PRP Records

Probable Primes Top 10000

(212140 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 ?
67517^80769+9068258Lelio R Paula07/2013
6752(88*10^68256-1)/368258Robert Price10/2017
67532^226741+6658768256Yves Minet10/2010
67542^226720-11240368250Enzo Doria06/2014
6755(78557*2^226694+1)/368247Lelio R Paula06/2014
6756(83*10^68231+7)/968232Robert Price10/2015
675765^37636+1668231Lelio R Paula01/2016
67585^97615-4^(97615+1)68230Robert Price04/2016
675912^63200-4368205Lelio R Paula07/2013
6760-330*Bern(21940)/22379062073368201Serge Batalov04/2015
67613^142925+868068193Lelio R Paula06/2013
67623*2^226512-768188Lelio R Paula04/2014
676314^59484+5768177Lelio R Paula08/2013
676411^65438-219068147Enzo Doria12/2012
676591^34784-268144Lelio R Paula09/2013
6766(2^226336-3)*6-768135Gilbert Mozzo06/2016
6767(22*10^68133-37)/368134Robert Price05/2017
67685^97476+3668133Lelio R Paula06/2013
67693*5^97474-268132Lelio R Paula09/2014
677012^63130+4968129Lelio R Paula07/2013
67712^226281+538568118Lelio R Paula04/2012
67722^226257-304968111Yves Minet10/2014
6773(28*10^68107-43)/368108Robert Price04/2016
67742^226243-258768106Yves Minet07/2014
677520^52346-1168104Lelio R Paula09/2013
67762^226205-9968095Lelio R Paula02/2012
67772^226187-4968090Lelio R Paula02/2012
67783^142708+7668090Lelio R Paula06/2013
67797*10^68088-8968089Robert Price01/2017
67802^226154+7183968080Enzo Doria04/2016
6781(10^68078+59)/368078Serge Batalov12/2014
678314^59387+6968066Lelio R Paula08/2013
67822^226108-11342968066Enzo Doria07/2014
6784(62*10^68059-197)/968060Robert Price10/2017
6785(24^49307-1)/2368053Robert Price04/2012
678615^57859-2868048Lelio R Paula08/2013
6787(509203*2^226003-1)/1368039Lelio R Paula04/2015
67882^226015-11136168038Enzo Doria05/2014
6789(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
67904*10^68020+9168021Robert Price11/2017
6791156*(10^(4*17000)-1)/101-168001Robert Price05/2014
67922^225878-101767997Lelio R Paula04/2012
67933*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
67943*2^225865+567993Lelio R Paula04/2014
679611^65284-582067987Enzo Doria01/2013
679519^53166+7067987Lelio R Paula08/2013
67972^225837+7540767984Enzo Doria04/2016
67983^142464-11265467973Enzo Doria06/2014
67992^225777+9567966Lelio R Paula02/2012
6800(2^225641-1017)/13881567920Lelio R Paula04/2012
68012^225609-1844567916Enzo Doria05/2013
68022^225542-17767895Lelio R Paula02/2012
68032^225536-2967894Henri Lifchitz05/2005
680411^65190-339067889Enzo Doria12/2012
68053^142249-2^(142249-1)67871Robert Price01/2016
680611^65168-483067866Enzo Doria01/2013
680710^67863+5862767864Patrick De Geest01/2016
680810^67863-1167863Robert Price05/2011
6809(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6810(19*2^225357-1)/1167840Lelio R Paula01/2014
68119*6^87164-767828Lelio R Paula09/2014
6812131^32034+13067825Norbert Schneider03/2015
6813(29*2^225314+1)/1088167824Lelio R Paula08/2012
6814(134*10^67816+7)/367818Robert Price02/2017
68152^225261+85567811Lelio R Paula04/2012
6816(29*2^225252-1)/293367806Lelio R Paula01/2014
6817(4*10^67796+23)/967796Robert Price11/2014
6818(23*2^225177+1)/3167785Lelio R Paula08/2012
6819(4*10^67784+149)/967784Robert Price03/2017
68202^225120+15167768Lelio R Paula02/2012
6821(44^41233+1)/4567763Robert Price11/2013
68228*10^67742+967743Dmitry Domanov11/2010
68232^224977+108967725Lelio R Paula04/2012
6824(2^224950+5)/1950967713Lelio R Paula04/2012
682511^65011-597067702Enzo Doria01/2013
682688*10^67691+767693Robert Price11/2016
682711^65000-714067691Enzo Doria01/2013
68282^224841+5967684Lelio R Paula02/2012
682933129!2+2^3312967684Robert Price09/2015
68302^224827+841567680Lelio R Paula02/2013
6831(9913*2^224821-1)/1982567678Lelio R Paula04/2015
68322^224815-4978967677Henri Lifchitz04/2005
6833(43*10^67664+11)/967665Robert Price06/2015
6834(292*10^67659-1)/367661Robert Price01/2017
