PRP Records

Probable Primes Top 10000

(173006 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 ?
92512^165561-215549839Yves Minet08/2013
92527406^12879+12879^740649837Norbert Schneider03/2016
92538530^12677+12677^853049833Norbert Schneider01/2016
9254(3^52222-69)^2-7149833Jorge Menendez02/2017
925512^46175+2949832Lelio R Paula10/2012
92562^165488-1296949817Enzo Doria10/2012
92572^165473+5890549813Lelio R Paula04/2009
925820^38284+4949809Lelio R Paula11/2012
92603^104388-2049806Lelio R Paula07/2012
9259(10^49806+119)/349806Serge Batalov12/2014
9261(1202206^8192+1)/6553749803Syoichiro Yamada06/2008
9262(4*10^49801+11)/349802Erik Branger05/2013
92635^71240-1547649795Enzo Doria02/2013
92647*3^104334-449781Lelio R Paula03/2014
9265(136*10^49774-1)/949776Serge Batalov12/2014
92663^104297+868049763Lelio R Paula07/2012
9267(F(10)^28579-F(9)^28579)/F(8)49737Wayne Halsdorf03/2010
9268(3^104243+1)/449736Kamil Duszenko05/2004
9269(10223*2^165183+1)/5549728Lelio R Paula05/2014
92706^63895+10149720Lelio R Paula06/2012
92713^104194+10049714Lelio R Paula07/2012
9272U(356793)49710Serge Batalov03/2015
927313321^5388+5388^1332149707Hans Havermann04/2016
927412166^12166+56549700Henri Lifchitz11/2004
9275(89*10^49689-53)/949690Erik Branger05/2013
9276(1163126^8192+1)/6553749685Syoichiro Yamada06/2008
927711^47709+4249684Lelio R Paula10/2012
9278(35*10^49682+1)/949683Serge Batalov05/2010
9279(12163^12163+1194)/37/19349683Makoto Morimoto07/2016
92803^104124+9249680Lelio R Paula07/2012
92822^165025+16502949678Henri Lifchitz04/2005
928114063^3408+3408^1406349678Hans Havermann04/2016
9283(2^165031+3)/4843949675Lelio R Paula01/2012
9284(7*2^165020-1)/26149675Lelio R Paula01/2014
92862^165000+522749670Lelio R Paula05/2011
9285(12161^12161+765)/2/13/29/277/31149670Makoto Morimoto07/2016
9287(110051^9851+1)/11005249660Faysal YAtim09/2007
92882^164962-63979149659Paul Bourdelais11/2012
928910^49657+3149658Robert Price01/2011
929010^49657-1289949657Patrick De Geest01/2012
92912^164937-19349651Lelio R Paula01/2011
929221^37549-20^3754949649Jean-Louis Charton02/2012
92931417^15754+15754^141749647Serge Batalov05/2014
9294(12157^12157+2611)/2^5/11/13/1019/48197/31440749643Makoto Morimoto07/2016
929512^45999+2549642Lelio R Paula10/2012
9296(3^104040+7)/849639Lelio R Paula03/2012
92972^164882-101749635Lelio R Paula06/2008
9298(3^104053-8)/38183002074345549632Lelio R Paula03/2012
929911^47658-18049631Enzo Doria07/2012
93002^164859-123749628Yves Minet08/2012
930117^40331+9849626Lelio R Paula11/2012
93021638^15437+15437^163849620Serge Batalov05/2014
9303113^24160+11249603Norbert Schneider09/2013
930413^44527+1649601Lelio R Paula11/2012
930583^25844+8249597Norbert Schneider01/2013
9306(12143^12143+1306)/3/7/5949593Makoto Morimoto07/2016
9307114667#-p(114667)49591Henri Lifchitz03/2007
93082^164731-183384749589Enzo Doria05/2015
9309(625^17737+1)/62649588Richard Fischer06/2013
93102^164714+2983549584Lelio R Paula11/2011
93117*10^49580-6949581Robert Price01/2017
93127*5^70922+449574Lelio R Paula09/2014
