PRP Records

Probable Primes Top 10000

(205869 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 ?
6751(2^224950+5)/1950967713Lelio R Paula04/2012
675211^65011-597067702Enzo Doria01/2013
675388*10^67691+767693Robert Price11/2016
675411^65000-714067691Enzo Doria01/2013
67552^224841+5967684Lelio R Paula02/2012
675633129!2+2^3312967684Robert Price09/2015
67572^224827+841567680Lelio R Paula02/2013
6758(9913*2^224821-1)/1982567678Lelio R Paula04/2015
67592^224815-4978967677Henri Lifchitz04/2005
6760(43*10^67664+11)/967665Robert Price06/2015
6761(292*10^67659-1)/367661Robert Price01/2017
6762(17*2^224766+1)/2900767659Lelio R Paula06/2012
67632^224744+57729457567655Lelio R Paula02/2016
6764((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
6765(2^224721+78557)/173967645Lelio R Paula05/2012
67662^224700+191567642Lelio R Paula04/2012
6767(29*2^224694-1)/19890567636Lelio R Paula01/2014
67682^224658-9367629Lelio R Paula02/2012
67692^224624-1307767619Enzo Doria10/2012
677018^53860-331967609Enzo Doria03/2013
6771(21181*2^224570+1)/567606Lelio R Paula06/2014
67722^224578-11104167605Enzo Doria05/2014
67732^224569-11323367603Enzo Doria07/2014
67742^224562-11317167600Enzo Doria07/2014
67752^224556-11312967599Enzo Doria07/2014
67766*7^79980-567592Lelio R Paula09/2014
6777(6883*2^224523-1)/1603167588Lelio R Paula04/2015
677810^67579+16477967580Patrick De Geest07/2017
6780(52*10^67578-61)/967579Robert Price09/2015
677910^67579-40167579Robert Price06/2017
6781(17^54919-1)/1667574Paul Bourdelais03/2010
6782(2^224363-9)/195167537Lelio R Paula04/2012
6783(709*10^67517-7)/967519Robert Price09/2017
678447719!3-5904967516Robert Price12/2015
6785(22^50287+1)/2367506Robert Price06/2013
67863*10^67499+6767500Robert Price11/2017
678711^64811-582067494Enzo Doria01/2013
6788131^31870+31870^13167478Serge Batalov05/2014
67899*10^67468+767469Dmitry Domanov11/2010
6790(31*2^224115-1)/4772367463Lelio R Paula01/2014
6791128^32001+32001^12867433Serge Batalov05/2014
6792(89*10^67431-17)/967432Robert Price11/2015
67932^223912-11105967405Enzo Doria05/2014
67952^223913+7369767405Enzo Doria04/2016
6794(2*10^67405-23)/367405Robert Price09/2017
6796(10^67404+179)/967404Serge Batalov12/2014
679718738^3955+3955^1873867404Hans Havermann09/2016
67989*7^79728-267379Lelio R Paula09/2014
6799(28*10^67378-43)/367379Robert Price04/2016
6800(3^141234-7)/43024128267378Lelio R Paula04/2012
6801211^28988-267377Lelio R Paula09/2013
68024*10^67375+9167376Robert Price11/2017
68032^223793-1806967369Enzo Doria05/2013
68042^223777-252167364Yves Minet07/2014
6805(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6806(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6807V(340138)67336Serge Batalov03/2015
680843125^14528-10667334Enzo Doria07/2012
68098*10^67302-5167303Robert Price10/2017
681017458^7153+7153^1745867292Hans Havermann08/2016
681116366^12925+12925^1636667288Hans Havermann08/2016
681237^42906-267286Lelio R Paula08/2013
681318^53592-1367273Lelio R Paula08/2013
6814V(396221)67256Serge Batalov03/2015
6816(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6815(14*10^67235-101)/367236Robert Price04/2017
681753^38993-52^3899367235Robert Price01/2013
6818(2^223349-7)/648567231Lelio R Paula04/2012
68192^223333+31567230Lelio R Paula04/2012
68202^223278-11104167214Enzo Doria05/2014
6821(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
68222^223256-4567207Lelio R Paula02/2012
68232^223253-11211167206Enzo Doria06/2014
682418407^4474+4474^1840767199Hans Havermann08/2016
682547^40182+40182^4767189Norbert Schneider11/2014
682613^60309+9467181Lelio R Paula07/2013
682711^64503-8467173Lelio R Paula07/2013
68283^140781+23667170Lelio R Paula06/2013
68292^223107-86505767162Paul Bourdelais03/2013
68302^223100-5967160Lelio R Paula02/2012
68312^223087+7196367156Enzo Doria04/2016
683218^53481-377967134Enzo Doria03/2013
6833(326^26713-1)/32567134Eric Chen09/2017
