PRP Records

Probable Primes Top 10000

(183432 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 ?
95017*2^166685+350179Lelio R Paula02/2014
95027*2^166671-950174Lelio R Paula02/2014
95039*2^166670+750174Lelio R Paula02/2014
95042^166670-11254150173Enzo Doria06/2014
95052^166657+46550169Lelio R Paula11/2011
950617^40768-2050163Lelio R Paula01/2013
95072^166596-7879550151Lelio R Paula07/2011
9508135^23541+13450151Norbert Schneider04/2015
951024^36335-67350150Enzo Doria03/2013
9509(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9511(28*10^50147-97)/350148Robert Price07/2016
9512263^20718-20718^26350137Norbert Schneider09/2015
9513t(167020)50133Robert Price01/2015
9514(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
95152868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
951612^46445-1950123Lelio R Paula12/2012
95172^166501-1459350122Enzo Doria04/2013
9518(31*2^166509-1)/368407750120Lelio R Paula01/2014
95192^166483-16950117Lelio R Paula01/2011
9520(188^22037+1)/18950114Eric Chen09/2017
95219^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9522(23*2^166487-1)/3377049950112Lelio R Paula01/2014
95232*5^71689-950109Lelio R Paula09/2014
952413495^5154+5154^1349550096Hans Havermann04/2016
95256^64369-11950089Lelio R Paula06/2012
95269224^12633-12633^922450089Norbert Schneider12/2016
95272^166370-11254150083Enzo Doria06/2014
9528(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
95292^166339-11232150074Enzo Doria06/2014
95305^71637-2250073Lelio R Paula06/2012
9531Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
9532(4*10^50060+137)/350061Robert Price07/2017
95335^71618-1382650059Enzo Doria02/2013
953415^42563-250058Lelio R Paula11/2012
95351943^15222+15222^194350058Serge Batalov05/2014
9536183^22125-250057Lelio R Paula10/2017
953711641^12310+12310^1164150053Norbert Schneider04/2014
953813537!-2^13537+150052Joe McLean06/2006
95392^166227-16446750040Gary Barnes08/2009
954012241^12241+475650039Makoto Morimoto07/2016
9541(106*10^50035-1)/350037Serge Batalov12/2014
954211^48044-81050033Enzo Doria11/2012
954315^42539+8850030Lelio R Paula11/2012
9544524^18397-523^1839750028Jean-Louis Charton10/2009
95452^166159-1449750019Enzo Doria04/2013
95462^166155+8785550018Lelio R Paula01/2009
95482^166138-1165550013Lelio R Paula07/2011
9547(L(239313)-1)/5-2^955150013Jorge Menendez06/2017
95492^166104-11262550003Enzo Doria06/2014
9550(L(239265)-1)/5-2^90650003Jorge Menendez03/2017
9551(L(239265)-1)/5-2^315250003Jorge Menendez04/2017
9552(L(239265)-1)/5-2^2015550003Jorge Menendez04/2017
9553(L(239265)-1)/5-2^7891250003Jorge Menendez04/2017
95542^166100+19901550002Lelio R Paula05/2008
955510^50000+6585950001Milton L. Brown02/2006
9556(598*10^49999-31)/950001Robert Price02/2017
955710^50000+581092721613350001Jorge Menendez09/2017
955810^50000+581092760537750001Jorge Menendez09/2017
955910^50000+581092765837950001Jorge Menendez09/2017
956010^50000+581092767222350001Jorge Menendez09/2017
958110^49999+9170150000Patrick De Geest03/2005
956110^50000-19430350000Patrick De Geest02/2009
9562(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9563(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9564(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9565(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9566(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9567(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9568(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9569(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9570(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9571(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
9572(2^6972593/10^381525)%10^5000050000Michael Vang05/2016
9573(2^30402457/10^1629036)%10^5000050000Michael Vang05/2016
9574(2^3021377/10^702316)%10^5000050000Michael Vang05/2016
9575(2^1398269/10^37827)%10^5000050000Michael Vang05/2016
9576(2^2976221/10^767789)%10^5000050000Michael Vang05/2016
9577(2^859433/10^42285)%10^5000050000Michael Vang06/2016
9578(2^1257787/10^119173)%10^5000050000Michael Vang06/2016
9579(2^756839/10^136257)%10^5000050000Michael Vang06/2016
