PRP Records

Probable Primes Top 10000

(252402 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 ?
7001lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
70022^228717+46768851Lelio R Paula02/2011
7003Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
7004(509203*2^228665-1)/3568840Lelio R Paula04/2015
70058^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
700611^66074-105068809Enzo Doria11/2012
7007(68*10^68798-11)/368800Robert Price10/2017
70082^228484+18168781Lelio R Paula02/2012
70092^228479-5869568780Lelio R Paula04/2012
70102^228465-1585368775Enzo Doria04/2013
701111^66040-540068774Enzo Doria01/2013
7012(13*2^228441-1)/57568766Lelio R Paula01/2014
7013(17*2^228393+1)/29568752Lelio R Paula08/2012
70142*10^68744+4168745Robert Price01/2017
701511^66011-15068744Enzo Doria08/2012
7016(13*2^228304-1)/8168726Lelio R Paula01/2014
70172^228295-11107968724Enzo Doria05/2014
7018(3^144039+7)/2268723Lelio R Paula04/2012
7019(8*10^68722+49)/368723Robert Price03/2016
7020(35*10^68718+1)/968719Serge Batalov11/2010
70212^228271-22827168717Henri Lifchitz11/2004
70222^228257+8287568713Lelio R Paula02/2013
70233^144013+4068712Lelio R Paula09/2013
702413^61671-8668699Lelio R Paula09/2013
7025(46*10^68698+683)/968699Robert Price12/2017
702617^55828-7268694Lelio R Paula09/2013
70276^88259+6168679Lelio R Paula09/2013
702818^54699-568663Lelio R Paula09/2013
702933^45216+268662Lelio R Paula05/2013
7031(2^228073-5)/368657Lelio R Paula04/2012
7030(2^(6*38012+1)-5)/368657Kevin Acres11/2013
70322^228055-11160768652Enzo Doria05/2014
70332^228054-11476168652Enzo Doria05/2015
70342^228041+118568648Lelio R Paula04/2012
70352^228040-103768647Yves Minet11/2012
70362*F(328450)-168642Henri Lifchitz12/2009
70375^98201-3468640Lelio R Paula06/2013
70389^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
70397*2^227780-368570Lelio R Paula04/2014
704015327^16382-16382^1532768567Norbert Schneider11/2018
70412^227733-12168555Lelio R Paula02/2012
70422^227702-1696768546Enzo Doria05/2013
70432^227689-11165568542Enzo Doria05/2014
7044gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
70455^98051+268535Ray Chandler07/2011
70465*10^68524+5168525Robert Price01/2017
7047(11*10^68520-149)/368521Robert Price01/2017
704819^53573-7868507Lelio R Paula09/2013
7049(68*10^68504+13)/968505Ray Chandler10/2010
70509*5^98003+468503Lelio R Paula09/2014
70512^227528+5168493Lelio R Paula02/2012
7052(146*28^47316+1)/368476Karsten Bonath06/2018
70533^143497+868466Lelio R Paula04/2012
70542^227430-9568464Lelio R Paula02/2012
7055(8*10^68455+13)/368456Robert Price11/2017
70563*5^97934-268454Lelio R Paula09/2014
705720^52613+7768452Lelio R Paula09/2013
70582^227371+3276968446Lelio R Paula04/2012
7059(3^143465+4)/2127042006768440Lelio R Paula04/2012
7060CopelandErdos(68433)68433Eric W. Weisstein08/2013
70612^227323+7543168432Enzo Doria04/2016
70622^227314-196568429Lelio R Paula04/2012
70632^227303-11061768426Enzo Doria05/2014
70657^80963+6668422Lelio R Paula07/2013
70642^227290+7384968422Enzo Doria04/2016
7066(14^59693-1)/1368415Paul Bourdelais06/2008
70672^227256-278624968411Enzo Doria03/2016
70688*10^68400-768401Dmitry Domanov11/2010
7069(15*2^227228-1)/58368401Lelio R Paula01/2014
70702^227210+186916968398Enzo Doria05/2016
70712^227159-183863568382Enzo Doria05/2015
707244*10^68368+368370Robert Price08/2017
70732^227115-780768369Lelio R Paula10/2009
70742^227078-4735568358Lelio R Paula04/2012
7075(2^227063-1017)/34968351Lelio R Paula04/2012
70762^227057+14809168351Lelio R Paula04/2012
70772^227046+18768348Lelio R Paula02/2012
70789*10^68331+5968332Robert Price10/2017
707911^65608-72068324Enzo Doria11/2012
7080(32*10^68320+319)/968321Robert Price10/2017
708133408!2-2^33408-168315Joe McLean05/2017
70822^226894-12368302Lelio R Paula02/2012
708310^68297+14155968298Patrick De Geest05/2013
