PRP Records

Probable Primes Top 10000

(252932 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 ?
67512*5^104888-773314Lelio R Paula10/2014
6752(58695*2^243516-1)/98373308Lelio R Paula04/2015
6753(3^153648-2)/3342313809773299Lelio R Paula06/2012
675418^58376-525573278Enzo Doria03/2013
675511^70363+3273276Lelio R Paula02/2015
67562^243413+425773275Lelio R Paula05/2013
6757104824^5+5^10482473269Andrey Kulsha07/2010
67587^86689-6^8668973261Predrag Minovic09/2004
67592^243296+9019573240Lelio R Paula05/2013
67602^243281-484373235Yves Minet05/2019
6762p(15433)#/2-473218Robert Price12/2016
6761(59*10^73217-77)/973218Robert Price11/2017
67632^243127+7135573189Lelio R Paula05/2013
67642^243116-24941973186Paul Bourdelais03/2013
6765(58695*2^243085-1)/1173180Lelio R Paula04/2015
676611^70262-9873171Lelio R Paula02/2015
6767(2^243034+47)/72270330373152Lelio R Paula07/2012
6768(2^242966+47)/4688773136Lelio R Paula07/2012
6769(43^44773-1)/4273134Robert Price04/2014
67706^93980-15835973131Mike Oakes02/2011
67716^93915+5373081Lelio R Paula01/2015
6772(5*10^73079+211)/973079Robert Price12/2017
6773(74*10^73076+43)/973077Robert Price10/2015
6774(3^153125+2)/114495573054Lelio R Paula06/2012
67752^242632-11219973040Enzo Doria06/2014
6776V(351646)73029Serge Batalov03/2015
677718^58175-8573026Lelio R Paula01/2015
6778p(15395)#/2-473019Robert Price12/2016
6779(4^121271+3^121271)/773012Jean-Louis Charton03/2011
67808*6^93825-573011Lelio R Paula10/2014
6781(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
6782(73^39181+1)/7473005Paul Bourdelais08/2017
67836^93815+14373003Lelio R Paula01/2015
67846^93812+573000Wojciech Florek03/2006
678519^57078-6272989Lelio R Paula01/2015
6786(29*10^72985+91)/372986Robert Price03/2016
678711^70082-252072983Enzo Doria12/2012
67886^93773+13372970Lelio R Paula01/2015
67892^242328-5972948Lelio R Paula03/2012
67905^104358-1301672944Enzo Doria02/2013
6791(75*10^72941-57)/9972941Ray Chandler03/2011
679212^67585-9572937Lelio R Paula02/2015
67932^242230-11328572919Enzo Doria07/2014
6794(5*10^72916-11)/372917Erik Branger12/2013
67952^242220-11039972916Enzo Doria05/2014
67962^242205-11341372911Enzo Doria07/2014
6797(3^152809+3^76405+1)/772908Serge Batalov03/2014
67982^242175+7424372902Yves Minet03/2011
67992^242150+1765972895Lelio R Paula11/2009
680011^69982-234072879Enzo Doria12/2012
6801(23*2^242093+1)/1011772875Lelio R Paula08/2012
6802(67607*2^242043+1)/3326372863Lelio R Paula06/2014
68032^242032+8772859Lelio R Paula03/2012
68042^241968-11059572840Enzo Doria05/2014
6805(10^72821+71)/972821Robert Price11/2014
68062^241852-6487572805Lelio R Paula05/2013
6807F(348307)/2056289086590809372776Donovan Johnson07/2007
6808(67*10^72772+23)/972773Ray Chandler11/2010
6809(8*10^72759+67)/372760Robert Price01/2017
68102^241670+14572750Lelio R Paula03/2012
68115^104074+5272745Lelio R Paula08/2014
6812(3^152466-5)/72472742Lelio R Paula06/2012
681320^55908-4172738Lelio R Paula01/2015
6814(73*10^72735+53)/972736Robert Price10/2015
681510^72730+22401172731Patrick De Geest05/2013
681610^72730-9972730Robert Price05/2011
68173*10^72723+6772724Robert Price11/2017
6818(11^69833+3^69833)/1472723Robert Price03/2013
6819(10^72723-79)/372723Robert Price10/2017
6820(88*10^72711-43)/972712Robert Price11/2015
68213^152379+28072704Lelio R Paula01/2015
6822(25*10^72703-241)/972704Robert Price01/2017
6823(47*10^72696+133)/972697Robert Price04/2017
682417^59077-9072692Lelio R Paula01/2015
682565^40096+5872691Lelio R Paula01/2016
6826(29*2^241446-1)/24572682Lelio R Paula01/2014
682811^69783-3840000072672Enzo Doria01/2013
68272^241409-11290372672Enzo Doria06/2014
6829(3^152287+1)/472659Paul Bourdelais04/2008
68303^152249-5672642Lelio R Paula01/2015
683110^72631+3772632Robert Price01/2011
683210^72631-881372631Patrick De Geest05/2013
6833(19*2^241254+1)/10172624Lelio R Paula08/2012
