PRP Records

Probable Primes Top 10000

(255244 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 (> 50000) Who ? When ?
700113^66628+4674220Lelio R Paula01/2015
70022^246476-1729574197Lelio R Paula05/2013
7003(61*10^74189-1)/374191Robert Price11/2017
7004(15185*2^246432-1)/1374187Lelio R Paula04/2015
70055*2^246413-374179Lelio R Paula05/2014
70062^246386-2863574170Lelio R Paula05/2013
70072^246334-11124574154Enzo Doria05/2014
70083*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
700915^63045+8274147Lelio R Paula01/2015
701019255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
70112^246268-11050774135Enzo Doria05/2014
70123^155328+266074111Lelio R Paula01/2015
70132^246148-278624974098Enzo Doria03/2016
7014(16*10^74092-19)/374093Robert Price03/2016
70152^246115-11076774088Enzo Doria05/2014
70167^87666-6874087Lelio R Paula08/2014
701710^74079+114514191974080Marisa Kirisame03/2015
701810^74079+621974080Patrick De Geest03/2016
701910^74079-28270774079Patrick De Geest03/2016
7020129^35098+274078Lelio R Paula05/2013
70212^246025-11212374061Enzo Doria06/2014
7022(67*10^74045+17)/374047Robert Price02/2017
70232^245823+6683174001Marek Hubal02/2017
70245^105869+4274000Lelio R Paula08/2014
7025(21*2^245806+1)/63455573991Lelio R Paula08/2012
7026(22699*2^245762+1)/11973985Lelio R Paula06/2014
7027(3^155048-7)/26273975Lelio R Paula06/2012
70289998*2^245696+373966Donovan Johnson10/2004
702913^66400-8073966Lelio R Paula01/2015
7031(2^245704+9)/2573963Lelio R Paula07/2012
703211^71023-717073963Enzo Doria01/2013
70303*10^73962+1373963Robert Price08/2017
7033(31*2^245660-1)/11419573948Lelio R Paula01/2014
70342^245629-279781373942Eric Chen03/2016
70352^245557-15373921Lelio R Paula03/2012
7037(77*10^73917-59)/973918Robert Price11/2017
703615010^17699+17699^1501073918Norbert Schneider11/2019
70382^245525+186988173911Enzo Doria06/2016
70392^245522+15973910Lelio R Paula03/2012
7040(13*10^73891-43)/373892Robert Price08/2017
704119^57783-5673891Lelio R Paula01/2015
70427*10^73888+7973889Robert Price02/2017
70436^94948+17428173884Mike Oakes02/2011
704411^70939-486073876Enzo Doria01/2013
70452^245372+5461573865Lelio R Paula05/2013
70462^245362-14373862Lelio R Paula03/2012
70477^87396+6^(87396-1)73859Robert Price03/2016
7048(22*10^73853-37)/373854Robert Price05/2017
70495^105646-1424673844Enzo Doria02/2013
70512^245290-4173840Lelio R Paula03/2012
70502^245290-9439573840Lelio R Paula05/2013
705215770^17589+17589^1577073836Norbert Schneider10/2019
705312352^18043+18043^1235273828Norbert Schneider11/2019
70548*5^105600-773813Lelio R Paula10/2014
70557*5^105573-473794Lelio R Paula10/2014
705618^58742-480573738Enzo Doria03/2013
705713^66179+6673720Lelio R Paula01/2015
7058(82*10^73714-1)/973715Robert Price12/2014
7059(29*2^244856-1)/18612173706Lelio R Paula01/2014
7060(13*2^244840-1)/279973702Lelio R Paula01/2014
7061(13*10^73701+17)/373702Robert Price06/2015
7062(2^244787-1017)/2841173684Lelio R Paula07/2012
7063(3^154421-4)/2373677Lelio R Paula06/2012
706414596^17691+17691^1459673670Norbert Schneider11/2019
70658*7^87170+573669Lelio R Paula10/2014
7066(29*10^73659-113)/373660Robert Price11/2017
7067Phi(40100,-40100)73651Henri Lifchitz06/2013
7068(4*10^73647-19)/373648Robert Price06/2017
70692^244618-229773638Yves Minet10/2009
70703*5^105344+873633Lelio R Paula10/2014
70715^105334-1409673626Enzo Doria02/2013
7072(2^244584-7)/1323707424303373614Lelio R Paula07/2012
70732^244465-11018573592Enzo Doria05/2014
70742^244443+4075573585Lelio R Paula05/2013
70752^244404+384173573Yves Minet03/2011
70762^244372-11062773564Enzo Doria05/2014
7077(3*2^244255+1)/24573527Lelio R Paula08/2012
7078(11*2^244245+1)/2373525Lelio R Paula08/2012
7079(15185*2^244187-1)/611173509Lelio R Paula04/2015
708017063^17362+17362^1706373477Norbert Schneider04/2019
7081(91^37507+1)/9273476Paul Bourdelais08/2017
708218^58521+6573460Lelio R Paula01/2015