6835(17*2^224766+1)/2900767659Lelio R Paula06/2012
68362^224744+57729457567655Lelio R Paula02/2016
6837((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
6838(2^224721+78557)/173967645Lelio R Paula05/2012
68392^224700+191567642Lelio R Paula04/2012
6840(29*2^224694-1)/19890567636Lelio R Paula01/2014
68412^224658-9367629Lelio R Paula02/2012
68422^224624-1307767619Enzo Doria10/2012
684318^53860-331967609Enzo Doria03/2013
6844(21181*2^224570+1)/567606Lelio R Paula06/2014
68452^224578-11104167605Enzo Doria05/2014
68462^224569-11323367603Enzo Doria07/2014
68472^224562-11317167600Enzo Doria07/2014
68482^224556-11312967599Enzo Doria07/2014
68496*7^79980-567592Lelio R Paula09/2014
6850(6883*2^224523-1)/1603167588Lelio R Paula04/2015
685110^67579+16477967580Patrick De Geest07/2017
6853(52*10^67578-61)/967579Robert Price09/2015
685210^67579-40167579Robert Price06/2017
6854(17^54919-1)/1667574Paul Bourdelais03/2010
6855(2^224363-9)/195167537Lelio R Paula04/2012
6856(709*10^67517-7)/967519Robert Price09/2017
685747719!3-5904967516Robert Price12/2015
6858(22^50287+1)/2367506Robert Price06/2013
68593*10^67499+6767500Robert Price11/2017
686011^64811-582067494Enzo Doria01/2013
6861131^31870+31870^13167478Serge Batalov05/2014
68629*10^67468+767469Dmitry Domanov11/2010
6863(31*2^224115-1)/4772367463Lelio R Paula01/2014
6864128^32001+32001^12867433Serge Batalov05/2014
6865(89*10^67431-17)/967432Robert Price11/2015
68662^223912-11105967405Enzo Doria05/2014
68682^223913+7369767405Enzo Doria04/2016
6867(2*10^67405-23)/367405Robert Price09/2017
6869(10^67404+179)/967404Serge Batalov12/2014
687018738^3955+3955^1873867404Hans Havermann09/2016
68719*7^79728-267379Lelio R Paula09/2014
6872(28*10^67378-43)/367379Robert Price04/2016
6873(3^141234-7)/43024128267378Lelio R Paula04/2012
6874211^28988-267377Lelio R Paula09/2013
68754*10^67375+9167376Robert Price11/2017
68762^223793-1806967369Enzo Doria05/2013
68772^223777-252167364Yves Minet07/2014
6878(15185*2^223775-1)/1518367363Lelio R Paula04/2015
6879(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6880V(340138)67336Serge Batalov03/2015
688143125^14528-10667334Enzo Doria07/2012
68828*10^67302-5167303Robert Price10/2017
688317458^7153+7153^1745867292Hans Havermann08/2016
688416366^12925+12925^1636667288Hans Havermann08/2016
688537^42906-267286Lelio R Paula08/2013
688618^53592-1367273Lelio R Paula08/2013
6887V(396221)67256Serge Batalov03/2015
6889(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6888(14*10^67235-101)/367236Robert Price04/2017
689053^38993-52^3899367235Robert Price01/2013
6891(2^223349-7)/648567231Lelio R Paula04/2012
68922^223333+31567230Lelio R Paula04/2012
68932^223278-11104167214Enzo Doria05/2014
6894(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
68952^223256-4567207Lelio R Paula02/2012
68962^223253-11211167206Enzo Doria06/2014
689718407^4474+4474^1840767199Hans Havermann08/2016
689847^40182+40182^4767189Norbert Schneider11/2014
689913^60309+9467181Lelio R Paula07/2013
690011^64503-8467173Lelio R Paula07/2013
69013^140781+23667170Lelio R Paula06/2013
69022^223107-86505767162Paul Bourdelais03/2013
69032^223100-5967160Lelio R Paula02/2012
69042^223087+7196367156Enzo Doria04/2016
690518^53481-377967134Enzo Doria03/2013
6906(326^26713-1)/32567134Eric Chen09/2017
69074^111473-6257367114Mike Oakes02/2011
69082^222943+2967113Henri Lifchitz08/2005
6909(2^222939-9)/10367110Lelio R Paula04/2012
69102^222862-45916167089Enzo Doria05/2015
69112^222828+819367078Lelio R Paula04/2012
69123^140570+266067069Lelio R Paula06/2013
69132^222744+85567053Lelio R Paula04/2012
691413^60189+8467048Lelio R Paula07/2013
69152*10^67043-5167044Robert Price11/2017
69162^222701+57729457567040Lelio R Paula02/2016
6917(13*10^67038-31)/967039Serge Batalov11/2008
6918(151*10^67027-7)/967029Robert Price07/2017