6834(9^76103+8^76103)/1772620Robert Price12/2012
68352^241220-11233772615Enzo Doria06/2014
6836(82*10^72612+449)/972613Robert Price02/2017
68372^241169-1579372600Enzo Doria04/2013
68389*10^72595+1172596Robert Kinser01/2017
6839(25*2^241048+1)/8972563Lelio R Paula08/2012
6840(22*10^72560+17)/372561Robert Price09/2015
68412^241032-2372558Lelio R Paula02/2012
684234485*10^72550+2^241004-372555Gilbert Mozzo12/2012
68432^241004-372550M. Frind & P. Underwood07/2002
684497*10^72522-372524Robert Price01/2017
6845(68*10^72516+7)/372518Robert Price03/2016
6846(78557*2^240844+1)/6372505Lelio R Paula06/2014
684767^39701-6672497Norbert Schneider11/2014
6848(185*10^72484+7)/372486Robert Price02/2017
6850(293*27^50631-1736)/1372473Curtis Bright05/2015
6849103^36005-10272473Norbert Schneider10/2016
685115^61616+8872467Lelio R Paula01/2015
685245^43831+272462Lelio R Paula05/2013
68532^240692-49238972456Paul Bourdelais03/2013
6854(646*10^72446-7)/972448Robert Price07/2016
68559*6^93083+772434Lelio R Paula10/2014
68562^240617-364572433Lelio R Paula05/2013
685711^69531-2400072410Enzo Doria12/2012
6858(22699*2^240396+1)/5572370Lelio R Paula06/2014
68596^92995+1372365Lelio R Paula01/2015
6860(11*10^72362-149)/372363Robert Price01/2017
6861(2^240381+3)/5165572358Lelio R Paula05/2012
68626^92974-5572348Lelio R Paula01/2015
68632^240295+1172337Lelio R Paula02/2012
6864(14*10^72326-53)/372327Robert Price12/2016
686515^61493-4672322Lelio R Paula01/2015
6866lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
68675*10^72302+972303Dmitry Domanov11/2010
6868(9787*2^240179-1)/26572303Lelio R Paula04/2015
686911^69419-312072293Enzo Doria12/2012
68704*10^72274-8372275Robert Price10/2017
687110^72267+3372268Robert Price01/2011
687210^72267-55394772267Patrick De Geest05/2013
687311^69389-138072262Enzo Doria12/2012
6874(16^60013-5^60013)/1172262Robert Price07/2013
68757^85507-3072262Lelio R Paula08/2014
6876(19*2^240026-1)/1572256Lelio R Paula02/2014
6877(3^151426-2)/66133772243Lelio R Paula06/2012
6878gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
68792^239863-11226772206Enzo Doria06/2014
68802^239853-11485372203Enzo Doria05/2015
6881(4*10^72174+149)/972174Robert Price03/2017
6882(2^239671+9)/29613172143Lelio R Paula05/2012
68832^239651-11066572143Enzo Doria05/2014
6884(29*2^239650-1)/330572140Lelio R Paula01/2014
6885241^30280+30280^24172128Norbert Schneider11/2014
6886(68*10^72120-23)/972121Robert Price10/2015
6887(9^75571+8^75571)/1772112Robert Price12/2012
6888(15*2^239530-1)/17372105Lelio R Paula01/2014
68892^239513-11251972101Enzo Doria06/2014
6890(10^72097+149)/372097Serge Batalov12/2014
68912^239442-655572080Lelio R Paula05/2012
68922*5^103106+372069Lelio R Paula10/2014
68932^239402-19772068Lelio R Paula02/2012
68942^239356-11187572054Enzo Doria05/2014
6895(38*10^72050-119)/972051Robert Price11/2016
68962^239339+1501572049Lelio R Paula01/2013
6897159^32728+272048Lelio R Paula05/2013
689815^61259-3872047Lelio R Paula01/2015
689992^36683-91^3668372038Robert Price08/2015
69002^239280+5461572031Lelio R Paula05/2012
6902(47*2^239267+1)/7772027Lelio R Paula04/2015
6901(85*10^72025-1)/372027Robert Price07/2017
69032^239236-9730572018Lelio R Paula05/2012
6904144^33361-14372006Norbert Schneider11/2018
69052^239169+5971998Lelio R Paula02/2012
6907lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
6906(15*2^239171-1)/10630171994Lelio R Paula01/2014
6908(29^49211-1)/2871965Robert Price04/2012
6909(299*10^71963+1)/371965Robert Price11/2017
6911L(344293)71953Renaud Lifchitz09/2003
6910V(344293)71953Serge Batalov03/2015
69126*10^71951+771952Dmitry Domanov11/2010
69133^150798+4071949Lelio R Paula01/2015
69142^238961+9571935Lelio R Paula02/2012
69152^238936-40771927Yves Minet02/2012
69162^238923-2863571923Lelio R Paula05/2012
691710^71910+2511971911Patrick De Geest05/2016