95802*10^49999+36350000Makoto Morimoto09/2016
958210^49999-414949999Patrick De Geest02/2009
958310484^12433-12433^1048449988Norbert Schneider07/2013
95842^166052+14549987Lelio R Paula01/2011
9585(10^50001+10936)/(2^3*19*241*5872003*15974507)49983Makoto Morimoto09/2016
95861111*2^166022-55549981Henri Lifchitz02/2005
958711^47993+3049980Lelio R Paula10/2012
95882^166000-7879549971Lelio R Paula07/2011
958913517!-13517#+14997003/2005
95912^165995-11322749970Enzo Doria07/2014
9590(12227^12227+1092)/5/11/17/37^249970Makoto Morimoto07/2016
959217^40609+1449968Lelio R Paula11/2012
9594(1257656^8192+1)/6553749963Syoichiro Yamada06/2008
9593(3^104735-8)/149319993149963Lelio R Paula03/2012
95952^165969-11271149962Enzo Doria06/2014
95962^165910-760549944Lelio R Paula04/2009
959736313!3-5904949942Robert Price12/2015
95982^165884-4549937Lelio R Paula08/2010
9601(1246892^8192+1)/6553749933Syoichiro Yamada06/2008
95993^104654+10449933Lelio R Paula07/2012
96007452^12895-12895^745249933Norbert Schneider05/2017
96029035^12622+12622^903549932Norbert Schneider01/2016
9603(22699*2^165838+1)/328749924Lelio R Paula05/2014
96046^64149-8549918Lelio R Paula06/2012
9605(7*10^49913+71)/349914Robert Price03/2016
96062^165799-11481749911Enzo Doria05/2015
96072^165789+3549908Lelio R Paula08/2010
96082^165783-12149906Lelio R Paula01/2011
96092^165760-11264949899Enzo Doria06/2014
9610(11*2^165758+1)/13549898Lelio R Paula01/2012
96112^165747+6349895Lelio R Paula04/2009
9612(7*10^49893-13)/349894Robert Price06/2016
9613298^20163-20163^29849888Norbert Schneider08/2015
9614(49885^49885)/(10^184474)49885James G. Merickel08/2015
961517^40540+3649883Lelio R Paula11/2012
9616(12211^12211+4312)/13/17/31/1297/1483/1627/9923/3643349882Makoto Morimoto07/2016
96172^165676-11294949874Enzo Doria06/2014
9618(12203^12203+992)/1149867Makoto Morimoto07/2016
96197784^12811-12811^778449851Norbert Schneider03/2017
96202^165581-74549845Yves Minet01/2012
96212^165576+7482149844Enzo Doria04/2016
962213318^5527+5527^1331849843Hans Havermann04/2016
96242^165561-215549839Yves Minet08/2013
9623(12197^12197+1755)/2^449839Makoto Morimoto07/2016
96257406^12879+12879^740649837Norbert Schneider03/2016
96268530^12677+12677^853049833Norbert Schneider01/2016
9627(3^52222-69)^2-7149833Jorge Menendez02/2017
962812^46175+2949832Lelio R Paula10/2012
96292^165488-1296949817Enzo Doria10/2012
96302^165473+5890549813Lelio R Paula04/2009
963120^38284+4949809Lelio R Paula11/2012
96333^104388-2049806Lelio R Paula07/2012
9632(10^49806+119)/349806Serge Batalov12/2014
9634(1202206^8192+1)/6553749803Syoichiro Yamada06/2008
9635(4*10^49801+11)/349802Erik Branger05/2013
96365^71240-1547649795Enzo Doria02/2013
96377*3^104334-449781Lelio R Paula03/2014
9638(136*10^49774-1)/949776Serge Batalov12/2014
96393^104297+868049763Lelio R Paula07/2012
9640(F(10)^28579-F(9)^28579)/F(8)49737Wayne Halsdorf03/2010
9641(3^104243+1)/449736Kamil Duszenko05/2004
9642(10223*2^165183+1)/5549728Lelio R Paula05/2014
96436^63895+10149720Lelio R Paula06/2012
96443^104194+10049714Lelio R Paula07/2012
964510^49711+10359349712Patrick De Geest07/2017
964610^49711-70149711Robert Price06/2017
9647U(356793)49710Serge Batalov03/2015
964813321^5388+5388^1332149707Hans Havermann04/2016
964912166^12166+56549700Henri Lifchitz11/2004
9650(89*10^49689-53)/949690Erik Branger05/2013
9651(1163126^8192+1)/6553749685Syoichiro Yamada06/2008
965211^47709+4249684Lelio R Paula10/2012
9653(35*10^49682+1)/949683Serge Batalov05/2010
9654(12163^12163+1194)/37/19349683Makoto Morimoto07/2016
96553^104124+9249680Lelio R Paula07/2012
96572^165025+16502949678Henri Lifchitz04/2005
965614063^3408+3408^1406349678Hans Havermann04/2016
9658(2^165031+3)/4843949675Lelio R Paula01/2012
9659(7*2^165020-1)/26149675Lelio R Paula01/2014
96612^165000+522749670Lelio R Paula05/2011
9660(12161^12161+765)/2/13/29/277/31149670Makoto Morimoto07/2016
9662(110051^9851+1)/11005249660Faysal YAtim09/2007
96632^164962-63979149659Paul Bourdelais11/2012
966410^49657+3149658Robert Price01/2011
966510^49657-1289949657Patrick De Geest01/2012