708410^68297-9368297Robert Price05/2011
7085680^24107-679^2410768284Jean-Louis Charton07/2010
708612^63267+5968277Lelio R Paula07/2013
70872^226785-115968270Yves Minet11/2012
70887^80769+9068258Lelio R Paula07/2013
7089(88*10^68256-1)/368258Robert Price10/2017
70902^226741+6658768256Yves Minet10/2010
70912^226720-11240368250Enzo Doria06/2014
7092(78557*2^226694+1)/368247Lelio R Paula06/2014
7093(83*10^68231+7)/968232Robert Price10/2015
709465^37636+1668231Lelio R Paula01/2016
70955^97615-4^(97615+1)68230Robert Price04/2016
709612^63200-4368205Lelio R Paula07/2013
7097-330*Bern(21940)/22379062073368201Serge Batalov04/2015
70983^142925+868068193Lelio R Paula06/2013
70993*2^226512-768188Lelio R Paula04/2014
710014^59484+5768177Lelio R Paula08/2013
710111^65438-219068147Enzo Doria12/2012
710291^34784-268144Lelio R Paula09/2013
7103(2^226336-3)*6-768135Gilbert Mozzo06/2016
7104(22*10^68133-37)/368134Robert Price05/2017
71055^97476+3668133Lelio R Paula06/2013
71063*5^97474-268132Lelio R Paula09/2014
710712^63130+4968129Lelio R Paula07/2013
71082^226281+538568118Lelio R Paula04/2012
71092^226257-304968111Yves Minet10/2014
7110(28*10^68107-43)/368108Robert Price04/2016
71112^226243-258768106Yves Minet07/2014
711220^52346-1168104Lelio R Paula09/2013
71132^226205-9968095Lelio R Paula02/2012
71142^226187-4968090Lelio R Paula02/2012
71153^142708+7668090Lelio R Paula06/2013
71167*10^68088-8968089Robert Price01/2017
71172^226154+7183968080Enzo Doria04/2016
7118(10^68078+59)/368078Serge Batalov12/2014
712014^59387+6968066Lelio R Paula08/2013
71192^226108-11342968066Enzo Doria07/2014
7121(62*10^68059-197)/968060Robert Price10/2017
7122(24^49307-1)/2368053Robert Price04/2012
712315^57859-2868048Lelio R Paula08/2013
7124(509203*2^226003-1)/1368039Lelio R Paula04/2015
71252^226015-11136168038Enzo Doria05/2014
7126(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
71274*10^68020+9168021Robert Price11/2017
7128156*(10^(4*17000)-1)/101-168001Robert Price05/2014
71292^225878-101767997Lelio R Paula04/2012
71303*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
71313*2^225865+567993Lelio R Paula04/2014
713311^65284-582067987Enzo Doria01/2013
713219^53166+7067987Lelio R Paula08/2013
71342^225837+7540767984Enzo Doria04/2016
71353^142464-11265467973Enzo Doria06/2014
71362^225777+9567966Lelio R Paula02/2012
7137(2^225641-1017)/13881567920Lelio R Paula04/2012
71382^225609-1844567916Enzo Doria05/2013
71392^225542-17767895Lelio R Paula02/2012
71402^225536-2967894Henri Lifchitz05/2005
714111^65190-339067889Enzo Doria12/2012
71423^142249-2^(142249-1)67871Robert Price01/2016
714311^65168-483067866Enzo Doria01/2013
714410^67863+5862767864Patrick De Geest01/2016
714510^67863-1167863Robert Price05/2011
7146(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
7147(19*2^225357-1)/1167840Lelio R Paula01/2014
71489*6^87164-767828Lelio R Paula09/2014
7149131^32034+13067825Norbert Schneider03/2015
7150(29*2^225314+1)/1088167824Lelio R Paula08/2012
7151(134*10^67816+7)/367818Robert Price02/2017
71522^225261+85567811Lelio R Paula04/2012
7153(29*2^225252-1)/293367806Lelio R Paula01/2014
7154(4*10^67796+23)/967796Robert Price11/2014
715515477^16180-16180^1547767790Norbert Schneider09/2018
7156(23*2^225177+1)/3167785Lelio R Paula08/2012
7157(4*10^67784+149)/967784Robert Price03/2017
71582^225120+15167768Lelio R Paula02/2012
7159(44^41233+1)/4567763Robert Price11/2013
716089933!6-1667747Robert Price08/2018
71618*10^67742+967743Dmitry Domanov11/2010
71622^224977+108967725Lelio R Paula04/2012
7163(2^224950+5)/1950967713Lelio R Paula04/2012
716411^65011-597067702Enzo Doria01/2013
716588*10^67691+767693Robert Price11/2016
716611^65000-714067691Enzo Doria01/2013
71672^224841+5967684Lelio R Paula02/2012
716833129!2+2^3312967684Robert Price09/2015
71692^224827+841567680Lelio R Paula02/2013