708313^65940+3673454Lelio R Paula01/2015
7084(625^26267+1)/62673437Richard Fischer12/2017
70855^105050-1473427Lelio R Paula08/2014
7086(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
708715^62410-4673400Lelio R Paula01/2015
70882^243733+186970773371Enzo Doria05/2016
708911^70439-543073355Enzo Doria01/2013
70902^243676-8773354Lelio R Paula03/2012
7091(101*10^73346-17)/373348Robert Price08/2016
70922^243621-11318573338Enzo Doria07/2014
7093(5*2^243610-1)/166973332Lelio R Paula01/2014
70942*5^104888-773314Lelio R Paula10/2014
7095(58695*2^243516-1)/98373308Lelio R Paula04/2015
7096(3^153648-2)/3342313809773299Lelio R Paula06/2012
709718^58376-525573278Enzo Doria03/2013
709811^70363+3273276Lelio R Paula02/2015
70992^243413+425773275Lelio R Paula05/2013
7100104824^5+5^10482473269Andrey Kulsha07/2010
71017^86689-6^8668973261Predrag Minovic09/2004
71022^243296+9019573240Lelio R Paula05/2013
71032^243281-484373235Yves Minet05/2019
7104p(15433)#/2-473218Robert Price12/2016
7105(59*10^73217-77)/973218Robert Price11/2017
71062^243127+7135573189Lelio R Paula05/2013
71072^243116-24941973186Paul Bourdelais03/2013
7108(58695*2^243085-1)/1173180Lelio R Paula04/2015
710911^70262-9873171Lelio R Paula02/2015
7110(2^243034+47)/72270330373152Lelio R Paula07/2012
7111(2^242966+47)/4688773136Lelio R Paula07/2012
7112(43^44773-1)/4273134Robert Price04/2014
71136^93980-15835973131Mike Oakes02/2011
711419953^4616+4616^1995373114Hans Havermann11/2019
71156^93915+5373081Lelio R Paula01/2015
7116(5*10^73079+211)/973079Robert Price12/2017
7117(74*10^73076+43)/973077Robert Price10/2015
7118(3^153125+2)/114495573054Lelio R Paula06/2012
71192^242632-11219973040Enzo Doria06/2014
7120V(351646)73029Serge Batalov03/2015
712118^58175-8573026Lelio R Paula01/2015
7122p(15395)#/2-473019Robert Price12/2016
7123(4^121271+3^121271)/773012Jean-Louis Charton03/2011
71248*6^93825-573011Lelio R Paula10/2014
7126(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
7125(73^39181+1)/7473005Paul Bourdelais08/2017
71276^93815+14373003Lelio R Paula01/2015
71286^93812+573000Wojciech Florek03/2006
712919^57078-6272989Lelio R Paula01/2015
7130(29*10^72985+91)/372986Robert Price03/2016
713120691^3368+3368^2069172985Hans Havermann10/2019
713211^70082-252072983Enzo Doria12/2012
71336^93773+13372970Lelio R Paula01/2015
71342^242328-5972948Lelio R Paula03/2012
71355^104358-1301672944Enzo Doria02/2013
7136(75*10^72941-57)/9972941Ray Chandler03/2011
713712^67585-9572937Lelio R Paula02/2015
71382^242230-11328572919Enzo Doria07/2014
7139(5*10^72916-11)/372917Erik Branger12/2013
71402^242220-11039972916Enzo Doria05/2014
71412^242205-11341372911Enzo Doria07/2014
7142(3^152809+3^76405+1)/772908Serge Batalov03/2014
71432^242175+7424372902Yves Minet03/2011
71442^242150+1765972895Lelio R Paula11/2009
714511^69982-234072879Enzo Doria12/2012
7146(23*2^242093+1)/1011772875Lelio R Paula08/2012
7147(67607*2^242043+1)/3326372863Lelio R Paula06/2014
71482^242032+8772859Lelio R Paula03/2012
71492^241968-11059572840Enzo Doria05/2014
715018850^7313+7313^1885072839Hans Havermann11/2019
7151(10^72821+71)/972821Robert Price11/2014
71522^241852-6487572805Lelio R Paula05/2013
7153F(348307)/2056289086590809372776Donovan Johnson07/2007
715413952^17559+17559^1395272776Norbert Schneider09/2019
7155(67*10^72772+23)/972773Ray Chandler11/2010
7156(8*10^72759+67)/372760Robert Price01/2017
71572^241670+14572750Lelio R Paula03/2012
71585^104074+5272745Lelio R Paula08/2014
7159(3^152466-5)/72472742Lelio R Paula06/2012
716020^55908-4172738Lelio R Paula01/2015
7161(73*10^72735+53)/972736Robert Price10/2015
716210^72730+22401172731Patrick De Geest05/2013
716310^72730-9972730Robert Price05/2011
71643*10^72723+6772724Robert Price11/2017
7166(11^69833+3^69833)/1472723Robert Price03/2013
7165(10^72723-79)/372723Robert Price10/2017
7167(88*10^72711-43)/972712Robert Price11/2015