6919(58695*2^222620-1)/6167019Lelio R Paula04/2015
69202^222614-11104167014Enzo Doria05/2014
69212^222520-190766986Yves Minet03/2013
6922(4^111231+23)/366968Robert Price02/2017
69232^222408-11127566952Enzo Doria05/2014
692410^66949-9^6694966949Jean-Louis Charton12/2005
69252^222378-100566943Lelio R Paula04/2012
6926(9*2^222366+1)/7366938Lelio R Paula08/2012
69277^79202-6^(79202+1)66934Robert Price06/2016
69282^222325-11225566927Enzo Doria06/2014
692920^51428+3366910Lelio R Paula08/2013
69312^222224-1850966897Enzo Doria05/2013
6930(38*10^66896+187)/966897Robert Price11/2017
69322^222192-86968810566887Lelio R Paula02/2016
6933(19*10^66878-43)/366879Robert Price10/2017
693411^64219-6466878Lelio R Paula07/2013
69352^222151-1729566875Lelio R Paula04/2012
6936gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
69372^222085-11103166855Enzo Doria05/2014
69388*10^66848-1366849Robert Price05/2017
6939(3^140087+4)/1366838Lelio R Paula04/2012
6940(3^140102+4)/884360943766836Lelio R Paula04/2012
694119^52265+5266835Lelio R Paula08/2013
69422*10^66826-2766827Robert Price02/2017
69434*6^85867+566819Lelio R Paula09/2014
694415^56800+866802Lelio R Paula08/2013
6945(2^221891-2^110946+1)/56679611/2006
694610^66793+6944166794Patrick De Geest05/2013
694710^66793-6366793Robert Price05/2011
694835^43256-170466791Enzo Doria03/2013
69493^139976+2^(139976-1)66786Robert Price05/2016
69507^79023-5466783Lelio R Paula06/2013
6951104^33109-10366782Norbert Schneider11/2016
6952(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6953(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
69552^221768+18366759Lelio R Paula02/2012
6954gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6956(154*10^66755-1)/966757Serge Batalov12/2014
695711^64097+4866751Lelio R Paula07/2013
6958(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6959(19*10^66748+413)/966749Robert Price10/2017
6960(3*2^221696-1)/1366737Lelio R Paula01/2014
69618*6^85758-766734Lelio R Paula09/2014
6962135^31325+266733Lelio R Paula05/2013
6963(49*10^66729+41)/966730Robert Price07/2015
6964(349*10^66720-7)/966722Robert Price03/2017
6965(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6966(25*10^66714+71)/366715Robert Price01/2017
696711^64061-78066713Enzo Doria11/2012
69687^78929+466703Lelio R Paula06/2013
696911^64048-93066700Enzo Doria11/2012
69702*7^78921+566697Lelio R Paula09/2014
6971(25*2^221526+1)/40966685Lelio R Paula08/2012
6972(2^221509-1)/29239188166673Jens K. Andersen02/2009
69732^221479+7295366672Enzo Doria04/2016
697410^66666+27540366667Patrick De Geest03/2010
697510^66666-11552166666Patrick De Geest03/2010
6976(18*10^66657-81)/9966657Ray Chandler01/2011
69774*10^66653+2166654Robert Price08/2016
6978(10^66650+149)/366650Serge Batalov12/2014
69799^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
69802^221391-214566646Lelio R Paula04/2012
6981(5*10^66613-119)/366614Robert Price04/2016
69822^221273-11323366610Enzo Doria07/2014
69833^139571-4666593Lelio R Paula06/2013
6984(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
69852^221181-86968810566583Lelio R Paula02/2016
6986(61*10^66575-7)/966576Ray Chandler02/2012
69872^221126+13366566Lelio R Paula02/2012
698812^61680+9166564Lelio R Paula07/2013
6989(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6990(13*10^66551-73)/366552Robert Price12/2016
699111^63901-159066547Enzo Doria12/2012
699211^63901-150066547Enzo Doria12/2012
69936^85517+2366546Lelio R Paula07/2013
699417^54069-4066530Lelio R Paula08/2013
6995(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6996(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6998(2^221008-1017)/7853366526Lelio R Paula04/2012
69973^139432+2666526Lelio R Paula06/2013
6999((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
7000((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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