9313(229*10^49571-1)/349573Robert Price12/2016
9314277^20295-29049571Enzo Doria06/2012
93152^164662-11288349569Enzo Doria06/2014
9316(1125424^8192+1)/6553749568Syoichiro Yamada06/2008
93176^63698-3549567Lelio R Paula06/2012
9318(2^164652-3)*6-749566Gilbert Mozzo04/2016
9319(11*10^49552+43)/949553Erik Branger05/2013
93202^164606+4349552Lelio R Paula08/2010
93212^164598-11311149549Enzo Doria07/2014
932211^47575-810049545Enzo Doria02/2013
93239420^12467-12467^942049545Norbert Schneider07/2013
93242^164581-81925349544Paul Bourdelais11/2012
93259001^12528-12528^900149540Norbert Schneider11/2016
9326(lucasV(1,2,329135)+2)/(5^2*179*10247)49533Mike Oakes02/2017
9327(4*10^49529-31)/949529Erik Branger05/2011
932813875^3712+3712^1387549529Hans Havermann03/2016
93297^58604-6249527Lelio R Paula06/2012
93302^164508+10549522Lelio R Paula04/2009
933124^35878-93749520Enzo Doria03/2013
9332(89*10^49516-17)/949517Erik Branger05/2013
93332^164478-16749513Lelio R Paula01/2011
933413^44446+3049511Lelio R Paula11/2012
93352^164466-79024149510Paul Bourdelais11/2012
9336-lucasV(-1,2,328901)49505Mike Oakes01/2017
9337(21*2^164421-1)/53349495Lelio R Paula01/2014
933835^32052-20649491Enzo Doria03/2013
93393^103726-1187849490Enzo Doria02/2013
9340(3^103726+7)/51249488Lelio R Paula03/2012
9341(12119^12119+6270)/1349487Makoto Morimoto07/2016
934210^49484+1653749485Patrick De Geest01/2016
934410^49484-10^5384-149484Serge Batalov01/2011
934310^49484-9153949484Patrick De Geest01/2016
93453*2^164365-749480Lelio R Paula02/2014
9346(7^58543-5^58543)/249475Robert Price05/2012
93478482^12591+12591^848249464Norbert Schneider11/2015
9348(29*2^164309-1)/2090749460Lelio R Paula01/2014
9349(12113^12113+3627)/2^2/5/19/1449629949451Makoto Morimoto07/2016
93505^70746-1601649450Enzo Doria02/2013
9351(2^164258+9)/1349446Lelio R Paula01/2012
93522^164255-11268749446Enzo Doria06/2014
9353(21*2^164222-1)/171749434Lelio R Paula01/2014
93542^164212+1270549433Lelio R Paula11/2011
93553*2^164205+749432Lelio R Paula02/2014
93562^164203+57729457549431Lelio R Paula02/2013
9357(12109^12109+2534)/3^2/23/24763/78102149430Makoto Morimoto07/2016
9358Pell-LucasQ(129127)/249427Eric W. Weisstein05/2006
93592^164187+769549426Lelio R Paula11/2011
93603^103585-2649423Lelio R Paula07/2012
9361(3*2^164194+1)/1425501749421Lelio R Paula07/2012
936210^49415+7683749416Patrick De Geest01/2016
936510^49415-6^49415-4^49415-149415Mike Oakes01/2010
936310^49415-3281349415Patrick De Geest01/2016
936412943^6574+6574^1294349415Hans Havermann02/2016
9366(6^63497-61)/2549409Lelio R Paula05/2014
936711376^12181+12181^1137649407Norbert Schneider12/2013
93682^164110-1749403Lelio R Paula08/2010
936912^45773+4149398Lelio R Paula10/2012
93702^164090+425749397Lelio R Paula04/2009
9371(12101^12101+1403)/2^4/193/349/160231/692768949389Makoto Morimoto07/2016
93722^164061-388949388Yves Minet04/2017
93732^164046+2549383Lelio R Paula01/2009
9374(24737*2^164045+1)/590658549381Lelio R Paula05/2014
9375(12097^12097+1922)/3/139/225340949380Makoto Morimoto07/2016