96662^164937-19349651Lelio R Paula01/2011
966721^37549-20^3754949649Jean-Louis Charton02/2012
96681417^15754+15754^141749647Serge Batalov05/2014
9669(12157^12157+2611)/2^5/11/13/1019/48197/31440749643Makoto Morimoto07/2016
967012^45999+2549642Lelio R Paula10/2012
9671(3^104040+7)/849639Lelio R Paula03/2012
96722^164882-101749635Lelio R Paula06/2008
9673(3^104053-8)/38183002074345549632Lelio R Paula03/2012
967411^47658-18049631Enzo Doria07/2012
96752^164859-123749628Yves Minet08/2012
967617^40331+9849626Lelio R Paula11/2012
96771638^15437+15437^163849620Serge Batalov05/2014
9678113^24160+11249603Norbert Schneider09/2013
967913^44527+1649601Lelio R Paula11/2012
968083^25844+8249597Norbert Schneider01/2013
9681(12143^12143+1306)/3/7/5949593Makoto Morimoto07/2016
9682114667#-p(114667)49591Henri Lifchitz03/2007
96832^164731-183384749589Enzo Doria05/2015
9684(625^17737+1)/62649588Richard Fischer06/2013
96852^164714+2983549584Lelio R Paula11/2011
96867*10^49580-6949581Robert Price01/2017
96877*5^70922+449574Lelio R Paula09/2014
9688(229*10^49571-1)/349573Robert Price12/2016
9689277^20295-29049571Enzo Doria06/2012
96902^164662-11288349569Enzo Doria06/2014
9691(1125424^8192+1)/6553749568Syoichiro Yamada06/2008
96926^63698-3549567Lelio R Paula06/2012
9693(2^164652-3)*6-749566Gilbert Mozzo04/2016
9694(11*10^49552+43)/949553Erik Branger05/2013
96952^164606+4349552Lelio R Paula08/2010
96962^164598-11311149549Enzo Doria07/2014
969711^47575-810049545Enzo Doria02/2013
96989420^12467-12467^942049545Norbert Schneider07/2013
96992^164581-81925349544Paul Bourdelais11/2012
97009001^12528-12528^900149540Norbert Schneider11/2016
9701(lucasV(1,2,329135)+2)/(5^2*179*10247)49533Mike Oakes02/2017
9702(4*10^49529-31)/949529Erik Branger05/2011
970313875^3712+3712^1387549529Hans Havermann03/2016
97047^58604-6249527Lelio R Paula06/2012
97052^164508+10549522Lelio R Paula04/2009
970624^35878-93749520Enzo Doria03/2013
9707(89*10^49516-17)/949517Erik Branger05/2013
97082^164478-16749513Lelio R Paula01/2011
970913^44446+3049511Lelio R Paula11/2012
97102^164466-79024149510Paul Bourdelais11/2012
9711-lucasV(-1,2,328901)49505Mike Oakes01/2017
9712(21*2^164421-1)/53349495Lelio R Paula01/2014
971335^32052-20649491Enzo Doria03/2013
97143^103726-1187849490Enzo Doria02/2013
9715(3^103726+7)/51249488Lelio R Paula03/2012
9716(12119^12119+6270)/1349487Makoto Morimoto07/2016
971710^49484+1653749485Patrick De Geest01/2016
971910^49484-10^5384-149484Serge Batalov01/2011
971810^49484-9153949484Patrick De Geest01/2016
97203*2^164365-749480Lelio R Paula02/2014
9721(7^58543-5^58543)/249475Robert Price05/2012
97228482^12591+12591^848249464Norbert Schneider11/2015
9723(29*2^164309-1)/2090749460Lelio R Paula01/2014
9724(12113^12113+3627)/2^2/5/19/1449629949451Makoto Morimoto07/2016
97255^70746-1601649450Enzo Doria02/2013
9726(2^164258+9)/1349446Lelio R Paula01/2012
97272^164255-11268749446Enzo Doria06/2014
9728(21*2^164222-1)/171749434Lelio R Paula01/2014
97292^164212+1270549433Lelio R Paula11/2011
97303*2^164205+749432Lelio R Paula02/2014
97312^164203+57729457549431Lelio R Paula02/2013
9732(12109^12109+2534)/3^2/23/24763/78102149430Makoto Morimoto07/2016
9733Pell-LucasQ(129127)/249427Eric W. Weisstein05/2006
97342^164187+769549426Lelio R Paula11/2011
97353^103585-2649423Lelio R Paula07/2012
9736(3*2^164194+1)/1425501749421Lelio R Paula07/2012
973710^49415+7683749416Patrick De Geest01/2016
974010^49415-6^49415-4^49415-149415Mike Oakes01/2010
973810^49415-3281349415Patrick De Geest01/2016
973912943^6574+6574^1294349415Hans Havermann02/2016
9741(6^63497-61)/2549409Lelio R Paula05/2014
974211376^12181+12181^1137649407Norbert Schneider12/2013
9743(7*10^49404+53)/349405Robert Price10/2017
97442^164110-1749403Lelio R Paula08/2010
974512^45773+4149398Lelio R Paula10/2012
97462^164090+425749397Lelio R Paula04/2009
9747(12101^12101+1403)/2^4/193/349/160231/692768949389Makoto Morimoto07/2016
97482^164061-388949388Yves Minet04/2017
97492^164046+2549383Lelio R Paula01/2009
9750(24737*2^164045+1)/590658549381Lelio R Paula05/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!