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 ?
925113739^4600+4600^1373950323Hans Havermann10/2015
925211508^12391+12391^1150850320Norbert Schneider06/2014
92532^167132-216350312Yves Minet08/2013
92547^59527-6250307Lelio R Paula06/2012
9255(310027^9161+1)/31002850302Faysal YAtim04/2008
9256(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
92572^167083-11251950297Enzo Doria06/2014
9258272^20659-20659^27250296Norbert Schneider09/2015
925925337!!-1650290Robert Price06/2015
92609722^12611-12611^972250290Norbert Schneider12/2016
9262(15*2^167013+1)/64950275Lelio R Paula07/2012
926119^39315-1250275Lelio R Paula01/2013
92635^71925-3650274Lelio R Paula06/2012
92642^167002+279913950273Enzo Doria04/2016
926510957^12444-12444^1095750270Norbert Schneider07/2013
92668*10^50253-9950254Robert Price02/2017
92685^71894-5450252Lelio R Paula06/2012
9267(127^23887+1)/12850252Richard Fischer04/2017
926918^40028-550247Lelio R Paula01/2013
9270(3*2^166904+1)/127950241Lelio R Paula07/2012
927124^36397+2350236Norbert Schneider12/2013
92727984*29^34345+2150230Curtis Bright05/2015
92733^105248-1352850217Enzo Doria02/2013
92746^64532-6550216Lelio R Paula06/2012
92755^71834-2061650210Enzo Doria03/2013
9276(31*2^166778-1)/365150204Lelio R Paula01/2014
92772^166752-11239750198Enzo Doria06/2014
9278(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
927911^48199-93050195Enzo Doria11/2012
92803*10^50194-750195Erik Branger11/2013
92819992^12549+12549^999250192Norbert Schneider10/2015
92822^166708+15750185Lelio R Paula01/2011
9283(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
92847*2^166685+350179Lelio R Paula02/2014
92857*2^166671-950174Lelio R Paula02/2014
92869*2^166670+750174Lelio R Paula02/2014
92872^166670-11254150173Enzo Doria06/2014
92882^166657+46550169Lelio R Paula11/2011
928917^40768-2050163Lelio R Paula01/2013
92902^166596-7879550151Lelio R Paula07/2011
9291135^23541+13450151Norbert Schneider04/2015
929224^36335-67350150Enzo Doria03/2013
9293(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9294(28*10^50147-97)/350148Robert Price07/2016
9295263^20718-20718^26350137Norbert Schneider09/2015
9296t(167020)50133Robert Price01/2015
9297(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
92982868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
929912^46445-1950123Lelio R Paula12/2012
93002^166501-1459350122Enzo Doria04/2013
9301(31*2^166509-1)/368407750120Lelio R Paula01/2014
93022^166483-16950117Lelio R Paula01/2011
93039^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9304(23*2^166487-1)/3377049950112Lelio R Paula01/2014
93052*5^71689-950109Lelio R Paula09/2014
930613495^5154+5154^1349550096Hans Havermann04/2016
93076^64369-11950089Lelio R Paula06/2012
93089224^12633-12633^922450089Norbert Schneider12/2016
93092^166370-11254150083Enzo Doria06/2014
9310(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
93112^166339-11232150074Enzo Doria06/2014
93125^71637-2250073Lelio R Paula06/2012
9313Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
9314(4*10^50060+137)/350061Robert Price07/2017
93155^71618-1382650059Enzo Doria02/2013
931615^42563-250058Lelio R Paula11/2012
93171943^15222+15222^194350058Serge Batalov05/2014
931811641^12310+12310^1164150053Norbert Schneider04/2014
931913537!-2^13537+150052Joe McLean06/2006
93202^166227-16446750040Gary Barnes08/2009
932112241^12241+475650039Makoto Morimoto07/2016
9322(106*10^50035-1)/350037Serge Batalov12/2014
932311^48044-81050033Enzo Doria11/2012
932415^42539+8850030Lelio R Paula11/2012
9325524^18397-523^1839750028Jean-Louis Charton10/2009
93262^166159-1449750019Enzo Doria04/2013
93272^166155+8785550018Lelio R Paula01/2009
93282^166138-1165550013Lelio R Paula07/2011
9329(L(239313)-1)/5-2^955150013Jorge Menendez06/2017
93342^166104-11262550003Enzo Doria06/2014
9330(L(239265)-1)/5-2^90650003Jorge Menendez03/2017
9331(L(239265)-1)/5-2^315250003Jorge Menendez04/2017
9332(L(239265)-1)/5-2^2015550003Jorge Menendez04/2017
9333(L(239265)-1)/5-2^7891250003Jorge Menendez04/2017
93352^166100+19901550002Lelio R Paula05/2008