93775^70640-1829649376Enzo Doria02/2013
9376(9179*2^164010-1)/549376Lelio R Paula03/2015
9378(-lucasV(1,2,328052)+2)/10896149372Mike Oakes02/2017
93799*2^164002-749371Lelio R Paula02/2014
93805^70626-4449366Lelio R Paula06/2012
938111^47396-105049358Enzo Doria11/2012
9382(13*2^163956+1)/749356Lelio R Paula07/2012
93842^163934-13549350Lelio R Paula01/2011
93833^103431+2049350Lelio R Paula07/2012
93857192^12795-12795^719249349Norbert Schneider03/2017
938613^44300+2249348Lelio R Paula11/2012
9387(2^163904+3)/749340Lelio R Paula01/2012
93882^163872+1291549331Lelio R Paula11/2011
9389130^23332-12949323Norbert Schneider03/2015
93907^58357-3849318Lelio R Paula06/2012
93917760^12677-12677^776049312Norbert Schneider01/2017
939213^44265-249309Lelio R Paula11/2012
9394(19*2^163785+1)/204349303Lelio R Paula01/2012
93932^163781-174149303Yves Minet09/2012
93954*5^70529+349299Lelio R Paula09/2014
9396(2^163742-3)/13149290Lelio R Paula01/2012
93975^70514-1721649288Enzo Doria02/2013
93982^163727-174149287Yves Minet09/2012
9399Linear(0,1,1,-1,327433)49283Henri Lifchitz04/2007
94005^70498-1757649276Enzo Doria02/2013
9401(12073^12073+1070)/3/13/3106349274Makoto Morimoto07/2016
94022^163667+7211349269Enzo Doria04/2016
94035^70484-1769649267Enzo Doria02/2013
9404(12071^12071+4263)/2/101/1148949265Makoto Morimoto07/2016
94057^58293+6649264Lelio R Paula06/2012
9406(52*10^49261-1)/349263Robert Price02/2017
94072671^14376-11449262Enzo Doria06/2012
9408(15185*2^163636-1)/20949262Lelio R Paula03/2015
94092^163630+18349258Lelio R Paula01/2011
94102^163560+1549237Lelio R Paula08/2010
94123^103189+11049234Lelio R Paula07/2012
9411(41*10^49233+31)/949234Erik Branger05/2013
9413(1023052^8192+1)/6553749229Syoichiro Yamada05/2008
94142*10^49216+9349217Robert Price07/2016
94152^163453+88549205Lelio R Paula10/2011
9416(67607*2^163432+1)/349203Lelio R Paula05/2014
941715^41835-4649202Lelio R Paula11/2012
941810^49190+4550749191Patrick De Geest01/2016
942010^49190-601865949190Marisa Kirisame02/2015
941910^49190-15443149190Patrick De Geest01/2016
94212^163385+9439549184Henri Lifchitz01/2005
94222^163382-202149183Yves Minet03/2013
9424(55*10^49169-1)/949170Ray Chandler02/2012
94232^163336-1517749170Enzo Doria04/2013
94258323^12542-12542^832349169Norbert Schneider11/2016
9426(10^49165-991)/949165Serge Batalov07/2010
94277^58169-6^(58169+1)49159Robert Price06/2016
9429(F(5)^70327-F(4)^70327)/F(3)49157Wayne Halsdorf01/2010
9428(5^70327-3^70327)/249157Robert Price08/2011
94302^163283+5461549154Lelio R Paula04/2009
943118388^471+471^1838849152Anatoly F. Selevich12/2006
9432(12043^12043+799)/2/15749142Makoto Morimoto07/2016
943314^42875+6949141Lelio R Paula11/2012
9434(2^163243+9)/1749140Lelio R Paula01/2012
9435(F(770)^307-F(769)^307)/F(768)49136Wayne Halsdorf02/2010
9436(12041^12041+467)/2^2/23/4749132Makoto Morimoto07/2016
94375^70290-1944649131Enzo Doria03/2013
9438(F(760)^311-F(759)^311)/F(758)49130Wayne Halsdorf02/2010
94395^70286-2004649128Enzo Doria03/2013
944012^45519-9149124Lelio R Paula10/2012