691810^71910-80171910Robert Price04/2016
69192^238845-11265171900Enzo Doria06/2014
69202^238792-11124571884Enzo Doria05/2014
69216*7^85059+571884Lelio R Paula10/2014
69222^238752-11058971872Enzo Doria05/2014
692312^66581+771853Lelio R Paula07/2014
6924(7*2^238691+1)/4122971850Lelio R Paula06/2012
69254*3^150568-571840Lelio R Paula04/2014
69266^92301+6771825Lelio R Paula01/2015
69272^238568+9876533171817Jason Earls01/2009
69282^238541-11272371808Enzo Doria06/2014
69292^238529-1594971805Enzo Doria04/2013
69309*5^102721-871800Lelio R Paula10/2014
69312^238494-16571794Lelio R Paula02/2012
69322^238389-11090571763Enzo Doria05/2014
6933(145*10^71760-1)/971762Serge Batalov12/2014
69347^84913+506271760Mike Oakes02/2010
6935(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
69362^238268-9730571726Lelio R Paula05/2012
6937gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
69382^238235-11324771716Enzo Doria07/2014
69392*12^66450-5^6645071712Mike Oakes11/2010
6940(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
69412^238199-11181771706Enzo Doria05/2014
6942lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
69432^238144+9876533171689Jason Earls01/2009
694418^57102-426571679Enzo Doria03/2013
6945(73*10^71670-1)/971671Robert Price01/2015
69462^238081+1155*23808171670Henri Lifchitz02/2005
69472^238067-11192571666Enzo Doria05/2014
694836^46030+3571637Norbert Schneider04/2014
6949(74*10^71621+313)/971622Robert Price11/2017
69502^237905-9171617Lelio R Paula02/2012
6951(31*2^237902-1)/12371616Lelio R Paula01/2014
6952(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6953(24737*2^237841+1)/2571601Lelio R Paula06/2014
69542^237846+129971599Lelio R Paula05/2012
69556^92004+19980171594Mike Oakes02/2011
6956159^32516+271581Lelio R Paula05/2013
69572^237781+85571580Lelio R Paula05/2012
69582^237720-407971561Yves Minet06/2011
69592^237698-11094571555Enzo Doria05/2014
69602^237695-11323971554Enzo Doria07/2014
69618*5^102362-971549Lelio R Paula10/2014
6962(4*10^71546-31)/971546Erik Branger05/2011
69632^237650+3771540Lelio R Paula02/2012
696418^56977-439171522Enzo Doria03/2013
6965(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6966((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
6967(26*10^71503+7)/371504Erik Branger11/2013
6968(4*10^71498+173)/371499Robert Price01/2017
69693^149848+11071496Lelio R Paula11/2014
69702^237498+51371495Lelio R Paula05/2012
69712^237485+10771491Lelio R Paula02/2012
6972(2^237465+9)/241971481Lelio R Paula05/2012
69732^237439-11223771477Enzo Doria06/2014
69742^237407-978771467Lelio R Paula11/2009
69752^237383+7295371460Enzo Doria04/2016
697682^37337-81^3733771457Robert Price01/2015
6977(1017*2^237313-1)/1971441Lelio R Paula04/2015
69782^237311+19171438Lelio R Paula02/2012
69792^237280-5971429Lelio R Paula02/2012
698011^68564-9871403Lelio R Paula01/2015
69812^237173+7480171397Enzo Doria04/2016
698215^60697+5671386Lelio R Paula01/2015
69832^237118+17771380Lelio R Paula02/2012
69842^237110+6971378Lelio R Paula02/2012
698515^60690-5871377Lelio R Paula01/2015
6986(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6987(3^149567+2)/53971359Lelio R Paula06/2012
6988(5*10^71357-143)/371358Robert Price04/2016
69892^237039-11462171356Enzo Doria05/2015
699012^66116-3771352Lelio R Paula02/2015
6991(3^149497+2^149497)/571328Jean-Louis Charton10/2010
69922^236941-6694571327Lelio R Paula05/2012
69932^236911-114771318Yves Minet10/2009
699465^39337+4271315Lelio R Paula01/2016
69956*10^71299+771300Dmitry Domanov11/2010
6996(25*2^236843+1)/375371295Lelio R Paula06/2012
699710^71291+1518771292Patrick De Geest03/2016
699910^71291-558730911971291Robert Price03/2015
699810^71291-27358171291Patrick De Geest03/2016
7000-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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