933610^50000+6585950001Milton L. Brown02/2006
9337(598*10^49999-31)/950001Robert Price02/2017
935810^49999+9170150000Patrick De Geest03/2005
933810^50000-19430350000Patrick De Geest02/2009
9339(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9340(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9341(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9342(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9343(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9344(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9345(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9346(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9347(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9348(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
9349(2^6972593/10^381525)%10^5000050000Michael Vang05/2016
9350(2^30402457/10^1629036)%10^5000050000Michael Vang05/2016
9351(2^3021377/10^702316)%10^5000050000Michael Vang05/2016
9352(2^1398269/10^37827)%10^5000050000Michael Vang05/2016
9353(2^2976221/10^767789)%10^5000050000Michael Vang05/2016
9354(2^859433/10^42285)%10^5000050000Michael Vang06/2016
9355(2^1257787/10^119173)%10^5000050000Michael Vang06/2016
9356(2^756839/10^136257)%10^5000050000Michael Vang06/2016
93572*10^49999+36350000Makoto Morimoto09/2016
935910^49999-414949999Patrick De Geest02/2009
936010484^12433-12433^1048449988Norbert Schneider07/2013
93612^166052+14549987Lelio R Paula01/2011
9362(10^50001+10936)/(2^3*19*241*5872003*15974507)49983Makoto Morimoto09/2016
93631111*2^166022-55549981Henri Lifchitz02/2005
936411^47993+3049980Lelio R Paula10/2012
93652^166000-7879549971Lelio R Paula07/2011
936613517!-13517#+14997003/2005
93682^165995-11322749970Enzo Doria07/2014
9367(12227^12227+1092)/5/11/17/37^249970Makoto Morimoto07/2016
936917^40609+1449968Lelio R Paula11/2012
9371(1257656^8192+1)/6553749963Syoichiro Yamada06/2008
9370(3^104735-8)/149319993149963Lelio R Paula03/2012
93722^165969-11271149962Enzo Doria06/2014
93732^165910-760549944Lelio R Paula04/2009
937436313!3-5904949942Robert Price12/2015
93752^165884-4549937Lelio R Paula08/2010
9378(1246892^8192+1)/6553749933Syoichiro Yamada06/2008
93763^104654+10449933Lelio R Paula07/2012
93777452^12895-12895^745249933Norbert Schneider05/2017
93799035^12622+12622^903549932Norbert Schneider01/2016
9380(22699*2^165838+1)/328749924Lelio R Paula05/2014
93816^64149-8549918Lelio R Paula06/2012
9382(7*10^49913+71)/349914Robert Price03/2016
93832^165799-11481749911Enzo Doria05/2015
93842^165789+3549908Lelio R Paula08/2010
93852^165783-12149906Lelio R Paula01/2011
93862^165760-11264949899Enzo Doria06/2014
9387(11*2^165758+1)/13549898Lelio R Paula01/2012
93882^165747+6349895Lelio R Paula04/2009
9389(7*10^49893-13)/349894Robert Price06/2016
9390298^20163-20163^29849888Norbert Schneider08/2015
9391(49885^49885)/(10^184474)49885James G. Merickel08/2015
939217^40540+3649883Lelio R Paula11/2012
9393(12211^12211+4312)/13/17/31/1297/1483/1627/9923/3643349882Makoto Morimoto07/2016
93942^165676-11294949874Enzo Doria06/2014
9395(12203^12203+992)/1149867Makoto Morimoto07/2016
93967784^12811-12811^778449851Norbert Schneider03/2017
93972^165581-74549845Yves Minet01/2012
93982^165576+7482149844Enzo Doria04/2016
939913318^5527+5527^1331849843Hans Havermann04/2016
94012^165561-215549839Yves Minet08/2013
9400(12197^12197+1755)/2^449839Makoto Morimoto07/2016
94027406^12879+12879^740649837Norbert Schneider03/2016
94038530^12677+12677^853049833Norbert Schneider01/2016
9404(3^52222-69)^2-7149833Jorge Menendez02/2017
940512^46175+2949832Lelio R Paula10/2012
94062^165488-1296949817Enzo Doria10/2012
94072^165473+5890549813Lelio R Paula04/2009
940820^38284+4949809Lelio R Paula11/2012
94103^104388-2049806Lelio R Paula07/2012
9409(10^49806+119)/349806Serge Batalov12/2014
9411(1202206^8192+1)/6553749803Syoichiro Yamada06/2008
9412(4*10^49801+11)/349802Erik Branger05/2013
94135^71240-1547649795Enzo Doria02/2013
94147*3^104334-449781Lelio R Paula03/2014
9415(136*10^49774-1)/949776Serge Batalov12/2014
94163^104297+868049763Lelio R Paula07/2012
9417(F(10)^28579-F(9)^28579)/F(8)49737Wayne Halsdorf03/2010