94417^58126+7249123Lelio R Paula06/2012
94427^58125+449122Lelio R Paula06/2012
9443(991537^8192+1)/249122Lelio R Paula12/2014
9444(14*10^49119-11)/349120Erik Branger05/2013
9445t(185595)49118Robert Price12/2013
9446(2*10^49117+457)/949117Robert Price01/2017
9447(988635^8192+1)/249112Lelio R Paula12/2014
9448(26*10^49106-23)/349107Robert Price08/2016
9449(986617^8192+1)/249104Lelio R Paula12/2014
945014313^2696+2696^1431349104Hans Havermann08/2015
9451(89*10^49101-53)/949102Erik Branger05/2013
94529*7^58099-449101Lelio R Paula09/2014
9453(-lucasV(1,2,326291)+2)/(5*83563*7935289)49100Mike Oakes02/2017
945423^36054-105049096Enzo Doria08/2012
9455(984325^8192+1)/13107449091Lelio R Paula12/2014
9456(3^51443-87)^2-8949090Jorge Menendez02/2017
9457928649*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9458592271*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9459580043*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9460555500*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9461512651*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9462143358*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9463107445*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9464117360*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
946528124*2*((10^49081-1)/9)+149085Danilo Nitsche01/2016
946618^39100-2949082Lelio R Paula11/2012
9467(10^49081-1)/949081Harvey Dubner09/1999
9468(978811^8192+1)/249076Lelio R Paula12/2014
946917200^713+713^1720049074Anatoly F. Selevich07/2006
94709*2^163006+549071Lelio R Paula02/2014
947111^47113-171049064Enzo Doria11/2012
947211^47106-141049056Enzo Doria11/2012
94732^162954-2349055Lelio R Paula08/2010
94742^162924-2863549046Lelio R Paula04/2009
947524771!2-849045Robert Price06/2015
9476(26*10^49039-77)/349040Robert Price02/2017
94775^70155-449037Theodore Burton11/2005
94783^102763-1449031Lelio R Paula06/2012
9479(21*2^162876+1)/2349031Lelio R Paula07/2012
94805^70146+5849030Lelio R Paula06/2012
94812^162864-74438949027Paul Bourdelais11/2012
94822^162860-11285949026Enzo Doria06/2014
9483(10^49025-1)/3-2*10^2451249025Patrick De Geest07/2005
94852^162856-22920949025Enzo Doria01/2013
9484(10^(2*24512+1)-6*10^24512-1)/349025Robert Price02/2016
9486(965897^8192+1)/32768249024Lelio R Paula12/2014
9487(5*2^162859-1)/5391949022Lelio R Paula01/2014
94886^62990+3149016Lelio R Paula06/2012
948946329!4+249014Robert Price03/2017
94902^162816-21920949013Enzo Doria11/2012
9491(127^23297-1)/12649011Alexander Zhirkov10/2010
9492(13^43997+12^43997)/2549009Robert Price04/2013
949310^49008+6666949009Patrick De Geest01/2016
949410^49008-503749008Robert Price09/2015
94955^70110+5249005Lelio R Paula06/2012
949610^49000+21303749001Patrick De Geest07/2012
949715^41664-9449001Lelio R Paula11/2012
94983^102699-34049000Lelio R Paula06/2012
949910^49000-62149000Patrick De Geest07/2012
950010^48999+26879149000Patrick De Geest07/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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