778Lelio R Paula12/2014
9710138^22794-13748777Norbert Schneider10/2015
97112^162033+7675748777Enzo Doria05/2016
971218^38850-3748768Lelio R Paula11/2012
9713(898286^8192+1)/78643348765Lelio R Paula11/2014
971468^26610+6748764Norbert Schneider10/2012
97152^161987+1501548763Lelio R Paula10/2011
9716(11959^11959+6523)/2/558148762Makoto Morimoto07/2016
97173^102198-8648761Lelio R Paula06/2012
9718(13224!+1)/22149748755Donovan Johnson04/2006
971918^38838-1348753Lelio R Paula11/2012
9720161923*2^161923+161923+248749Robert Price05/2016
9721(892493^8192+1)/13107448743Lelio R Paula12/2014
9722(11953^11953+133)/2/4686148734Makoto Morimoto06/2016
97232^161881-1494148732Enzo Doria04/2013
9724(888215^8192+1)/248730Lelio R Paula12/2014
9725-lucasV(1,2,323749)-248730Mike Oakes02/2017
972610268^12147+12147^1026848728Norbert Schneider11/2013
9727(26*10^48726-11)/348727Erik Branger05/2013
97283*6^62618-748727Lelio R Paula09/2014
97302^161857-4548724Lelio R Paula08/2010
9729(889160^8192+1)/7328363315348724Lelio R Paula11/2014
97312^161837+46748718Lelio R Paula11/2007
97323^102102+1048716Lelio R Paula01/2007
97332^161806-829548709Lelio R Paula04/2009
9734(25*2^161811-1)/45748709Lelio R Paula01/2014
973513311^4558+4558^1331148702Hans Havermann05/2016
973624^35284-45748700Enzo Doria03/2013
97373^102058+868048695Lelio R Paula06/2012
973813537^3948+3948^1353748685Hans Havermann05/2016
9739(11941^11941+6414)/548684Makoto Morimoto07/2016
97402^161719-1509748683Enzo Doria04/2013
9741(41*10^48678+373)/948679Robert Price04/2017
97423*10^48668-7^4866848669Mike Oakes01/2010
974313201!+13201!2+13201#-248666Joe McLean10/2007
97442*3^101994-548664Lelio R Paula03/2014
9745(11939^11939+2801)/2^2/5/19/307/221047348664Makoto Morimoto07/2016
974611933^11933+131648648Makoto Morimoto07/2016
9747(-lucasV(1,2,323096)+2)/(3*193)48629Mike Oakes02/2017
9748(lucasV(1,2,323208)-2)/(3^3*5*7*11*37*1733*2011*16603*17957*80803)48622Mike Oakes02/2017
974995^24584+9448621Norbert Schneider05/2013
9750(11927^11927+2091)/2/2273/6268348613Makoto Morimoto07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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