68344^111473-6257367114Mike Oakes02/2011
68352^222943+2967113Henri Lifchitz08/2005
6836(2^222939-9)/10367110Lelio R Paula04/2012
68372^222862-45916167089Enzo Doria05/2015
68382^222828+819367078Lelio R Paula04/2012
68393^140570+266067069Lelio R Paula06/2013
68402^222744+85567053Lelio R Paula04/2012
684113^60189+8467048Lelio R Paula07/2013
68422*10^67043-5167044Robert Price11/2017
68432^222701+57729457567040Lelio R Paula02/2016
6844(13*10^67038-31)/967039Serge Batalov11/2008
6845(151*10^67027-7)/967029Robert Price07/2017
6846(58695*2^222620-1)/6167019Lelio R Paula04/2015
68472^222614-11104167014Enzo Doria05/2014
68482^222520-190766986Yves Minet03/2013
6849(4^111231+23)/366968Robert Price02/2017
68502^222408-11127566952Enzo Doria05/2014
685110^66949-9^6694966949Jean-Louis Charton12/2005
68522^222378-100566943Lelio R Paula04/2012
6853(9*2^222366+1)/7366938Lelio R Paula08/2012
68547^79202-6^(79202+1)66934Robert Price06/2016
68552^222325-11225566927Enzo Doria06/2014
685620^51428+3366910Lelio R Paula08/2013
68582^222224-1850966897Enzo Doria05/2013
6857(38*10^66896+187)/966897Robert Price11/2017
68592^222192-86968810566887Lelio R Paula02/2016
6860(19*10^66878-43)/366879Robert Price10/2017
686111^64219-6466878Lelio R Paula07/2013
68622^222151-1729566875Lelio R Paula04/2012
6863gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
68642^222085-11103166855Enzo Doria05/2014
68658*10^66848-1366849Robert Price05/2017
6866(3^140087+4)/1366838Lelio R Paula04/2012
6867(3^140102+4)/884360943766836Lelio R Paula04/2012
686819^52265+5266835Lelio R Paula08/2013
68692*10^66826-2766827Robert Price02/2017
68704*6^85867+566819Lelio R Paula09/2014
687115^56800+866802Lelio R Paula08/2013
6872(2^221891-2^110946+1)/56679611/2006
687310^66793+6944166794Patrick De Geest05/2013
687410^66793-6366793Robert Price05/2011
687535^43256-170466791Enzo Doria03/2013
68763^139976+2^(139976-1)66786Robert Price05/2016
68777^79023-5466783Lelio R Paula06/2013
6878104^33109-10366782Norbert Schneider11/2016
6879(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6880(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
68822^221768+18366759Lelio R Paula02/2012
6881gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6883(154*10^66755-1)/966757Serge Batalov12/2014
688411^64097+4866751Lelio R Paula07/2013
6885(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6886(19*10^66748+413)/966749Robert Price10/2017
6887(3*2^221696-1)/1366737Lelio R Paula01/2014
68888*6^85758-766734Lelio R Paula09/2014
6889135^31325+266733Lelio R Paula05/2013
6890(49*10^66729+41)/966730Robert Price07/2015
6891(349*10^66720-7)/966722Robert Price03/2017
6892(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6893(25*10^66714+71)/366715Robert Price01/2017
689411^64061-78066713Enzo Doria11/2012
68957^78929+466703Lelio R Paula06/2013
689611^64048-93066700Enzo Doria11/2012
68972*7^78921+566697Lelio R Paula09/2014
6898(25*2^221526+1)/40966685Lelio R Paula08/2012
6899(2^221509-1)/29239188166673Jens K. Andersen02/2009
69002^221479+7295366672Enzo Doria04/2016
690110^66666+27540366667Patrick De Geest03/2010
690210^66666-11552166666Patrick De Geest03/2010
6903(18*10^66657-81)/9966657Ray Chandler01/2011
69044*10^66653+2166654Robert Price08/2016
6905(10^66650+149)/366650Serge Batalov12/2014
69069^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
69072^221391-214566646Lelio R Paula04/2012
6908(5*10^66613-119)/366614Robert Price04/2016
69092^221273-11323366610Enzo Doria07/2014
69103^139571-4666593Lelio R Paula06/2013
6911(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
69122^221181-86968810566583Lelio R Paula02/2016
6913(61*10^66575-7)/966576Ray Chandler02/2012
69142^221126+13366566Lelio R Paula02/2012
691512^61680+9166564Lelio R Paula07/2013
6916(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6917(13*10^66551-73)/366552Robert Price12/2016