9418(3^104243+1)/449736Kamil Duszenko05/2004
9419(10223*2^165183+1)/5549728Lelio R Paula05/2014
94206^63895+10149720Lelio R Paula06/2012
94213^104194+10049714Lelio R Paula07/2012
942210^49711+10359349712Patrick De Geest07/2017
942310^49711-70149711Robert Price06/2017
9424U(356793)49710Serge Batalov03/2015
942513321^5388+5388^1332149707Hans Havermann04/2016
942612166^12166+56549700Henri Lifchitz11/2004
9427(89*10^49689-53)/949690Erik Branger05/2013
9428(1163126^8192+1)/6553749685Syoichiro Yamada06/2008
942911^47709+4249684Lelio R Paula10/2012
9431(35*10^49682+1)/949683Serge Batalov05/2010
9430(12163^12163+1194)/37/19349683Makoto Morimoto07/2016
94323^104124+9249680Lelio R Paula07/2012
94342^165025+16502949678Henri Lifchitz04/2005
943314063^3408+3408^1406349678Hans Havermann04/2016
9435(2^165031+3)/4843949675Lelio R Paula01/2012
9436(7*2^165020-1)/26149675Lelio R Paula01/2014
94372^165000+522749670Lelio R Paula05/2011
9438(12161^12161+765)/2/13/29/277/31149670Makoto Morimoto07/2016
9439(110051^9851+1)/11005249660Faysal YAtim09/2007
94402^164962-63979149659Paul Bourdelais11/2012
944110^49657+3149658Robert Price01/2011
944210^49657-1289949657Patrick De Geest01/2012
94432^164937-19349651Lelio R Paula01/2011
944421^37549-20^3754949649Jean-Louis Charton02/2012
94451417^15754+15754^141749647Serge Batalov05/2014
9446(12157^12157+2611)/2^5/11/13/1019/48197/31440749643Makoto Morimoto07/2016
944712^45999+2549642Lelio R Paula10/2012
9448(3^104040+7)/849639Lelio R Paula03/2012
94492^164882-101749635Lelio R Paula06/2008
9450(3^104053-8)/38183002074345549632Lelio R Paula03/2012
945111^47658-18049631Enzo Doria07/2012
94522^164859-123749628Yves Minet08/2012
945317^40331+9849626Lelio R Paula11/2012
94541638^15437+15437^163849620Serge Batalov05/2014
9455113^24160+11249603Norbert Schneider09/2013
945613^44527+1649601Lelio R Paula11/2012
945783^25844+8249597Norbert Schneider01/2013
9458(12143^12143+1306)/3/7/5949593Makoto Morimoto07/2016
9459114667#-p(114667)49591Henri Lifchitz03/2007
94602^164731-183384749589Enzo Doria05/2015
9461(625^17737+1)/62649588Richard Fischer06/2013
94622^164714+2983549584Lelio R Paula11/2011
94637*10^49580-6949581Robert Price01/2017
94647*5^70922+449574Lelio R Paula09/2014
9465(229*10^49571-1)/349573Robert Price12/2016
9466277^20295-29049571Enzo Doria06/2012
94672^164662-11288349569Enzo Doria06/2014
9468(1125424^8192+1)/6553749568Syoichiro Yamada06/2008
94696^63698-3549567Lelio R Paula06/2012
9470(2^164652-3)*6-749566Gilbert Mozzo04/2016
9471(11*10^49552+43)/949553Erik Branger05/2013
94722^164606+4349552Lelio R Paula08/2010
94732^164598-11311149549Enzo Doria07/2014
947411^47575-810049545Enzo Doria02/2013
94759420^12467-12467^942049545Norbert Schneider07/2013
94762^164581-81925349544Paul Bourdelais11/2012
94779001^12528-12528^900149540Norbert Schneider11/2016
9478(lucasV(1,2,329135)+2)/(5^2*179*10247)49533Mike Oakes02/2017
9479(4*10^49529-31)/949529Erik Branger05/2011
948013875^3712+3712^1387549529Hans Havermann03/2016
94817^58604-6249527Lelio R Paula06/2012
94822^164508+10549522Lelio R Paula04/2009
948324^35878-93749520Enzo Doria03/2013
9484(89*10^49516-17)/949517Erik Branger05/2013
94852^164478-16749513Lelio R Paula01/2011
948613^44446+3049511Lelio R Paula11/2012
94872^164466-79024149510Paul Bourdelais11/2012
9488-lucasV(-1,2,328901)49505Mike Oakes01/2017
9489(21*2^164421-1)/53349495Lelio R Paula01/2014
949035^32052-20649491Enzo Doria03/2013
94913^103726-1187849490Enzo Doria02/2013
9492(3^103726+7)/51249488Lelio R Paula03/2012
9493(12119^12119+6270)/1349487Makoto Morimoto07/2016
949410^49484+1653749485Patrick De Geest01/2016
949610^49484-10^5384-149484Serge Batalov01/2011
949510^49484-9153949484Patrick De Geest01/2016
94973*2^164365-749480Lelio R Paula02/2014
9498(7^58543-5^58543)/249475Robert Price05/2012
94998482^12591+12591^848249464Norbert Schneider11/2015
9500(29*2^164309-1)/2090749460Lelio R Paula01/2014


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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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