71683^152379+28072704Lelio R Paula01/2015
7169(25*10^72703-241)/972704Robert Price01/2017
7170(47*10^72696+133)/972697Robert Price04/2017
717117^59077-9072692Lelio R Paula01/2015
717265^40096+5872691Lelio R Paula01/2016
7173(29*2^241446-1)/24572682Lelio R Paula01/2014
717511^69783-3840000072672Enzo Doria01/2013
71742^241409-11290372672Enzo Doria06/2014
717618895^7014+7014^1889572670Hans Havermann11/2019
7177(3^152287+1)/472659Paul Bourdelais04/2008
71783^152249-5672642Lelio R Paula01/2015
717910^72631+3772632Robert Price01/2011
718010^72631-881372631Patrick De Geest05/2013
7181(19*2^241254+1)/10172624Lelio R Paula08/2012
7182(9^76103+8^76103)/1772620Robert Price12/2012
71832^241220-11233772615Enzo Doria06/2014
7184(82*10^72612+449)/972613Robert Price02/2017
71852^241169-1579372600Enzo Doria04/2013
71869*10^72595+1172596Robert Kinser01/2017
7187(25*2^241048+1)/8972563Lelio R Paula08/2012
7188(22*10^72560+17)/372561Robert Price09/2015
71892^241032-2372558Lelio R Paula02/2012
719034485*10^72550+2^241004-372555Gilbert Mozzo12/2012
71912^241004-372550M. Frind & P. Underwood07/2002
719222061^1942+1942^2206172543Hans Havermann11/2019
719397*10^72522-372524Robert Price01/2017
7194(68*10^72516+7)/372518Robert Price03/2016
7195(78557*2^240844+1)/6372505Lelio R Paula06/2014
719667^39701-6672497Norbert Schneider11/2014
7197(185*10^72484+7)/372486Robert Price02/2017
7199(293*27^50631-1736)/1372473Curtis Bright05/2015
7198103^36005-10272473Norbert Schneider10/2016
720015^61616+8872467Lelio R Paula01/2015
720145^43831+272462Lelio R Paula05/2013
72022^240692-49238972456Paul Bourdelais03/2013
7203(646*10^72446-7)/972448Robert Price07/2016
72049*6^93083+772434Lelio R Paula10/2014
72052^240617-364572433Lelio R Paula05/2013
720611^69531-2400072410Enzo Doria12/2012
7207(22699*2^240396+1)/5572370Lelio R Paula06/2014
72086^92995+1372365Lelio R Paula01/2015
7209(11*10^72362-149)/372363Robert Price01/2017
7210(2^240381+3)/5165572358Lelio R Paula05/2012
72116^92974-5572348Lelio R Paula01/2015
72122^240295+1172337Lelio R Paula02/2012
7213(14*10^72326-53)/372327Robert Price12/2016
721415^61493-4672322Lelio R Paula01/2015
7215lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
72165*10^72302+972303Dmitry Domanov11/2010
7217(9787*2^240179-1)/26572303Lelio R Paula04/2015
721811^69419-312072293Enzo Doria12/2012
72194*10^72274-8372275Robert Price10/2017
722010^72267+3372268Robert Price01/2011
722110^72267-55394772267Patrick De Geest05/2013
722211^69389-138072262Enzo Doria12/2012
7223(16^60013-5^60013)/1172262Robert Price07/2013
72247^85507-3072262Lelio R Paula08/2014
7225(19*2^240026-1)/1572256Lelio R Paula02/2014
7226(3^151426-2)/66133772243Lelio R Paula06/2012
7227gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
72282^239863-11226772206Enzo Doria06/2014
72292^239853-11485372203Enzo Doria05/2015
7230(4*10^72174+149)/972174Robert Price03/2017
7232(2^239671+9)/29613172143Lelio R Paula05/2012
72312^239651-11066572143Enzo Doria05/2014
7233(29*2^239650-1)/330572140Lelio R Paula01/2014
7234241^30280+30280^24172128Norbert Schneider11/2014
7235(68*10^72120-23)/972121Robert Price10/2015
7236(9^75571+8^75571)/1772112Robert Price12/2012
7237(15*2^239530-1)/17372105Lelio R Paula01/2014
72382^239513-11251972101Enzo Doria06/2014
7239(10^72097+149)/372097Serge Batalov12/2014
72402^239442-655572080Lelio R Paula05/2012
72412*5^103106+372069Lelio R Paula10/2014
72422^239402-19772068Lelio R Paula02/2012
72432^239356-11187572054Enzo Doria05/2014
7244(38*10^72050-119)/972051Robert Price11/2016
72452^239339+1501572049Lelio R Paula01/2013
7246159^32728+272048Lelio R Paula05/2013
724715^61259-3872047Lelio R Paula01/2015
724892^36683-91^3668372038Robert Price08/2015
72492^239280+5461572031Lelio R Paula05/2012
7250(47*2^239267+1)/7772027Lelio R Paula04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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