691811^63901-159066547Enzo Doria12/2012
691911^63901-150066547Enzo Doria12/2012
69206^85517+2366546Lelio R Paula07/2013
692117^54069-4066530Lelio R Paula08/2013
6922(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6923(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6925(2^221008-1017)/7853366526Lelio R Paula04/2012
69243^139432+2666526Lelio R Paula06/2013
6926((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6927((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
69286^85481+8548166518Henri Lifchitz08/2014
6929(9179*2^220913-1)/39966503Lelio R Paula04/2015
693013^59687+6666488Lelio R Paula07/2013
6931(49*10^66485-31)/966486Robert Price07/2015
6932(46*10^66469+17)/966470Robert Price06/2015
69332^220790+9766465Lelio R Paula02/2012
6934(23*2^220790+1)/80766463Lelio R Paula06/2012
693540009^14441-10266460Enzo Doria07/2012
69362^220736-14366449Lelio R Paula02/2012
6937(79*10^66447-97)/9966447Ray Chandler01/2011
69382^220675+6966430Lelio R Paula02/2012
69392^220633-11138166418Enzo Doria05/2014
6940(2^220625-509203)/400032166409Lelio R Paula05/2012
69412^220596-1581366407Enzo Doria04/2013
6942(5*10^66394-17)/366395Serge Batalov05/2009
69432^220549-185917366392Enzo Doria04/2016
69442^220478-16166371Lelio R Paula02/2012
69455^94938-1463666359Enzo Doria02/2013
6946(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
69472^220253-11487166303Enzo Doria05/2015
694812^61432+9566297Lelio R Paula07/2013
69492^220192-11156366285Enzo Doria05/2014
69502^220188-11144966284Enzo Doria05/2014
6951(4*10^66284+23)/966284Robert Price11/2014
695232501!2+266266Robert Price01/2015
6953(8*10^66261-101)/366262Robert Price10/2017
69541530*10^66254+R(66254)66258Patrick De Geest05/2016
6955(47^39623-1)/4666252Robert Price06/2014
69562^220044-9730566240Lelio R Paula04/2012
6957(77*10^66237-257)/966238Robert Price10/2017
695829^45285+266225Ray Chandler08/2011
695915^56289+3866202Lelio R Paula08/2013
69603^138749+9866201Lelio R Paula06/2013
6961(21*2^219912-1)/566201Lelio R Paula01/2014
69622^219904-1699566198Lelio R Paula10/2011
6963(3^138712-2)/529766179Lelio R Paula04/2012
6964Phi(198552,10)66177Ray Chandler07/2010
69654*6^85041+766176Lelio R Paula09/2014
69662^219812-314966171Yves Minet10/2009
69672^219795-61116766165Paul Bourdelais03/2013
696832455!2+51266162Robert Price02/2015
6969(27*2^219760-1)/22766154Lelio R Paula01/2014
6971(11^63521-4^63521)/766150Robert Price03/2013
69705*7^78274-666150Lelio R Paula09/2014
6972(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
69732^219679-11201566130Enzo Doria05/2014
69742^219653+15015*21965366123Henri Lifchitz04/2005
69752^219600+7656166107Enzo Doria05/2016
69762^219594+25525566105Lelio R Paula10/2011
69774*7^78210-366096Lelio R Paula09/2014
6978(15185*2^219557-1)/6366096Lelio R Paula04/2015
6979(19*2^219499-1)/1366076Lelio R Paula01/2014
69802^219496+6661566075Lelio R Paula10/2011
6981(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6982(2^219414+7)/44365766045Lelio R Paula04/2012
6983(115*10^66043-1)/366045Serge Batalov12/2014
698410^66033+1966034Robert Price01/2011
698510^66033-7830966033Patrick De Geest05/2013
6986(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
69872^219304+45424566018Henri Lifchitz03/2007
6988(27*2^219293+1)/914566012Lelio R Paula08/2012
69892^219273-11263566008Enzo Doria06/2014
69902^219250+2566001Lelio R Paula08/2011
6991132^31123+13165999Norbert Schneider03/2015
6992V(319871)65987Serge Batalov03/2015
69932^219189-19565983Lelio R Paula08/2011
6994(7*2^219143-1)/5565968Lelio R Paula01/2014
6995(73^35401-1)/7265962Paul Bourdelais08/2017
69962^219112-1700965960Enzo Doria05/2013
69972^219093-11120165954Enzo Doria05/2014
69982^219089-11209965953Enzo Doria06/2014
699946714!3+8165950Robert Price09/2014
7000(11*10^65944-131)/365945Robert Price02/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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