7170(9913*2^224821-1)/1982567678Lelio R Paula04/2015
71712^224815-4978967677Henri Lifchitz04/2005
7172(43*10^67664+11)/967665Robert Price06/2015
7173(292*10^67659-1)/367661Robert Price01/2017
7174(17*2^224766+1)/2900767659Lelio R Paula06/2012
71752^224744+57729457567655Lelio R Paula02/2016
7176((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
7177(2^224721+78557)/173967645Lelio R Paula05/2012
71782^224700+191567642Lelio R Paula04/2012
7179(29*2^224694-1)/19890567636Lelio R Paula01/2014
71802^224658-9367629Lelio R Paula02/2012
71812^224624-1307767619Enzo Doria10/2012
718218^53860-331967609Enzo Doria03/2013
7183(21181*2^224570+1)/567606Lelio R Paula06/2014
718489762!6-367606Robert Price08/2018
71852^224578-11104167605Enzo Doria05/2014
71862^224569-11323367603Enzo Doria07/2014
71872^224562-11317167600Enzo Doria07/2014
71882^224556-11312967599Enzo Doria07/2014
71896*7^79980-567592Lelio R Paula09/2014
7190(6883*2^224523-1)/1603167588Lelio R Paula04/2015
719110^67579+16477967580Patrick De Geest07/2017
7193(52*10^67578-61)/967579Robert Price09/2015
719210^67579-40167579Robert Price06/2017
7194(17^54919-1)/1667574Paul Bourdelais03/2010
7195(2^224363-9)/195167537Lelio R Paula04/2012
7196(709*10^67517-7)/967519Robert Price09/2017
719747719!3-5904967516Robert Price12/2015
7198(22^50287+1)/2367506Robert Price06/2013
71993*10^67499+6767500Robert Price11/2017
720011^64811-582067494Enzo Doria01/2013
7201131^31870+31870^13167478Serge Batalov05/2014
72029*10^67468+767469Dmitry Domanov11/2010
7203(31*2^224115-1)/4772367463Lelio R Paula01/2014
7204128^32001+32001^12867433Serge Batalov05/2014
7205(89*10^67431-17)/967432Robert Price11/2015
72062^223912-11105967405Enzo Doria05/2014
72072^223913+7369767405Enzo Doria04/2016
7208(2*10^67405-23)/367405Robert Price09/2017
7210(10^67404+179)/967404Serge Batalov12/2014
720918738^3955+3955^1873867404Hans Havermann09/2016
72119*7^79728-267379Lelio R Paula09/2014
7212(28*10^67378-43)/367379Robert Price04/2016
7213(3^141234-7)/43024128267378Lelio R Paula04/2012
7214211^28988-267377Lelio R Paula09/2013
72154*10^67375+9167376Robert Price11/2017
72162^223793-1806967369Enzo Doria05/2013
72172^223777-252167364Yves Minet07/2014
7218(15185*2^223775-1)/1518367363Lelio R Paula04/2015
7219(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
7220V(340138)67336Serge Batalov03/2015
722143125^14528-10667334Enzo Doria07/2012
722215275^16086-16086^1527567304Norbert Schneider09/2018
72238*10^67302-5167303Robert Price10/2017
722417458^7153+7153^1745867292Hans Havermann08/2016
722516366^12925+12925^1636667288Hans Havermann08/2016
722637^42906-267286Lelio R Paula08/2013
722718^53592-1367273Lelio R Paula08/2013
7228V(396221)67256Serge Batalov03/2015
7229(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
7230(14*10^67235-101)/367236Robert Price04/2017
723153^38993-52^3899367235Robert Price01/2013
7232(2^223349-7)/648567231Lelio R Paula04/2012
72332^223333+31567230Lelio R Paula04/2012
72342^223278-11104167214Enzo Doria05/2014
7235(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
72362^223256-4567207Lelio R Paula02/2012
72372^223253-11211167206Enzo Doria06/2014
723818407^4474+4474^1840767199Hans Havermann08/2016
723947^40182+40182^4767189Norbert Schneider11/2014
724013^60309+9467181Lelio R Paula07/2013
724111^64503-8467173Lelio R Paula07/2013
72423^140781+23667170Lelio R Paula06/2013
72432^223107-86505767162Paul Bourdelais03/2013
72442^223100-5967160Lelio R Paula02/2012
72452^223087+7196367156Enzo Doria04/2016
724618^53481-377967134Enzo Doria03/2013
7247(326^26713-1)/32567134Eric Chen09/2017
72484^111473-6257367114Mike Oakes02/2011
72492^222943+2967113Henri Lifchitz08/2005
7250(2^222939-9)/10367110Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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